Weekly Sales Analysis

Loading data

#Loading sales from the downloaded file
sales <- vroom::vroom(here::here("data","sales.csv")) %>% 
  janitor::clean_names()


#Loading details from the downloaded file
details <- vroom::vroom(here::here("data","details.csv")) %>% 
  janitor::clean_names()


#Loading stores from the downloaded file
stores <- vroom::vroom(here::here("data","stores.csv")) %>% 
  janitor::clean_names()

Merging datasets

#Merging sales and details
sales_details <- left_join(sales, details, by = c("store" = "store", "date" = "date", "is_holiday" = "is_holiday"))

# Merging sales_details and stores
sales1 <- left_join(sales_details, stores, by = "store")

glimpse(sales1)

## Rows: 421,570
## Columns: 16
## $ store        <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …
## $ dept         <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …
## $ date         <chr> "05/02/2010", "12/02/2010", "19/02/2010", "26/02/2010", "…
## $ is_holiday   <lgl> FALSE, TRUE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FA…
## $ weekly_sales <dbl> 25355, 45621, 43678, 19192, 21564, 21474, 22396, 26049, 5…
## $ temperature  <dbl> 42.3, 38.5, 39.9, 46.6, 46.5, 57.8, 54.6, 51.5, 62.3, 65.…
## $ fuel_price   <dbl> 2.57, 2.55, 2.51, 2.56, 2.62, 2.67, 2.72, 2.73, 2.72, 2.7…
## $ mark_down1   <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
## $ mark_down2   <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
## $ mark_down3   <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
## $ mark_down4   <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
## $ mark_down5   <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
## $ cpi          <dbl> 211, 211, 211, 211, 211, 211, 211, 211, 211, 211, 210, 21…
## $ unemployment <dbl> 8.11, 8.11, 8.11, 8.11, 8.11, 8.11, 8.11, 8.11, 7.81, 7.8…
## $ type         <chr> "A", "A", "A", "A", "A", "A", "A", "A", "A", "A", "A", "A…
## $ size         <dbl> 151315, 151315, 151315, 151315, 151315, 151315, 151315, 1…

skim(sales1) #check for NAs - exist in mark_down variables

(#tab:merging & inspecting)Data summary
Name	sales1
Number of rows	421570
Number of columns	16
_______________________
Column type frequency:
character	2
logical	1
numeric	13
________________________
Group variables	None

Variable type: character

skim_variable	n_missing	complete_rate	min	max	empty	n_unique	whitespace
date	0	1	10	10	0	143	0
type	0	1	1	1	0	3	0

Variable type: logical

skim_variable	n_missing	complete_rate	mean	count
is_holiday	0	1	0.07	FAL: 391909, TRU: 29661

Variable type: numeric

skim_variable	n_missing	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
store	0	1.00	2.22e+01	12.79	1.00	11.00	2.20e+01	3.30e+01	4.50e+01	▇▇▇▇▇
dept	0	1.00	4.43e+01	30.49	1.00	18.00	3.70e+01	7.40e+01	9.90e+01	▇▇▅▂▆
weekly_sales	0	1.00	1.61e+04	22873.10	-4990.98	2095.37	7.67e+03	2.03e+04	6.72e+05	▇▁▁▁▁
temperature	0	1.00	6.01e+01	18.45	-2.06	46.68	6.21e+01	7.43e+01	1.00e+02	▁▃▆▇▃
fuel_price	0	1.00	3.36e+00	0.46	2.47	2.93	3.45e+00	3.74e+00	4.47e+00	▆▆▇▇▁
mark_down1	270889	0.36	7.25e+03	8291.22	0.27	2240.27	5.35e+03	9.21e+03	8.86e+04	▇▁▁▁▁
mark_down2	310322	0.26	3.33e+03	9475.36	-265.76	41.60	1.92e+02	1.93e+03	1.05e+05	▇▁▁▁▁
mark_down3	284479	0.33	1.44e+03	9623.08	-29.10	5.08	2.46e+01	1.04e+02	1.42e+05	▇▁▁▁▁
mark_down4	286603	0.32	3.38e+03	6292.38	0.22	504.22	1.48e+03	3.60e+03	6.75e+04	▇▁▁▁▁
mark_down5	270138	0.36	4.63e+03	5962.89	135.16	1878.44	3.36e+03	5.56e+03	1.09e+05	▇▁▁▁▁
cpi	0	1.00	1.71e+02	39.16	126.06	132.02	1.82e+02	2.12e+02	2.27e+02	▇▁▁▂▆
unemployment	0	1.00	7.96e+00	1.86	3.88	6.89	7.87e+00	8.57e+00	1.43e+01	▂▇▆▁▁
size	0	1.00	1.37e+05	60980.58	34875.00	93638.00	1.40e+05	2.03e+05	2.20e+05	▅▂▅▂▇

# treating NAs in markdowns as 0 due to the interpretation of 0 promotional markdown
sales1 <- sales1 %>%
  mutate(mark_down1 = ifelse(is.na(mark_down1),0,mark_down1),
         mark_down2 = ifelse(is.na(mark_down2),0,mark_down2),
         mark_down3 = ifelse(is.na(mark_down3),0,mark_down3),
         mark_down4 = ifelse(is.na(mark_down4),0,mark_down4),
         mark_down5 = ifelse(is.na(mark_down5),0,mark_down5)) %>%
  mutate(date = dmy(date))

# negative weekly_sales values
check <- sales1 %>%
    filter(weekly_sales < 0) # check for negatives - 1200+


# There are some negative weekly sales observations. We have proceeded to interpret them as negative weekly net sales, indicating that these stores made losses in those weeks.

Exploratory Data Analysis

Inspecting dataset

glimpse(sales1)

## Rows: 421,570
## Columns: 16
## $ store        <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …
## $ dept         <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …
## $ date         <date> 2010-02-05, 2010-02-12, 2010-02-19, 2010-02-26, 2010-03-…
## $ is_holiday   <lgl> FALSE, TRUE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FA…
## $ weekly_sales <dbl> 25355, 45621, 43678, 19192, 21564, 21474, 22396, 26049, 5…
## $ temperature  <dbl> 42.3, 38.5, 39.9, 46.6, 46.5, 57.8, 54.6, 51.5, 62.3, 65.…
## $ fuel_price   <dbl> 2.57, 2.55, 2.51, 2.56, 2.62, 2.67, 2.72, 2.73, 2.72, 2.7…
## $ mark_down1   <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ mark_down2   <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ mark_down3   <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ mark_down4   <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ mark_down5   <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ cpi          <dbl> 211, 211, 211, 211, 211, 211, 211, 211, 211, 211, 210, 21…
## $ unemployment <dbl> 8.11, 8.11, 8.11, 8.11, 8.11, 8.11, 8.11, 8.11, 7.81, 7.8…
## $ type         <chr> "A", "A", "A", "A", "A", "A", "A", "A", "A", "A", "A", "A…
## $ size         <dbl> 151315, 151315, 151315, 151315, 151315, 151315, 151315, 1…

skim(sales1) #check for NAs

Table 1: Data summary
Name	sales1
Number of rows	421570
Number of columns	16
_______________________
Column type frequency:
character	1
Date	1
logical	1
numeric	13
________________________
Group variables	None

Variable type: character

skim_variable	n_missing	complete_rate	min	max	empty	n_unique	whitespace
type	0	1	1	1	0	3	0

Variable type: Date

skim_variable	n_missing	complete_rate	min	max	median	n_unique
date	0	1	2010-02-05	2012-10-26	2011-06-17	143

Variable type: logical

skim_variable	n_missing	complete_rate	mean	count
is_holiday	0	1	0.07	FAL: 391909, TRU: 29661

Variable type: numeric

skim_variable	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
store	1	2.22e+01	12.79	1.00	11.00	2.20e+01	3.30e+01	4.50e+01	▇▇▇▇▇
dept	1	4.43e+01	30.49	1.00	18.00	3.70e+01	7.40e+01	9.90e+01	▇▇▅▂▆
weekly_sales	1	1.61e+04	22873.10	-4990.98	2095.37	7.67e+03	2.03e+04	6.72e+05	▇▁▁▁▁
temperature	1	6.01e+01	18.45	-2.06	46.68	6.21e+01	7.43e+01	1.00e+02	▁▃▆▇▃
fuel_price	1	3.36e+00	0.46	2.47	2.93	3.45e+00	3.74e+00	4.47e+00	▆▆▇▇▁
mark_down1	1	2.59e+03	6052.39	0.00	0.00	0.00e+00	2.81e+03	8.86e+04	▇▁▁▁▁
mark_down2	1	8.80e+02	5084.54	-265.76	0.00	0.00e+00	2.20e+00	1.05e+05	▇▁▁▁▁
mark_down3	1	4.68e+02	5528.87	-29.10	0.00	0.00e+00	4.54e+00	1.42e+05	▇▁▁▁▁
mark_down4	1	1.08e+03	3894.53	0.00	0.00	0.00e+00	4.25e+02	6.75e+04	▇▁▁▁▁
mark_down5	1	1.66e+03	4207.63	0.00	0.00	0.00e+00	2.17e+03	1.09e+05	▇▁▁▁▁
cpi	1	1.71e+02	39.16	126.06	132.02	1.82e+02	2.12e+02	2.27e+02	▇▁▁▂▆
unemployment	1	7.96e+00	1.86	3.88	6.89	7.87e+00	8.57e+00	1.43e+01	▂▇▆▁▁
size	1	1.37e+05	60980.58	34875.00	93638.00	1.40e+05	2.03e+05	2.20e+05	▅▂▅▂▇

# we found that weekly_sales, all of the markdowns (1 to 5), size, unemployment, cpi, temperature and fuel_price

Summary details:

“Sales1” (created by merging sales, details and stores) contains 16 variables, only four of which are categorical: type, is_holiday, store, dept. The data contains 13 numerical variables, 1 chatacter variable, 1 date and 1 logical variable. “is_holiday” is specified as the logical variable.

The NAs from the markdown files have been replaced with 0s.

Within “sales1”, the variable “weekly_sales” there are some values which are negative. Whereas this should not be possible considering a strict definition of the term sales/revenues, whe interpret the variable as comprising also of depreciated products/lost merchandise. As such, we will keep the negative values as well.

Important Variables

weekly_sales: a density plot shows that most stores have a similar amount of weekly sales, with the density plot presenting a stark peak and being skewed to the right.The median measures around 7667 with the maximum amount being 671916. On a histogram, this value and other like it appear as outliers. We also found clear peaks in sales in the period of late December and late November of both 2011 and 2012.

favstats(sales1$weekly_sales)

min	Q1	median	Q3	max	mean	sd	n	missing
-4.99e+03	2.1e+03	7.67e+03	2.03e+04	6.72e+05	1.61e+04	2.29e+04	421570	0

sales1 %>%
  ggplot(aes(x= weekly_sales)) +
  geom_histogram(binwidth=5000) +
  scale_x_continuous(labels = scales::comma, limits = c(0,200000)) +
  scale_y_continuous(labels = scales::comma) +
  labs(title = "Histogram of Right Skewed distribution of weekly_sales variable",x="Weekly Sales",y=NULL) +
  theme_minimal()

all of the markdowns (1 to 5) The various markdown types represent the kinds of discounts which can be brought on products. We analysed these together to try and see which type seems to be more successful using boxplots. At a glance, it is clear that markdown_1 and markdown_5’s distributions are more skewed to the right, whereas the other markdowns are skewed very little. Furthermore, markdown_3 generates relatively few outliers compared to the other ones.

m1 <- sales1 %>%
  ggplot(aes(x= mark_down1)) +
  geom_boxplot() +
  scale_x_continuous(labels = scales::comma, limits = c(-10000,112000)) +
  scale_y_continuous(labels = scales::comma) +
  labs(x="Markdown 1",y=NULL) +
  theme_minimal() +
  theme(axis.text.y = element_blank())

m2 <- sales1 %>%
  ggplot(aes(x= mark_down2)) +
  geom_boxplot() +
  scale_x_continuous(labels = scales::comma, limits = c(-10000,112000)) +
  scale_y_continuous(labels = scales::comma) +
  labs(x="Markdown 2",y=NULL) +
  theme_minimal() +
  theme(axis.text.y = element_blank())

m3 <- sales1 %>%
  ggplot(aes(x= mark_down3)) +
  geom_boxplot() +
  scale_x_continuous(labels = scales::comma, limits = c(-10000,112000)) +
  scale_y_continuous(labels = scales::comma) +
  labs(x="Markdown 3",y=NULL) +
  theme_minimal() +
  theme(axis.text.y = element_blank())

m4 <- sales1 %>%
  ggplot(aes(x= mark_down4)) +
  geom_boxplot() +
  scale_x_continuous(labels = scales::comma, limits = c(-10000,112000)) +
  scale_y_continuous(labels = scales::comma) +
  labs(x="Markdown 4",y=NULL) +
  theme_minimal() +
  theme(axis.text.y = element_blank())

m5 <- sales1 %>%
  ggplot(aes(x= mark_down5)) +
  geom_boxplot() +
  scale_x_continuous(labels = scales::comma, limits = c(-10000,112000)) +
  scale_y_continuous(labels = scales::comma) +
  labs(x="Markdown 5",y=NULL) +
  theme_minimal() +
  theme(axis.text.y = element_blank())

ggarrange(m1,m2,m3,m4,m5,nrow=5)

Correlation Exploration between Variables

To Explore the correlation between the various variables, we analysed the correlations between weekly_sales, temperature, fuel_price, markdown_1, markdown_2, markdown_3, markdown_4, markdown_5, cpi, unemployment and size. There is quite a high correlation amongst the markdowns, with 1 and 3 presentin an correlation factor of 0.83, but it is insignificant as it doesn’t make much sense.

cor(sales1[,c(1,2,4:14,16)])

##                  store      dept is_holiday weekly_sales temperature fuel_price
## store         1.000000  0.024004  -0.000548    -0.085257    -0.05010   0.065290
## dept          0.024004  1.000000   0.000916     0.148003     0.00444   0.003572
## is_holiday   -0.000548  0.000916   1.000000     0.012758    -0.15595  -0.078281
## weekly_sales -0.085257  0.148003   0.012758     1.000000    -0.00230  -0.000116
## temperature  -0.050097  0.004437  -0.155949    -0.002299     1.00000   0.143859
## fuel_price    0.065290  0.003572  -0.078281    -0.000116     0.14386   1.000000
## mark_down1   -0.059844  0.001494  -0.003521     0.047231    -0.02642   0.297056
## mark_down2   -0.033829  0.000587   0.207604     0.020738    -0.17967   0.029153
## mark_down3   -0.020331  0.001475   0.266471     0.038528    -0.05603   0.018615
## mark_down4   -0.042724  0.001937   0.011565     0.037473    -0.05028   0.166622
## mark_down5   -0.012452  0.002668  -0.015235     0.050438    -0.01475   0.215420
## cpi          -0.211088 -0.007477  -0.001944    -0.020941     0.18211  -0.164210
## unemployment  0.208552  0.007837   0.010460    -0.025909     0.09673  -0.033853
## size         -0.182881 -0.002966   0.000593     0.243812    -0.05831   0.003361
##              mark_down1 mark_down2 mark_down3 mark_down4 mark_down5      cpi
## store          -0.05984  -0.033829   -0.02033   -0.04272   -0.01245 -0.21109
## dept            0.00149   0.000587    0.00148    0.00194    0.00267 -0.00748
## is_holiday     -0.00352   0.207604    0.26647    0.01157   -0.01524 -0.00194
## weekly_sales    0.04723   0.020738    0.03853    0.03747    0.05044 -0.02094
## temperature    -0.02642  -0.179672   -0.05603   -0.05028   -0.01475  0.18211
## fuel_price      0.29706   0.029153    0.01861    0.16662    0.21542 -0.16421
## mark_down1      1.00000   0.174868   -0.01441    0.83890    0.41505  0.01091
## mark_down2      0.17487   1.000000   -0.00608    0.11325    0.13174 -0.00355
## mark_down3     -0.01441  -0.006080    1.00000   -0.01202    0.04247 -0.00584
## mark_down4      0.83890   0.113250   -0.01202    1.00000    0.30337 -0.00205
## mark_down5      0.41505   0.131735    0.04247    0.30337    1.00000  0.06791
## cpi             0.01091  -0.003554   -0.00584   -0.00205    0.06791  1.00000
## unemployment   -0.10517  -0.041427   -0.01808   -0.07651   -0.12041 -0.29995
## size            0.16979   0.078372    0.03364    0.12733    0.15301 -0.00331
##              unemployment      size
## store             0.20855 -0.182881
## dept              0.00784 -0.002966
## is_holiday        0.01046  0.000593
## weekly_sales     -0.02591  0.243812
## temperature       0.09673 -0.058313
## fuel_price       -0.03385  0.003361
## mark_down1       -0.10517  0.169788
## mark_down2       -0.04143  0.078372
## mark_down3       -0.01808  0.033641
## mark_down4       -0.07651  0.127334
## mark_down5       -0.12041  0.153011
## cpi              -0.29995 -0.003314
## unemployment      1.00000 -0.068238
## size             -0.06824  1.000000

Q1

#number of distinct date, i.e weeks of data in details table
a <- details %>% summarise(n_distinct(date))

#number of distinct date, i.e weeks of data in sales table
b <- sales %>% summarise(n_distinct(date))

#Difference between the number of weeks in details & sales table
a-b

n_distinct(date)
39

In details.csv there are 39 more weeks of data compared to sales.csv

Q2

Before answering, we had to reformat the dates in the sales dataset. We then proceeded to analyse how many days and weeks have passed between the first day of sales and the last one. We found out that 142 weeks had passed. This amount is consistent with the number of years in the data set and previous analyses.

date_min <- min(dmy(sales$date))

date_max <- max(dmy(sales$date))

#Range of date in sales data in days
as.numeric(difftime(date_max, date_min))/7

## [1] 142

Q3

The maximum department count per store is 79, with stores 15, 13 and 19 having this amount of departments in some cases.

sales1 %>%
  group_by(store) %>%
  summarise(dept_count = n_distinct(dept)) %>%
  arrange(desc(dept_count))

store	dept_count
13	79
15	79
19	79
2	78
4	78
11	78
18	78
20	78
27	78
34	78
1	77
6	77
10	77
14	77
21	77
23	77
24	77
25	77
28	77
29	77
32	77
40	77
41	77
7	76
8	76
16	76
17	76
22	76
26	76
31	76
12	75
39	75
35	74
45	74
9	73
3	72
5	72
30	64
33	63
36	63
38	63
37	62
42	62
44	62
43	61

Q4

From Question 3, It is noticeable how most stores have a similar amount of maximum departments, except for those stores with codes 30,33,36, 38, 37, 42 and 43. These stores have less departments as they measure in their sixties.

#Look at mean, median & standard deviation of sales across stores
sales1 %>%
  group_by(date,store) %>%
  summarise(base_weekly_sales=sum(weekly_sales)) %>%
  group_by(store) %>%
  summarise(median_weekly_sales=median(base_weekly_sales),mean_weekly_sales=mean(base_weekly_sales),sd_weekly_sales=sd(base_weekly_sales))

store	median_weekly_sales	mean_weekly_sales	sd_weekly_sales
1	1.54e+06	1.57e+06	1.58e+05
2	1.89e+06	1.94e+06	2.39e+05
3	3.99e+05	4.06e+05	4.7e+04
4	2.09e+06	2.11e+06	2.69e+05
5	3.13e+05	3.2e+05	3.81e+04
6	1.54e+06	1.58e+06	2.15e+05
7	5.61e+05	5.75e+05	1.13e+05
8	8.98e+05	9.15e+05	1.08e+05
9	5.41e+05	5.48e+05	6.96e+04
10	1.84e+06	1.91e+06	3.03e+05
11	1.33e+06	1.37e+06	1.67e+05
12	9.89e+05	1.02e+06	1.4e+05
13	1.98e+06	2.02e+06	2.67e+05
14	2.02e+06	2.03e+06	3.19e+05
15	6.07e+05	6.28e+05	1.22e+05
16	5.13e+05	5.23e+05	8.63e+04
17	8.78e+05	9e+05	1.13e+05
18	1.07e+06	1.09e+06	1.77e+05
19	1.42e+06	1.46e+06	1.93e+05
20	2.07e+06	2.12e+06	2.78e+05
21	7.43e+05	7.61e+05	1.29e+05
22	1e+06	1.04e+06	1.63e+05
23	1.37e+06	1.4e+06	2.52e+05
24	1.35e+06	1.37e+06	1.69e+05
25	6.91e+05	7.12e+05	1.14e+05
26	1e+06	1.01e+06	1.11e+05
27	1.75e+06	1.79e+06	2.42e+05
28	1.27e+06	1.33e+06	1.83e+05
29	5.23e+05	5.43e+05	1e+05
30	4.43e+05	4.42e+05	2.31e+04
31	1.39e+06	1.41e+06	1.28e+05
32	1.15e+06	1.18e+06	1.39e+05
33	2.6e+05	2.62e+05	2.44e+04
34	9.56e+05	9.73e+05	1.05e+05
35	8.57e+05	9.26e+05	2.12e+05
36	3.75e+05	3.76e+05	6.11e+04
37	5.22e+05	5.22e+05	2.22e+04
38	3.83e+05	3.88e+05	4.32e+04
39	1.42e+06	1.46e+06	2.19e+05
40	9.61e+05	9.71e+05	1.2e+05
41	1.25e+06	1.28e+06	1.9e+05
42	5.61e+05	5.6e+05	5.03e+04
43	6.37e+05	6.38e+05	4.1e+04
44	3.01e+05	3.05e+05	2.5e+04
45	7.68e+05	7.91e+05	1.3e+05

Q5

Store number 4 has the highest number of sales in this timeframe.

#Filtering for the mentioned dates, grouping by store and ordering based on sum of sales
sales1 %>%
  filter(between(date,as.Date('2011-11-07'),as.Date('2011-12-30'))) %>%
  group_by(store) %>%
  summarise(sum_sales = sum(weekly_sales)) %>%
  arrange(desc(sum_sales))

store	sum_sales
4	2.07e+07
20	2.07e+07
13	1.99e+07
10	1.95e+07
14	1.93e+07
2	1.83e+07
27	1.66e+07
6	1.53e+07
39	1.49e+07
23	1.43e+07
1	1.43e+07
19	1.39e+07
11	1.3e+07
31	1.29e+07
24	1.26e+07
41	1.26e+07
28	1.2e+07
32	1.13e+07
18	1.08e+07
22	1.04e+07
12	1e+07
26	9.2e+06
40	9.16e+06
34	9.13e+06
35	8.91e+06
8	8.6e+06
17	8.14e+06
45	8.09e+06
21	7.66e+06
25	7.38e+06
15	6.44e+06
7	5.92e+06
29	5.5e+06
9	5.39e+06
16	5.14e+06
43	5e+06
42	4.56e+06
37	4.22e+06
3	3.81e+06
30	3.49e+06
38	3.24e+06
5	3.08e+06
36	2.58e+06
44	2.48e+06
33	2.01e+06

Q6

Store number 20 has the highest level of weekly median sales in this timeframe.

median_weekly <- sales1 %>%
  group_by(store) %>%
  summarise(median_weekly_sales=median(weekly_sales))

median_weekly %>%
  ggplot(aes(x=median_weekly_sales,y=fct_reorder(factor(store),median_weekly_sales))) +
  geom_col() +
  labs(title = "Store sales ranked by weekly median sales", x = "Weekly median sales",y = "Store") +
  theme_bw()

Q7

The variable which has the highest correlation with weekly_sales is the size variable, which represents the size of the store.

details2<-sales1 %>% 
  select(-c(dept))

cor(details2[,c(4:13,1,15)])

##              weekly_sales temperature fuel_price mark_down1 mark_down2
## weekly_sales     1.000000     -0.0023  -0.000116     0.0472    0.02074
## temperature     -0.002299      1.0000   0.143859    -0.0264   -0.17967
## fuel_price      -0.000116      0.1439   1.000000     0.2971    0.02915
## mark_down1       0.047231     -0.0264   0.297056     1.0000    0.17487
## mark_down2       0.020738     -0.1797   0.029153     0.1749    1.00000
## mark_down3       0.038528     -0.0560   0.018615    -0.0144   -0.00608
## mark_down4       0.037473     -0.0503   0.166622     0.8389    0.11325
## mark_down5       0.050438     -0.0148   0.215420     0.4151    0.13174
## cpi             -0.020941      0.1821  -0.164210     0.0109   -0.00355
## unemployment    -0.025909      0.0967  -0.033853    -0.1052   -0.04143
## store           -0.085257     -0.0501   0.065290    -0.0598   -0.03383
## size             0.243812     -0.0583   0.003361     0.1698    0.07837
##              mark_down3 mark_down4 mark_down5      cpi unemployment   store
## weekly_sales    0.03853    0.03747     0.0504 -0.02094      -0.0259 -0.0853
## temperature    -0.05603   -0.05028    -0.0148  0.18211       0.0967 -0.0501
## fuel_price      0.01861    0.16662     0.2154 -0.16421      -0.0339  0.0653
## mark_down1     -0.01441    0.83890     0.4151  0.01091      -0.1052 -0.0598
## mark_down2     -0.00608    0.11325     0.1317 -0.00355      -0.0414 -0.0338
## mark_down3      1.00000   -0.01202     0.0425 -0.00584      -0.0181 -0.0203
## mark_down4     -0.01202    1.00000     0.3034 -0.00205      -0.0765 -0.0427
## mark_down5      0.04247    0.30337     1.0000  0.06791      -0.1204 -0.0125
## cpi            -0.00584   -0.00205     0.0679  1.00000      -0.3000 -0.2111
## unemployment   -0.01808   -0.07651    -0.1204 -0.29995       1.0000  0.2086
## store          -0.02033   -0.04272    -0.0125 -0.21109       0.2086  1.0000
## size            0.03364    0.12733     0.1530 -0.00331      -0.0682 -0.1829
##                  size
## weekly_sales  0.24381
## temperature  -0.05831
## fuel_price    0.00336
## mark_down1    0.16979
## mark_down2    0.07837
## mark_down3    0.03364
## mark_down4    0.12733
## mark_down5    0.15301
## cpi          -0.00331
## unemployment -0.06824
## store        -0.18288
## size          1.00000

Q8

Stores which have higher mean sales out of the holidays include 30, 36, 37, 38, 44.

#Finding weekly means by store divided by is_holiday variable, compare to find which stores have anomalous holiday sales lower than normal sales
anomaly_mean <- sales1 %>%
  group_by(date,store,is_holiday) %>%
  summarise(base_weekly_sales=sum(weekly_sales)) %>%
  group_by(store,is_holiday) %>%
  summarise(mean_weekly_sales = mean(base_weekly_sales)) %>%
  pivot_wider(names_from = "is_holiday",
              values_from = "mean_weekly_sales")

colnames(anomaly_mean) <- c("store","noholiday","yesholiday")
  
anomaly_mean %>%
    group_by(store) %>%
    summarise(anomaly_flag = ifelse(noholiday>yesholiday,1,0)) %>%
    arrange(desc(anomaly_flag))

store	anomaly_flag
30	1
36	1
37	1
38	1
44	1
1	0
2	0
3	0
4	0
5	0
6	0
7	0
8	0
9	0
10	0
11	0
12	0
13	0
14	0
15	0
16	0
17	0
18	0
19	0
20	0
21	0
22	0
23	0
24	0
25	0
26	0
27	0
28	0
29	0
31	0
32	0
33	0
34	0
35	0
39	0
40	0
41	0
42	0
43	0
45	0

Q9

Stores which have higher median sales out of the holidays include 25, 32, 36, 38.

#Finding weekly medians by store divided by is_holiday variable, compare to find which stores have anomalous holiday sales lower than normal sales
anomaly_median <- sales1 %>%
  group_by(date,store,is_holiday) %>%
  summarise(base_weekly_sales=sum(weekly_sales)) %>%
  group_by(store,is_holiday) %>%
  summarise(median_weekly_sales = median(base_weekly_sales)) %>%
  pivot_wider(names_from = "is_holiday",
              values_from = "median_weekly_sales")

colnames(anomaly_median) <- c("store","noholiday","yesholiday")
  
  
anomaly_median %>%
    group_by(store) %>%
    summarise(anomaly_flag = ifelse(noholiday>yesholiday,1,0)) %>%
    arrange(desc(anomaly_flag))

store	anomaly_flag
25	1
32	1
36	1
38	1
1	0
2	0
3	0
4	0
5	0
6	0
7	0
8	0
9	0
10	0
11	0
12	0
13	0
14	0
15	0
16	0
17	0
18	0
19	0
20	0
21	0
22	0
23	0
24	0
26	0
27	0
28	0
29	0
30	0
31	0
33	0
34	0
35	0
37	0
39	0
40	0
41	0
42	0
43	0
44	0
45	0

Inferential Statistics

Average weekly sales in holidays

Sales are expected to spike during holiday periods as the demand for gifts increase. There are 4 major holiday periods in the US: the Super Bowl in February, Labour Day in September, Thanksgiving in November, and Christmas in December. Between February 2010 and October 2012, each of the holidays have generated around a hundred million dollars of net sales. In this dataset, the Thanksgiving festival in November generates the highest average weekly sales of 22k out of all four holidays.

# Use sales & details dataset holiday
sales_holiday <- sales1 %>%
  filter(is_holiday == TRUE) %>% # filter for holiday periods only
  mutate(month = strftime(date, "%m")) %>% # create new variable as month component of date
  group_by(month) %>% # group by month to show which holiday it is, of all sales of all stores
  summarise(average_sales = mean(weekly_sales), sum_sales = sum(weekly_sales)) %>% # summarise by holiday 
  arrange(desc(average_sales))

# Display summary table
sales_holiday

month	average_sales	sum_sales
11	2.24e+04	1.33e+08
02	1.65e+04	1.47e+08
09	1.6e+04	1.42e+08
12	1.46e+04	8.71e+07

Labour day, on average, has just above 1.8k fewer weekly net sales relative to other major holiday periods.

sales_holiday_vs_labour <- sales1 %>%
  filter(is_holiday == TRUE) %>% # filter for holiday periods only
  mutate(month = strftime(date, "%m")) %>% # extract month component of date as new variable
  mutate(month = as.numeric(month)) %>% # change class of month to numeric
  group_by(month) %>% # group by holiday (which is by month)
  summarise(average_sales = mean(weekly_sales), sum_sales = sum(weekly_sales)) %>% # summarise sales by holiday 
  mutate(is_labour_day = ifelse(month == 9, TRUE, FALSE)) %>% # generate logical variable to separate holidays - labour day and others
  group_by(is_labour_day) %>% # calculate summary statistics by holiday average sales
  summarise(average_holiday = mean(average_sales))

# Display summary table
sales_holiday_vs_labour

is_labour_day	average_holiday
FALSE	1.78e+04
TRUE	1.6e+04

# Calculate difference in average weekly sales
15995 - 17834

## [1] -1839

Difference in means of weekly net sales between holiday and non-holiday periods

With Thanksgiving

One question that may be asked is whether holiday weekly net sales differ statistically significantly to non-holiday weekly net sales. Graphically, the 95% confidence intervals do not overlap at all, and that holiday average weekly net sales significantly differ from those in non-holiday periods. Running a t-test with the null hypothesis of average weekly net sales is the same between holiday and non-holiday periods, and alternative hypothesis of average weekly net sales differ between the two periods. The t test returned a very low p-value, suggesting that there is enough evidence to reject the null hypothesis of same mean weekly net sales between holiday and non-holiday periods.

t_test_holiday <- sales1 %>%
  group_by(is_holiday) %>%
  summarise(mean = mean(weekly_sales),
            count = n(),
            t = qt(0.975, count - 1),
            sd = sd(weekly_sales),
            se = sd/sqrt(count),
            margin = t * se,
            l_ci = mean - margin,
            h_ci = mean + margin)

ggplot(data = t_test_holiday, aes(x = mean, y = is_holiday, colour = is_holiday)) +
  geom_point() +
  geom_errorbarh(aes(xmax = h_ci, xmin = l_ci, height = .1)) +
  labs(title = "95% Confidence Interval comparison between holiday and non-holiday periods",
       x = "Mean Weekly Sales",
       y = "Holiday Period") +
  theme_bw() +
  theme (legend.position = "none") +
  NULL

t.test(weekly_sales ~ is_holiday,
       alternative = "two.sided",
       conf.level = 0.95,
       data = sales1)

## 
##  Welch Two Sample t-test
## 
## data:  weekly_sales by is_holiday
## t = -7, df = 32761, p-value = 3e-12
## alternative hypothesis: true difference in means between group FALSE and group TRUE is not equal to 0
## 95 percent confidence interval:
##  -1460  -822
## sample estimates:
## mean in group FALSE  mean in group TRUE 
##               16012               17153

# p-value = 3e-12

Without Thanksgiving

Thanksgiving, as previously determined, has the highest weekly net sales. Keeping in mind that this holiday period may be an outlier, an analysis of the difference between holiday and non-holiday weekly sales excluding thanksgiving is due.

# Excluding thanksgiving
sales_thanksgiving <- sales1 %>%
  mutate(month = strftime(date, "%m")) %>% # extract month component of date as new variable
  mutate(month = as.numeric(month)) %>% # change class of month to numeric
  mutate(is_thanksgiving = ifelse(is_holiday == TRUE & month == 11, TRUE, FALSE)) %>% # generate thanksgiving indicator
  filter(is_thanksgiving == FALSE) # exclude thanksgiving

Firstly, confidence intervals of these subgroups are compared. It seems like the 95% confidence interval of non-holiday periods is completely contained within those of the holiday periods.

t_test_holiday <- sales_thanksgiving %>%
  group_by(is_holiday) %>%
  summarise(mean = mean(weekly_sales),
            count = n(),
            t = qt(0.975, count - 1),
            sd = sd(weekly_sales),
            se = sd/sqrt(count),
            margin = t * se,
            l_ci = mean - margin,
            h_ci = mean + margin)

# ggplot
ggplot(data = t_test_holiday, aes(x = mean, y = is_holiday, colour = is_holiday)) +
  geom_point() +
  geom_errorbarh(aes(xmax = h_ci, xmin = l_ci, height = .1)) +
  labs(title = "95% Confidence Interval comparison between holiday and non-holiday periods",
       x = "Mean Weekly Sales",
       y = "Holiday Period") +
  theme_bw() +
  theme (legend.position = "none") +
  NULL

Running t-test of difference in means of weekly net sales returned not enough evidence to reject the null hypothesis, and that holiday average weekly sales do not differ at 95% from non-holiday periods when thanksgiving is excluded. We can safely conclude our analysis of holiday vs non-holiday weekly net sales, concluding that Thanksgiving is indeed an outlier of the holiday periods with significantly higher weekly sales relative to both other holiday and non-holiday periods.

t.test(weekly_sales ~ is_holiday,
       alternative = "two.sided",
       conf.level = 0.95,
       data = sales_thanksgiving)

## 
##  Welch Two Sample t-test
## 
## data:  weekly_sales by is_holiday
## t = 1, df = 26693, p-value = 0.3
## alternative hypothesis: true difference in means between group FALSE and group TRUE is not equal to 0
## 95 percent confidence interval:
##  -124  462
## sample estimates:
## mean in group FALSE  mean in group TRUE 
##               16012               15844

# p-value = 0.3

Regression Models

The purpose of this exercise is to explain the variability of the weekly sales in the retailer’s stores.

Running regression with all variables

In the first attempt to explain weekly sales, we are using all available variables in their current format.

model1 <- lm(weekly_sales ~ ., data = sales1)

get_regression_table(model1)

term	estimate	std_error	statistic	p_value	lower_ci	upper_ci
intercept	2.64e+04	3.28e+03	8.05	0	2e+04	3.28e+04
store	-142	3.1	-45.8	0	-148	-136
dept	111	1.1	101	0	109	113
date	-1.38	0.237	-5.81	0	-1.84	-0.912
is_holidayTRUE	652	142	4.6	0	374	929
temperature	15.9	2.01	7.89	0	11.9	19.8
fuel_price	50.5	130	0.388	0.698	-205	306
mark_down1	0.028	0.012	2.41	0.016	0.005	0.051
mark_down2	0	0.007	-0.048	0.962	-0.014	0.013
mark_down3	0.117	0.006	18.4	0	0.105	0.13
mark_down4	-0.002	0.016	-0.127	0.899	-0.034	0.03
mark_down5	0.106	0.009	11.2	0	0.087	0.124
cpi	-25.9	0.991	-26.1	0	-27.8	-23.9
unemployment	-263	20.6	-12.7	0	-303	-223
type: B	-347	108	-3.2	0.001	-560	-135
type: C	5.81e+03	185	31.4	0	5.45e+03	6.17e+03
size	0.098	0.001	100	0	0.096	0.1

get_regression_summaries(model1)

r_squared	adj_r_squared	mse	rmse	sigma	statistic	p_value	df	nobs
0.09	0.09	4.76e+08	2.18e+04	2.18e+04	2.6e+03	0	16	4.22e+05

mosaic::msummary(model1)

##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     2.64e+04   3.28e+03    8.05  8.2e-16 ***
## store          -1.42e+02   3.10e+00  -45.82  < 2e-16 ***
## dept            1.11e+02   1.10e+00  100.67  < 2e-16 ***
## date           -1.38e+00   2.37e-01   -5.81  6.3e-09 ***
## is_holidayTRUE  6.52e+02   1.42e+02    4.60  4.2e-06 ***
## temperature     1.59e+01   2.01e+00    7.89  3.0e-15 ***
## fuel_price      5.05e+01   1.30e+02    0.39   0.6981    
## mark_down1      2.83e-02   1.17e-02    2.41   0.0158 *  
## mark_down2     -3.39e-04   7.05e-03   -0.05   0.9617    
## mark_down3      1.17e-01   6.36e-03   18.43  < 2e-16 ***
## mark_down4     -2.07e-03   1.63e-02   -0.13   0.8990    
## mark_down5      1.06e-01   9.42e-03   11.21  < 2e-16 ***
## cpi            -2.59e+01   9.91e-01  -26.13  < 2e-16 ***
## unemployment   -2.63e+02   2.06e+01  -12.75  < 2e-16 ***
## typeB          -3.47e+02   1.08e+02   -3.20   0.0014 ** 
## typeC           5.81e+03   1.85e+02   31.42  < 2e-16 ***
## size            9.78e-02   9.77e-04  100.12  < 2e-16 ***
## 
## Residual standard error: 21800 on 421553 degrees of freedom
## Multiple R-squared:  0.0899, Adjusted R-squared:  0.0899 
## F-statistic: 2.6e+03 on 16 and 421553 DF,  p-value: <2e-16

When regression is run on dataset as given, then our model explains only 9% of variability of the data. Similarly, ‘date’ variable, even though significant, is not interpretable. Therefore, we decided to split this variable into year, and seasons.

sales_reg <- sales1 %>% 
  mutate(year= factor(year(date)),
         month = month(date),
         season_name = case_when(
           month %in%  c("12", "1", "2")  ~ "Winter",
           month %in%  c("3", "4", "5")  ~ "Spring",
           month %in%  c("6", "7", "8")  ~ "Summer",
           month %in%  c("9", "10", "11")  ~ "Autumn",
    ),
    season_name = factor(season_name, 
                         levels = c("Winter", "Spring", "Summer", "Autumn")))

Running model 2

We run the next model after removing the date and month variables and keeping seasons and year as a factor instead.

model2 <- lm(weekly_sales~ . - date - month, data = sales_reg)

get_regression_table(model2)

term	estimate	std_error	statistic	p_value	lower_ci	upper_ci
intercept	261	596	0.439	0.661	-906	1.43e+03
store	-137	3.14	-43.6	0	-143	-131
dept	111	1.1	101	0	109	113
is_holidayTRUE	229	146	1.57	0.117	-57.2	515
temperature	44.8	3.17	14.1	0	38.6	51
fuel_price	2.55e+03	181	14.1	0	2.2e+03	2.91e+03
mark_down1	0.071	0.012	5.84	0	0.047	0.095
mark_down2	-0.012	0.007	-1.64	0.1	-0.026	0.002
mark_down3	0.134	0.006	20.8	0	0.121	0.147
mark_down4	-0.037	0.016	-2.23	0.026	-0.069	-0.004
mark_down5	0.104	0.009	11.1	0	0.085	0.122
cpi	-22.8	1.07	-21.3	0	-24.9	-20.7
unemployment	-411	21.1	-19.5	0	-452	-370
type: B	-314	110	-2.86	0.004	-529	-98.7
type: C	5.71e+03	185	30.9	0	5.35e+03	6.08e+03
size	0.097	0.001	99.3	0	0.096	0.099
year: 2011	-2.66e+03	163	-16.3	0	-2.98e+03	-2.34e+03
year: 2012	-4.1e+03	200	-20.5	0	-4.49e+03	-3.7e+03
season_name: Spring	-2.47e+03	129	-19.1	0	-2.72e+03	-2.21e+03
season_name: Summer	-2.69e+03	161	-16.7	0	-3.01e+03	-2.38e+03
season_name: Autumn	-2.76e+03	133	-20.7	0	-3.02e+03	-2.5e+03

get_regression_summaries(model2)

r_squared	adj_r_squared	mse	rmse	sigma	statistic	p_value	df	nobs
0.091	0.091	4.75e+08	2.18e+04	2.18e+04	2.12e+03	0	20	4.22e+05

mosaic::msummary(model2)

##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)        2.61e+02   5.96e+02    0.44   0.6609    
## store             -1.37e+02   3.14e+00  -43.64  < 2e-16 ***
## dept               1.11e+02   1.10e+00  100.75  < 2e-16 ***
## is_holidayTRUE     2.29e+02   1.46e+02    1.57   0.1169    
## temperature        4.48e+01   3.17e+00   14.11  < 2e-16 ***
## fuel_price         2.55e+03   1.81e+02   14.08  < 2e-16 ***
## mark_down1         7.08e-02   1.21e-02    5.85  5.1e-09 ***
## mark_down2        -1.17e-02   7.13e-03   -1.64   0.1000    
## mark_down3         1.34e-01   6.44e-03   20.83  < 2e-16 ***
## mark_down4        -3.66e-02   1.64e-02   -2.23   0.0260 *  
## mark_down5         1.04e-01   9.32e-03   11.11  < 2e-16 ***
## cpi               -2.28e+01   1.07e+00  -21.35  < 2e-16 ***
## unemployment      -4.11e+02   2.11e+01  -19.45  < 2e-16 ***
## typeB             -3.14e+02   1.10e+02   -2.86   0.0042 ** 
## typeC              5.71e+03   1.85e+02   30.86  < 2e-16 ***
## size               9.75e-02   9.82e-04   99.29  < 2e-16 ***
## year2011          -2.66e+03   1.63e+02  -16.34  < 2e-16 ***
## year2012          -4.10e+03   2.00e+02  -20.46  < 2e-16 ***
## season_nameSpring -2.47e+03   1.29e+02  -19.13  < 2e-16 ***
## season_nameSummer -2.69e+03   1.61e+02  -16.72  < 2e-16 ***
## season_nameAutumn -2.76e+03   1.33e+02  -20.75  < 2e-16 ***
## 
## Residual standard error: 21800 on 421549 degrees of freedom
## Multiple R-squared:  0.0914, Adjusted R-squared:  0.0913 
## F-statistic: 2.12e+03 on 20 and 421549 DF,  p-value: <2e-16

We create a variable for each of the holiday weeks (Christmas, Thanksgiving, Labour day and Superbowl) to compare weekly sales for diffreent holidays.

sales_reg<-sales_reg %>% 
  mutate(superbowl = ifelse(month == "2" & is_holiday =="TRUE", TRUE, FALSE),
         christmas = ifelse(month == "12" & is_holiday =="TRUE", TRUE, FALSE),
         labor = ifelse(month == "9" & is_holiday =="TRUE", TRUE, FALSE),
         thanksgiving = ifelse(month == "11" & is_holiday =="TRUE", TRUE, FALSE))

Additionally, variables ‘store’ and ‘dept’ are interpreted as numerical variables, when in fact they are factors. Therefore, this will be accounted for in our next model.

Running model 3

model3 <- lm(weekly_sales ~ factor(dept) + factor(store) + temperature + cpi + unemployment + type + size  + season_name + fuel_price + superbowl + christmas + labor + thanksgiving + mark_down1  + mark_down2  + mark_down3  + mark_down4  + mark_down5, data = sales_reg)

get_regression_table(model3)

term	estimate	std_error	statistic	p_value	lower_ci	upper_ci
intercept	3.01e+04	2.61e+03	11.5	0	2.5e+04	3.52e+04
factor(dept): 2	2.46e+04	236	104	0	2.41e+04	2.5e+04
factor(dept): 3	-7.46e+03	236	-31.7	0	-7.93e+03	-7e+03
factor(dept): 4	6.81e+03	236	28.9	0	6.35e+03	7.27e+03
factor(dept): 5	2.04e+03	236	8.64	0	1.58e+03	2.51e+03
factor(dept): 6	-1.54e+04	240	-64	0	-1.58e+04	-1.49e+04
factor(dept): 7	4.97e+03	236	21.1	0	4.5e+03	5.43e+03
factor(dept): 8	1.1e+04	236	46.9	0	1.06e+04	1.15e+04
factor(dept): 9	837	236	3.54	0	373	1.3e+03
factor(dept): 10	-902	236	-3.83	0	-1.36e+03	-440
factor(dept): 11	-4.75e+03	236	-20.1	0	-5.21e+03	-4.28e+03
factor(dept): 12	-1.52e+04	236	-64.4	0	-1.57e+04	-1.47e+04
factor(dept): 13	1.15e+04	236	48.9	0	1.11e+04	1.2e+04
factor(dept): 14	-4.37e+03	236	-18.5	0	-4.83e+03	-3.91e+03
factor(dept): 16	-5e+03	236	-21.2	0	-5.47e+03	-4.54e+03
factor(dept): 17	-9.13e+03	236	-38.7	0	-9.59e+03	-8.67e+03
factor(dept): 18	-1.27e+04	252	-50.3	0	-1.31e+04	-1.22e+04
factor(dept): 19	-2.06e+04	267	-77	0	-2.11e+04	-2e+04
factor(dept): 20	-1.44e+04	240	-60.2	0	-1.49e+04	-1.4e+04
factor(dept): 21	-1.43e+04	236	-60.8	0	-1.48e+04	-1.39e+04
factor(dept): 22	-1.02e+04	245	-41.5	0	-1.07e+04	-9.7e+03
factor(dept): 23	3.56e+03	242	14.7	0	3.08e+03	4.03e+03
factor(dept): 24	-1.49e+04	247	-60.4	0	-1.54e+04	-1.44e+04
factor(dept): 25	-1.05e+04	236	-44.2	0	-1.09e+04	-1e+04
factor(dept): 26	-1.28e+04	243	-52.6	0	-1.33e+04	-1.23e+04
factor(dept): 27	-1.93e+04	244	-79.1	0	-1.98e+04	-1.88e+04
factor(dept): 28	-1.94e+04	239	-81.1	0	-1.98e+04	-1.89e+04
factor(dept): 29	-1.59e+04	248	-64	0	-1.64e+04	-1.54e+04
factor(dept): 30	-1.75e+04	248	-70.3	0	-1.8e+04	-1.7e+04
factor(dept): 31	-1.77e+04	239	-74.1	0	-1.82e+04	-1.72e+04
factor(dept): 32	-1.33e+04	240	-55.4	0	-1.38e+04	-1.29e+04
factor(dept): 33	-1.48e+04	247	-60.1	0	-1.53e+04	-1.44e+04
factor(dept): 34	-5.79e+03	248	-23.4	0	-6.27e+03	-5.3e+03
factor(dept): 35	-1.87e+04	248	-75.1	0	-1.91e+04	-1.82e+04
factor(dept): 36	-1.96e+04	248	-78.8	0	-2e+04	-1.91e+04
factor(dept): 37	-2.26e+04	313	-72.2	0	-2.32e+04	-2.2e+04
factor(dept): 38	4.22e+04	236	179	0	4.17e+04	4.26e+04
factor(dept): 39	-2.73e+04	3.35e+03	-8.16	0	-3.39e+04	-2.08e+04
factor(dept): 40	2.59e+04	236	110	0	2.54e+04	2.63e+04
factor(dept): 41	-1.93e+04	247	-78.2	0	-1.98e+04	-1.88e+04
factor(dept): 42	-1.42e+04	236	-60.1	0	-1.47e+04	-1.37e+04
factor(dept): 43	-1.85e+04	3.86e+03	-4.79	0	-2.61e+04	-1.09e+04
factor(dept): 44	-1.65e+04	246	-67.1	0	-1.7e+04	-1.6e+04
factor(dept): 45	-2.24e+04	347	-64.5	0	-2.31e+04	-2.17e+04
factor(dept): 46	743	236	3.15	0.002	281	1.21e+03
factor(dept): 47	-2.27e+04	552	-41.1	0	-2.38e+04	-2.16e+04
factor(dept): 48	-2.39e+04	362	-66	0	-2.46e+04	-2.32e+04
factor(dept): 49	-1.44e+04	260	-55.4	0	-1.49e+04	-1.39e+04
factor(dept): 50	-2.34e+04	379	-61.9	0	-2.42e+04	-2.27e+04
factor(dept): 51	-2.15e+04	396	-54.3	0	-2.22e+04	-2.07e+04
factor(dept): 52	-1.77e+04	237	-74.8	0	-1.82e+04	-1.73e+04
factor(dept): 54	-2.2e+04	256	-86	0	-2.25e+04	-2.15e+04
factor(dept): 55	-1e+04	244	-40.9	0	-1.05e+04	-9.53e+03
factor(dept): 56	-1.65e+04	241	-68.5	0	-1.7e+04	-1.61e+04
factor(dept): 58	-1.93e+04	262	-73.8	0	-1.99e+04	-1.88e+04
factor(dept): 59	-1.92e+04	239	-80.3	0	-1.97e+04	-1.87e+04
factor(dept): 60	-1.89e+04	242	-77.9	0	-1.93e+04	-1.84e+04
factor(dept): 65	2.77e+04	1.14e+03	24.3	0	2.54e+04	2.99e+04
factor(dept): 67	-1.19e+04	236	-50.3	0	-1.23e+04	-1.14e+04
factor(dept): 71	-1.58e+04	248	-63.7	0	-1.63e+04	-1.53e+04
factor(dept): 72	3.08e+04	239	129	0	3.04e+04	3.13e+04
factor(dept): 74	-5.45e+03	236	-23.1	0	-5.91e+03	-4.99e+03
factor(dept): 77	-2.46e+04	1.11e+03	-22.3	0	-2.68e+04	-2.25e+04
factor(dept): 78	-2.32e+04	888	-26.2	0	-2.5e+04	-2.15e+04
factor(dept): 79	2.78e+03	236	11.8	0	2.31e+03	3.24e+03
factor(dept): 80	-7.73e+03	241	-32.1	0	-8.21e+03	-7.26e+03
factor(dept): 81	-3.77e+03	236	-16	0	-4.23e+03	-3.31e+03
factor(dept): 82	-3.77e+03	236	-16	0	-4.24e+03	-3.31e+03
factor(dept): 83	-1.67e+04	241	-69.2	0	-1.71e+04	-1.62e+04
factor(dept): 85	-1.78e+04	239	-74.3	0	-1.83e+04	-1.73e+04
factor(dept): 87	-5.9e+03	236	-25	0	-6.36e+03	-5.43e+03
factor(dept): 90	2.62e+04	236	111	0	2.57e+04	2.66e+04
factor(dept): 91	1.46e+04	236	61.9	0	1.41e+04	1.5e+04
factor(dept): 92	5.64e+04	236	239	0	5.59e+04	5.68e+04
factor(dept): 93	7.13e+03	241	29.6	0	6.65e+03	7.6e+03
factor(dept): 94	1.38e+04	243	56.7	0	1.33e+04	1.43e+04
factor(dept): 95	5.1e+04	236	216	0	5.05e+04	5.14e+04
factor(dept): 96	-3.8e+03	254	-14.9	0	-4.3e+03	-3.3e+03
factor(dept): 97	-5.17e+03	237	-21.8	0	-5.64e+03	-4.71e+03
factor(dept): 98	-1.31e+04	242	-54	0	-1.35e+04	-1.26e+04
factor(dept): 99	-2.51e+04	486	-51.8	0	-2.61e+04	-2.42e+04
factor(store): 2	5.19e+03	187	27.8	0	4.82e+03	5.56e+03
factor(store): 3	-1.67e+04	199	-83.9	0	-1.71e+04	-1.63e+04
factor(store): 4	7.62e+03	1.1e+03	6.9	0	5.45e+03	9.78e+03
factor(store): 5	-1.84e+04	203	-90.8	0	-1.88e+04	-1.8e+04
factor(store): 6	-255	192	-1.33	0.184	-631	121
factor(store): 7	-1.35e+04	334	-40.3	0	-1.41e+04	-1.28e+04
factor(store): 8	-9.65e+03	202	-47.8	0	-1e+04	-9.25e+03
factor(store): 9	-1.48e+04	208	-71.3	0	-1.52e+04	-1.44e+04
factor(store): 10	6.04e+03	1.09e+03	5.54	0	3.9e+03	8.17e+03
factor(store): 11	-3.01e+03	192	-15.7	0	-3.39e+03	-2.64e+03
factor(store): 12	-4.56e+03	1.06e+03	-4.3	0	-6.64e+03	-2.48e+03
factor(store): 13	6.6e+03	1.09e+03	6.03	0	4.45e+03	8.74e+03
factor(store): 14	7.7e+03	412	18.7	0	6.89e+03	8.51e+03
factor(store): 15	-1.22e+04	1.02e+03	-12	0	-1.42e+04	-1.02e+04
factor(store): 16	-1.49e+04	353	-42.2	0	-1.56e+04	-1.42e+04
factor(store): 17	-8.63e+03	1.1e+03	-7.86	0	-1.08e+04	-6.48e+03
factor(store): 18	-5.13e+03	1e+03	-5.12	0	-7.09e+03	-3.16e+03
factor(store): 19	-506	1.02e+03	-0.496	0.62	-2.5e+03	1.49e+03
factor(store): 20	8.13e+03	216	37.6	0	7.71e+03	8.55e+03
factor(store): 21	-1.12e+04	190	-58.9	0	-1.16e+04	-1.08e+04
factor(store): 22	-6.26e+03	964	-6.5	0	-8.15e+03	-4.37e+03
factor(store): 23	-2.31e+03	1.06e+03	-2.18	0.029	-4.38e+03	-238
factor(store): 24	-1.64e+03	1.01e+03	-1.62	0.105	-3.63e+03	345
factor(store): 25	-1.18e+04	218	-53.9	0	-1.22e+04	-1.13e+04
factor(store): 26	-6.96e+03	1.01e+03	-6.87	0	-8.94e+03	-4.97e+03
factor(store): 27	4.03e+03	973	4.14	0	2.12e+03	5.93e+03
factor(store): 28	-434	1.06e+03	-0.409	0.683	-2.51e+03	1.65e+03
factor(store): 29	-1.29e+04	991	-13	0	-1.49e+04	-1.1e+04
factor(store): 30	-1.79e+04	207	-86.6	0	-1.83e+04	-1.75e+04
factor(store): 31	-2.31e+03	188	-12.3	0	-2.68e+03	-1.94e+03
factor(store): 32	-4.9e+03	327	-15	0	-5.54e+03	-4.26e+03
factor(store): 33	-2.06e+04	1.09e+03	-19	0	-2.28e+04	-1.85e+04
factor(store): 34	-7.41e+03	1.05e+03	-7.04	0	-9.48e+03	-5.35e+03
factor(store): 35	-7.58e+03	955	-7.94	0	-9.45e+03	-5.71e+03
factor(store): 36	-1.94e+04	216	-89.7	0	-1.98e+04	-1.9e+04
factor(store): 37	-1.63e+04	207	-78.6	0	-1.67e+04	-1.58e+04
factor(store): 38	-1.61e+04	1.06e+03	-15.2	0	-1.82e+04	-1.4e+04
factor(store): 39	-1.5e+03	193	-7.77	0	-1.87e+03	-1.12e+03
factor(store): 40	-8.57e+03	1.06e+03	-8.1	0	-1.06e+04	-6.5e+03
factor(store): 41	-4.01e+03	344	-11.7	0	-4.69e+03	-3.34e+03
factor(store): 42	-1.39e+04	1.09e+03	-12.8	0	-1.6e+04	-1.18e+04
factor(store): 43	-1.31e+04	241	-54.2	0	-1.35e+04	-1.26e+04
factor(store): 44	-2.03e+04	1.09e+03	-18.6	0	-2.25e+04	-1.82e+04
factor(store): 45	-1.01e+04	410	-24.7	0	-1.09e+04	-9.32e+03
temperature	4.36	2.88	1.52	0.13	-1.28	10
cpi	7.97	12.2	0.655	0.513	-15.9	31.8
unemployment	-371	45.6	-8.15	0	-460	-282
type: B
type: C
size
season_name: Spring	-1.25e+03	84	-14.8	0	-1.41e+03	-1.08e+03
season_name: Summer	-1.03e+03	128	-8.05	0	-1.28e+03	-778
season_name: Autumn	-1.81e+03	95.6	-18.9	0	-1.99e+03	-1.62e+03
fuel_price	-434	80.9	-5.36	0	-592	-275
superbowlTRUE	-396	151	-2.63	0.009	-692	-101
christmasTRUE	-1.71e+03	203	-8.43	0	-2.1e+03	-1.31e+03
laborTRUE	674	153	4.4	0	374	975
thanksgivingTRUE	6.07e+03	229	26.5	0	5.62e+03	6.52e+03
mark_down1	0.005	0.007	0.74	0.459	-0.009	0.019
mark_down2	-0.029	0.005	-5.92	0	-0.038	-0.019
mark_down3	0.043	0.005	9.01	0	0.034	0.052
mark_down4	-0.038	0.01	-3.72	0	-0.057	-0.018
mark_down5	0.034	0.006	5.6	0	0.022	0.045

mosaic::msummary(model3)

##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)        3.01e+04   2.61e+03   11.54  < 2e-16 ***
## factor(dept)2      2.46e+04   2.36e+02  104.18  < 2e-16 ***
## factor(dept)3     -7.46e+03   2.36e+02  -31.68  < 2e-16 ***
## factor(dept)4      6.81e+03   2.36e+02   28.89  < 2e-16 ***
## factor(dept)5      2.04e+03   2.36e+02    8.64  < 2e-16 ***
## factor(dept)6     -1.54e+04   2.40e+02  -64.01  < 2e-16 ***
## factor(dept)7      4.97e+03   2.36e+02   21.07  < 2e-16 ***
## factor(dept)8      1.10e+04   2.36e+02   46.88  < 2e-16 ***
## factor(dept)9      8.37e+02   2.36e+02    3.54  0.00040 ***
## factor(dept)10    -9.02e+02   2.36e+02   -3.83  0.00013 ***
## factor(dept)11    -4.75e+03   2.36e+02  -20.14  < 2e-16 ***
## factor(dept)12    -1.52e+04   2.36e+02  -64.43  < 2e-16 ***
## factor(dept)13     1.15e+04   2.36e+02   48.92  < 2e-16 ***
## factor(dept)14    -4.37e+03   2.36e+02  -18.54  < 2e-16 ***
## factor(dept)16    -5.00e+03   2.36e+02  -21.23  < 2e-16 ***
## factor(dept)17    -9.13e+03   2.36e+02  -38.71  < 2e-16 ***
## factor(dept)18    -1.27e+04   2.52e+02  -50.26  < 2e-16 ***
## factor(dept)19    -2.06e+04   2.67e+02  -76.95  < 2e-16 ***
## factor(dept)20    -1.44e+04   2.40e+02  -60.20  < 2e-16 ***
## factor(dept)21    -1.43e+04   2.36e+02  -60.81  < 2e-16 ***
## factor(dept)22    -1.02e+04   2.45e+02  -41.52  < 2e-16 ***
## factor(dept)23     3.56e+03   2.42e+02   14.67  < 2e-16 ***
## factor(dept)24    -1.49e+04   2.47e+02  -60.44  < 2e-16 ***
## factor(dept)25    -1.05e+04   2.36e+02  -44.24  < 2e-16 ***
## factor(dept)26    -1.28e+04   2.43e+02  -52.65  < 2e-16 ***
## factor(dept)27    -1.93e+04   2.44e+02  -79.08  < 2e-16 ***
## factor(dept)28    -1.94e+04   2.39e+02  -81.12  < 2e-16 ***
## factor(dept)29    -1.59e+04   2.48e+02  -63.99  < 2e-16 ***
## factor(dept)30    -1.75e+04   2.48e+02  -70.33  < 2e-16 ***
## factor(dept)31    -1.77e+04   2.39e+02  -74.05  < 2e-16 ***
## factor(dept)32    -1.33e+04   2.40e+02  -55.44  < 2e-16 ***
## factor(dept)33    -1.48e+04   2.47e+02  -60.08  < 2e-16 ***
## factor(dept)34    -5.79e+03   2.48e+02  -23.35  < 2e-16 ***
## factor(dept)35    -1.87e+04   2.48e+02  -75.13  < 2e-16 ***
## factor(dept)36    -1.96e+04   2.48e+02  -78.80  < 2e-16 ***
## factor(dept)37    -2.26e+04   3.13e+02  -72.22  < 2e-16 ***
## factor(dept)38     4.22e+04   2.36e+02  178.97  < 2e-16 ***
## factor(dept)39    -2.73e+04   3.35e+03   -8.16  3.3e-16 ***
## factor(dept)40     2.59e+04   2.36e+02  109.85  < 2e-16 ***
## factor(dept)41    -1.93e+04   2.47e+02  -78.22  < 2e-16 ***
## factor(dept)42    -1.42e+04   2.36e+02  -60.14  < 2e-16 ***
## factor(dept)43    -1.85e+04   3.86e+03   -4.79  1.7e-06 ***
## factor(dept)44    -1.65e+04   2.46e+02  -67.12  < 2e-16 ***
## factor(dept)45    -2.24e+04   3.47e+02  -64.54  < 2e-16 ***
## factor(dept)46     7.43e+02   2.36e+02    3.15  0.00161 ** 
## factor(dept)47    -2.27e+04   5.52e+02  -41.12  < 2e-16 ***
## factor(dept)48    -2.39e+04   3.62e+02  -65.97  < 2e-16 ***
## factor(dept)49    -1.44e+04   2.60e+02  -55.42  < 2e-16 ***
## factor(dept)50    -2.34e+04   3.79e+02  -61.91  < 2e-16 ***
## factor(dept)51    -2.15e+04   3.96e+02  -54.27  < 2e-16 ***
## factor(dept)52    -1.77e+04   2.37e+02  -74.79  < 2e-16 ***
## factor(dept)54    -2.20e+04   2.56e+02  -86.05  < 2e-16 ***
## factor(dept)55    -1.00e+04   2.44e+02  -40.92  < 2e-16 ***
## factor(dept)56    -1.65e+04   2.41e+02  -68.54  < 2e-16 ***
## factor(dept)58    -1.93e+04   2.62e+02  -73.81  < 2e-16 ***
## factor(dept)59    -1.92e+04   2.39e+02  -80.33  < 2e-16 ***
## factor(dept)60    -1.89e+04   2.42e+02  -77.87  < 2e-16 ***
## factor(dept)65     2.77e+04   1.14e+03   24.32  < 2e-16 ***
## factor(dept)67    -1.19e+04   2.36e+02  -50.30  < 2e-16 ***
## factor(dept)71    -1.58e+04   2.48e+02  -63.71  < 2e-16 ***
## factor(dept)72     3.08e+04   2.39e+02  128.77  < 2e-16 ***
## factor(dept)74    -5.45e+03   2.36e+02  -23.11  < 2e-16 ***
## factor(dept)77    -2.46e+04   1.11e+03  -22.28  < 2e-16 ***
## factor(dept)78    -2.32e+04   8.88e+02  -26.17  < 2e-16 ***
## factor(dept)79     2.78e+03   2.36e+02   11.78  < 2e-16 ***
## factor(dept)80    -7.73e+03   2.41e+02  -32.08  < 2e-16 ***
## factor(dept)81    -3.77e+03   2.36e+02  -16.00  < 2e-16 ***
## factor(dept)82    -3.77e+03   2.36e+02  -16.02  < 2e-16 ***
## factor(dept)83    -1.67e+04   2.41e+02  -69.20  < 2e-16 ***
## factor(dept)85    -1.78e+04   2.39e+02  -74.33  < 2e-16 ***
## factor(dept)87    -5.90e+03   2.36e+02  -24.97  < 2e-16 ***
## factor(dept)90     2.62e+04   2.36e+02  111.08  < 2e-16 ***
## factor(dept)91     1.46e+04   2.36e+02   61.86  < 2e-16 ***
## factor(dept)92     5.64e+04   2.36e+02  239.17  < 2e-16 ***
## factor(dept)93     7.13e+03   2.41e+02   29.58  < 2e-16 ***
## factor(dept)94     1.38e+04   2.43e+02   56.72  < 2e-16 ***
## factor(dept)95     5.10e+04   2.36e+02  216.29  < 2e-16 ***
## factor(dept)96    -3.80e+03   2.54e+02  -14.93  < 2e-16 ***
## factor(dept)97    -5.17e+03   2.37e+02  -21.82  < 2e-16 ***
## factor(dept)98    -1.31e+04   2.42e+02  -54.02  < 2e-16 ***
## factor(dept)99    -2.51e+04   4.86e+02  -51.76  < 2e-16 ***
## factor(store)2     5.19e+03   1.87e+02   27.76  < 2e-16 ***
## factor(store)3    -1.67e+04   1.99e+02  -83.89  < 2e-16 ***
## factor(store)4     7.62e+03   1.10e+03    6.90  5.2e-12 ***
## factor(store)5    -1.84e+04   2.03e+02  -90.83  < 2e-16 ***
## factor(store)6    -2.55e+02   1.92e+02   -1.33  0.18437    
## factor(store)7    -1.35e+04   3.34e+02  -40.31  < 2e-16 ***
## factor(store)8    -9.65e+03   2.02e+02  -47.83  < 2e-16 ***
## factor(store)9    -1.48e+04   2.08e+02  -71.32  < 2e-16 ***
## factor(store)10    6.04e+03   1.09e+03    5.54  3.0e-08 ***
## factor(store)11   -3.01e+03   1.92e+02  -15.69  < 2e-16 ***
## factor(store)12   -4.56e+03   1.06e+03   -4.30  1.7e-05 ***
## factor(store)13    6.60e+03   1.09e+03    6.03  1.7e-09 ***
## factor(store)14    7.70e+03   4.12e+02   18.69  < 2e-16 ***
## factor(store)15   -1.22e+04   1.02e+03  -12.02  < 2e-16 ***
## factor(store)16   -1.49e+04   3.53e+02  -42.24  < 2e-16 ***
## factor(store)17   -8.63e+03   1.10e+03   -7.86  3.7e-15 ***
## factor(store)18   -5.13e+03   1.00e+03   -5.12  3.0e-07 ***
## factor(store)19   -5.06e+02   1.02e+03   -0.50  0.61954    
## factor(store)20    8.13e+03   2.16e+02   37.64  < 2e-16 ***
## factor(store)21   -1.12e+04   1.90e+02  -58.94  < 2e-16 ***
## factor(store)22   -6.26e+03   9.64e+02   -6.50  8.3e-11 ***
## factor(store)23   -2.31e+03   1.06e+03   -2.19  0.02889 *  
## factor(store)24   -1.64e+03   1.01e+03   -1.62  0.10529    
## factor(store)25   -1.18e+04   2.18e+02  -53.90  < 2e-16 ***
## factor(store)26   -6.96e+03   1.01e+03   -6.87  6.5e-12 ***
## factor(store)27    4.03e+03   9.73e+02    4.14  3.4e-05 ***
## factor(store)28   -4.34e+02   1.06e+03   -0.41  0.68290    
## factor(store)29   -1.29e+04   9.91e+02  -13.04  < 2e-16 ***
## factor(store)30   -1.79e+04   2.07e+02  -86.60  < 2e-16 ***
## factor(store)31   -2.31e+03   1.88e+02  -12.33  < 2e-16 ***
## factor(store)32   -4.90e+03   3.27e+02  -14.98  < 2e-16 ***
## factor(store)33   -2.06e+04   1.09e+03  -18.98  < 2e-16 ***
## factor(store)34   -7.41e+03   1.05e+03   -7.03  2.0e-12 ***
## factor(store)35   -7.58e+03   9.55e+02   -7.94  2.1e-15 ***
## factor(store)36   -1.94e+04   2.16e+02  -89.69  < 2e-16 ***
## factor(store)37   -1.63e+04   2.07e+02  -78.64  < 2e-16 ***
## factor(store)38   -1.61e+04   1.06e+03  -15.22  < 2e-16 ***
## factor(store)39   -1.50e+03   1.93e+02   -7.77  8.1e-15 ***
## factor(store)40   -8.57e+03   1.06e+03   -8.10  5.3e-16 ***
## factor(store)41   -4.01e+03   3.44e+02  -11.67  < 2e-16 ***
## factor(store)42   -1.39e+04   1.09e+03  -12.78  < 2e-16 ***
## factor(store)43   -1.31e+04   2.41e+02  -54.21  < 2e-16 ***
## factor(store)44   -2.03e+04   1.09e+03  -18.59  < 2e-16 ***
## factor(store)45   -1.01e+04   4.10e+02  -24.69  < 2e-16 ***
## temperature        4.36e+00   2.88e+00    1.52  0.12954    
## cpi                7.97e+00   1.22e+01    0.65  0.51267    
## unemployment      -3.71e+02   4.56e+01   -8.15  3.8e-16 ***
## season_nameSpring -1.25e+03   8.40e+01  -14.84  < 2e-16 ***
## season_nameSummer -1.03e+03   1.28e+02   -8.06  7.9e-16 ***
## season_nameAutumn -1.81e+03   9.56e+01  -18.91  < 2e-16 ***
## fuel_price        -4.34e+02   8.09e+01   -5.36  8.4e-08 ***
## superbowlTRUE     -3.96e+02   1.51e+02   -2.63  0.00864 ** 
## christmasTRUE     -1.71e+03   2.03e+02   -8.43  < 2e-16 ***
## laborTRUE          6.74e+02   1.53e+02    4.40  1.1e-05 ***
## thanksgivingTRUE   6.07e+03   2.29e+02   26.46  < 2e-16 ***
## mark_down1         5.34e-03   7.22e-03    0.74  0.45925    
## mark_down2        -2.86e-02   4.83e-03   -5.92  3.3e-09 ***
## mark_down3         4.28e-02   4.76e-03    9.01  < 2e-16 ***
## mark_down4        -3.76e-02   1.01e-02   -3.72  0.00020 ***
## mark_down5         3.36e-02   5.99e-03    5.60  2.1e-08 ***
## 
## Residual standard error: 13400 on 421429 degrees of freedom
## Multiple R-squared:  0.659,  Adjusted R-squared:  0.658 
## F-statistic: 5.81e+03 on 140 and 421429 DF,  p-value: <2e-16

# vif(model3) problem of collinearity arise

There is problem of collinearity between variables in the model. Hence we remove store as a variable. By doing this,although we arrive at a model with less model explainability, the problem of collinearity is resolved.

Running final model

model_final <- lm(weekly_sales ~ factor(dept)  + temperature + cpi + unemployment + type + size  + season_name + fuel_price + superbowl + christmas + labor + thanksgiving + mark_down1  + mark_down2  + mark_down3  + mark_down4  + mark_down5, data = sales_reg)

get_regression_table(model_final)

term	estimate	std_error	statistic	p_value	lower_ci	upper_ci
intercept	1e+04	328	30.5	0	9.37e+03	1.07e+04
factor(dept): 2	2.46e+04	246	99.7	0	2.41e+04	2.5e+04
factor(dept): 3	-7.46e+03	246	-30.3	0	-7.95e+03	-6.98e+03
factor(dept): 4	6.81e+03	246	27.6	0	6.33e+03	7.29e+03
factor(dept): 5	2e+03	247	8.09	0	1.52e+03	2.49e+03
factor(dept): 6	-1.54e+04	251	-61.2	0	-1.59e+04	-1.49e+04
factor(dept): 7	4.97e+03	246	20.2	0	4.48e+03	5.45e+03
factor(dept): 8	1.1e+04	246	44.8	0	1.06e+04	1.15e+04
factor(dept): 9	841	247	3.4	0.001	356	1.33e+03
factor(dept): 10	-902	246	-3.66	0	-1.38e+03	-419
factor(dept): 11	-4.75e+03	246	-19.3	0	-5.23e+03	-4.26e+03
factor(dept): 12	-1.52e+04	247	-61.6	0	-1.57e+04	-1.47e+04
factor(dept): 13	1.15e+04	246	46.8	0	1.1e+04	1.2e+04
factor(dept): 14	-4.37e+03	246	-17.7	0	-4.85e+03	-3.89e+03
factor(dept): 16	-5e+03	246	-20.3	0	-5.49e+03	-4.52e+03
factor(dept): 17	-9.13e+03	247	-37	0	-9.61e+03	-8.64e+03
factor(dept): 18	-1.26e+04	263	-47.9	0	-1.31e+04	-1.21e+04
factor(dept): 19	-2.02e+04	279	-72.4	0	-2.08e+04	-1.97e+04
factor(dept): 20	-1.44e+04	250	-57.6	0	-1.49e+04	-1.39e+04
factor(dept): 21	-1.43e+04	246	-58.2	0	-1.48e+04	-1.38e+04
factor(dept): 22	-1.01e+04	256	-39.6	0	-1.07e+04	-9.65e+03
factor(dept): 23	3.54e+03	253	14	0	3.04e+03	4.04e+03
factor(dept): 24	-1.49e+04	258	-57.8	0	-1.54e+04	-1.44e+04
factor(dept): 25	-1.04e+04	247	-42.2	0	-1.09e+04	-9.96e+03
factor(dept): 26	-1.28e+04	254	-50.5	0	-1.33e+04	-1.23e+04
factor(dept): 27	-1.93e+04	255	-75.6	0	-1.98e+04	-1.88e+04
factor(dept): 28	-1.93e+04	250	-77.5	0	-1.98e+04	-1.88e+04
factor(dept): 29	-1.58e+04	259	-61	0	-1.63e+04	-1.53e+04
factor(dept): 30	-1.74e+04	260	-67.1	0	-1.79e+04	-1.69e+04
factor(dept): 31	-1.77e+04	250	-70.6	0	-1.81e+04	-1.72e+04
factor(dept): 32	-1.34e+04	251	-53.2	0	-1.39e+04	-1.29e+04
factor(dept): 33	-1.48e+04	258	-57.4	0	-1.53e+04	-1.43e+04
factor(dept): 34	-5.75e+03	259	-22.2	0	-6.26e+03	-5.24e+03
factor(dept): 35	-1.86e+04	259	-71.7	0	-1.91e+04	-1.81e+04
factor(dept): 36	-1.95e+04	260	-75.2	0	-2e+04	-1.9e+04
factor(dept): 37	-2.23e+04	326	-68.4	0	-2.3e+04	-2.17e+04
factor(dept): 38	4.22e+04	246	171	0	4.17e+04	4.27e+04
factor(dept): 39	-2.66e+04	3.5e+03	-7.62	0	-3.35e+04	-1.98e+04
factor(dept): 40	2.59e+04	246	105	0	2.54e+04	2.64e+04
factor(dept): 41	-1.93e+04	258	-74.8	0	-1.98e+04	-1.88e+04
factor(dept): 42	-1.42e+04	247	-57.5	0	-1.47e+04	-1.37e+04
factor(dept): 43	-2.07e+04	4.04e+03	-5.14	0	-2.87e+04	-1.28e+04
factor(dept): 44	-1.65e+04	257	-64	0	-1.7e+04	-1.6e+04
factor(dept): 45	-2.16e+04	362	-59.7	0	-2.24e+04	-2.09e+04
factor(dept): 46	743	246	3.02	0.003	260	1.23e+03
factor(dept): 47	-2.2e+04	577	-38.2	0	-2.32e+04	-2.09e+04
factor(dept): 48	-2.18e+04	378	-57.8	0	-2.26e+04	-2.11e+04
factor(dept): 49	-1.43e+04	272	-52.5	0	-1.48e+04	-1.38e+04
factor(dept): 50	-2.15e+04	395	-54.5	0	-2.23e+04	-2.07e+04
factor(dept): 51	-2.12e+04	413	-51.2	0	-2.2e+04	-2.04e+04
factor(dept): 52	-1.77e+04	248	-71.5	0	-1.82e+04	-1.73e+04
factor(dept): 54	-2.18e+04	267	-81.5	0	-2.23e+04	-2.13e+04
factor(dept): 55	-1e+04	256	-39.2	0	-1.05e+04	-9.52e+03
factor(dept): 56	-1.65e+04	252	-65.4	0	-1.7e+04	-1.6e+04
factor(dept): 58	-1.89e+04	274	-69	0	-1.94e+04	-1.84e+04
factor(dept): 59	-1.92e+04	250	-76.8	0	-1.97e+04	-1.87e+04
factor(dept): 60	-1.87e+04	253	-73.9	0	-1.92e+04	-1.82e+04
factor(dept): 65	2.4e+04	1.18e+03	20.3	0	2.17e+04	2.63e+04
factor(dept): 67	-1.19e+04	246	-48.1	0	-1.23e+04	-1.14e+04
factor(dept): 71	-1.58e+04	259	-60.8	0	-1.63e+04	-1.53e+04
factor(dept): 72	3.09e+04	250	123	0	3.04e+04	3.14e+04
factor(dept): 74	-5.45e+03	246	-22.1	0	-5.93e+03	-4.96e+03
factor(dept): 77	-2.48e+04	1.16e+03	-21.5	0	-2.71e+04	-2.25e+04
factor(dept): 78	-2.31e+04	928	-24.9	0	-2.49e+04	-2.13e+04
factor(dept): 79	2.78e+03	246	11.3	0	2.29e+03	3.26e+03
factor(dept): 80	-7.57e+03	252	-30	0	-8.06e+03	-7.07e+03
factor(dept): 81	-3.77e+03	246	-15.3	0	-4.25e+03	-3.29e+03
factor(dept): 82	-3.77e+03	246	-15.3	0	-4.26e+03	-3.29e+03
factor(dept): 83	-1.66e+04	252	-65.8	0	-1.71e+04	-1.61e+04
factor(dept): 85	-1.78e+04	250	-71.1	0	-1.83e+04	-1.73e+04
factor(dept): 87	-5.91e+03	247	-24	0	-6.4e+03	-5.43e+03
factor(dept): 90	2.62e+04	246	106	0	2.57e+04	2.67e+04
factor(dept): 91	1.46e+04	246	59.2	0	1.41e+04	1.51e+04
factor(dept): 92	5.64e+04	246	229	0	5.59e+04	5.68e+04
factor(dept): 93	7.22e+03	252	28.7	0	6.73e+03	7.71e+03
factor(dept): 94	1.38e+04	254	54.2	0	1.33e+04	1.43e+04
factor(dept): 95	5.1e+04	246	207	0	5.05e+04	5.15e+04
factor(dept): 96	-3.9e+03	266	-14.7	0	-4.42e+03	-3.38e+03
factor(dept): 97	-5.02e+03	248	-20.2	0	-5.5e+03	-4.53e+03
factor(dept): 98	-1.3e+04	253	-51.4	0	-1.35e+04	-1.25e+04
factor(dept): 99	-2.52e+04	508	-49.6	0	-2.62e+04	-2.42e+04
temperature	72.9	2.01	36.2	0	69	76.9
cpi	-25.8	0.634	-40.6	0	-27	-24.5
unemployment	-505	13	-38.9	0	-530	-479
type: B	2.36e+03	68.9	34.2	0	2.22e+03	2.49e+03
type: C	3.04e+03	116	26.2	0	2.81e+03	3.27e+03
size	0.126	0.001	202	0	0.125	0.128
season_name: Spring	-2.25e+03	77.9	-28.9	0	-2.4e+03	-2.1e+03
season_name: Summer	-3.5e+03	103	-34	0	-3.7e+03	-3.29e+03
season_name: Autumn	-3.19e+03	85.9	-37.2	0	-3.36e+03	-3.03e+03
fuel_price	-665	54	-12.3	0	-771	-560
superbowlTRUE	-118	158	-0.752	0.452	-427	190
christmasTRUE	-2.18e+03	212	-10.3	0	-2.6e+03	-1.77e+03
laborTRUE	-138	158	-0.875	0.382	-448	171
thanksgivingTRUE	6.36e+03	238	26.7	0	5.89e+03	6.82e+03
mark_down1	0.024	0.007	3.29	0.001	0.01	0.038
mark_down2	0.009	0.005	1.83	0.068	-0.001	0.019
mark_down3	0.067	0.005	13.4	0	0.057	0.076
mark_down4	-0.017	0.01	-1.58	0.114	-0.037	0.004
mark_down5	0.049	0.006	8.48	0	0.038	0.061

mosaic::msummary(model_final)

##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)        1.00e+04   3.29e+02   30.47  < 2e-16 ***
## factor(dept)2      2.46e+04   2.46e+02   99.65  < 2e-16 ***
## factor(dept)3     -7.46e+03   2.46e+02  -30.30  < 2e-16 ***
## factor(dept)4      6.81e+03   2.46e+02   27.63  < 2e-16 ***
## factor(dept)5      2.00e+03   2.47e+02    8.09  5.8e-16 ***
## factor(dept)6     -1.54e+04   2.51e+02  -61.20  < 2e-16 ***
## factor(dept)7      4.97e+03   2.46e+02   20.16  < 2e-16 ***
## factor(dept)8      1.10e+04   2.46e+02   44.85  < 2e-16 ***
## factor(dept)9      8.41e+02   2.47e+02    3.40  0.00067 ***
## factor(dept)10    -9.02e+02   2.46e+02   -3.66  0.00025 ***
## factor(dept)11    -4.75e+03   2.46e+02  -19.27  < 2e-16 ***
## factor(dept)12    -1.52e+04   2.47e+02  -61.61  < 2e-16 ***
## factor(dept)13     1.15e+04   2.46e+02   46.79  < 2e-16 ***
## factor(dept)14    -4.37e+03   2.46e+02  -17.74  < 2e-16 ***
## factor(dept)16    -5.00e+03   2.46e+02  -20.31  < 2e-16 ***
## factor(dept)17    -9.13e+03   2.47e+02  -37.02  < 2e-16 ***
## factor(dept)18    -1.26e+04   2.63e+02  -47.86  < 2e-16 ***
## factor(dept)19    -2.02e+04   2.79e+02  -72.39  < 2e-16 ***
## factor(dept)20    -1.44e+04   2.50e+02  -57.57  < 2e-16 ***
## factor(dept)21    -1.43e+04   2.46e+02  -58.17  < 2e-16 ***
## factor(dept)22    -1.01e+04   2.56e+02  -39.61  < 2e-16 ***
## factor(dept)23     3.54e+03   2.53e+02   13.97  < 2e-16 ***
## factor(dept)24    -1.49e+04   2.58e+02  -57.77  < 2e-16 ***
## factor(dept)25    -1.04e+04   2.47e+02  -42.25  < 2e-16 ***
## factor(dept)26    -1.28e+04   2.54e+02  -50.49  < 2e-16 ***
## factor(dept)27    -1.93e+04   2.55e+02  -75.58  < 2e-16 ***
## factor(dept)28    -1.93e+04   2.50e+02  -77.48  < 2e-16 ***
## factor(dept)29    -1.58e+04   2.59e+02  -61.04  < 2e-16 ***
## factor(dept)30    -1.74e+04   2.60e+02  -67.10  < 2e-16 ***
## factor(dept)31    -1.77e+04   2.50e+02  -70.60  < 2e-16 ***
## factor(dept)32    -1.34e+04   2.51e+02  -53.21  < 2e-16 ***
## factor(dept)33    -1.48e+04   2.58e+02  -57.40  < 2e-16 ***
## factor(dept)34    -5.75e+03   2.59e+02  -22.19  < 2e-16 ***
## factor(dept)35    -1.86e+04   2.59e+02  -71.71  < 2e-16 ***
## factor(dept)36    -1.95e+04   2.60e+02  -75.21  < 2e-16 ***
## factor(dept)37    -2.23e+04   3.26e+02  -68.44  < 2e-16 ***
## factor(dept)38     4.22e+04   2.46e+02  171.20  < 2e-16 ***
## factor(dept)39    -2.66e+04   3.50e+03   -7.62  2.6e-14 ***
## factor(dept)40     2.59e+04   2.46e+02  105.07  < 2e-16 ***
## factor(dept)41    -1.93e+04   2.58e+02  -74.82  < 2e-16 ***
## factor(dept)42    -1.42e+04   2.47e+02  -57.49  < 2e-16 ***
## factor(dept)43    -2.07e+04   4.04e+03   -5.14  2.8e-07 ***
## factor(dept)44    -1.65e+04   2.57e+02  -64.05  < 2e-16 ***
## factor(dept)45    -2.16e+04   3.62e+02  -59.71  < 2e-16 ***
## factor(dept)46     7.43e+02   2.46e+02    3.02  0.00256 ** 
## factor(dept)47    -2.20e+04   5.77e+02  -38.18  < 2e-16 ***
## factor(dept)48    -2.18e+04   3.78e+02  -57.79  < 2e-16 ***
## factor(dept)49    -1.43e+04   2.72e+02  -52.50  < 2e-16 ***
## factor(dept)50    -2.15e+04   3.95e+02  -54.46  < 2e-16 ***
## factor(dept)51    -2.12e+04   4.13e+02  -51.23  < 2e-16 ***
## factor(dept)52    -1.77e+04   2.48e+02  -71.51  < 2e-16 ***
## factor(dept)54    -2.18e+04   2.67e+02  -81.52  < 2e-16 ***
## factor(dept)55    -1.00e+04   2.56e+02  -39.19  < 2e-16 ***
## factor(dept)56    -1.65e+04   2.52e+02  -65.40  < 2e-16 ***
## factor(dept)58    -1.89e+04   2.74e+02  -69.05  < 2e-16 ***
## factor(dept)59    -1.92e+04   2.50e+02  -76.81  < 2e-16 ***
## factor(dept)60    -1.87e+04   2.53e+02  -73.95  < 2e-16 ***
## factor(dept)65     2.40e+04   1.18e+03   20.29  < 2e-16 ***
## factor(dept)67    -1.19e+04   2.46e+02  -48.11  < 2e-16 ***
## factor(dept)71    -1.58e+04   2.59e+02  -60.77  < 2e-16 ***
## factor(dept)72     3.09e+04   2.50e+02  123.32  < 2e-16 ***
## factor(dept)74    -5.45e+03   2.46e+02  -22.11  < 2e-16 ***
## factor(dept)77    -2.48e+04   1.16e+03  -21.45  < 2e-16 ***
## factor(dept)78    -2.31e+04   9.28e+02  -24.86  < 2e-16 ***
## factor(dept)79     2.78e+03   2.46e+02   11.27  < 2e-16 ***
## factor(dept)80    -7.57e+03   2.52e+02  -30.03  < 2e-16 ***
## factor(dept)81    -3.77e+03   2.46e+02  -15.30  < 2e-16 ***
## factor(dept)82    -3.77e+03   2.46e+02  -15.32  < 2e-16 ***
## factor(dept)83    -1.66e+04   2.52e+02  -65.82  < 2e-16 ***
## factor(dept)85    -1.78e+04   2.50e+02  -71.14  < 2e-16 ***
## factor(dept)87    -5.91e+03   2.47e+02  -23.95  < 2e-16 ***
## factor(dept)90     2.62e+04   2.46e+02  106.26  < 2e-16 ***
## factor(dept)91     1.46e+04   2.46e+02   59.17  < 2e-16 ***
## factor(dept)92     5.64e+04   2.46e+02  228.78  < 2e-16 ***
## factor(dept)93     7.22e+03   2.52e+02   28.68  < 2e-16 ***
## factor(dept)94     1.38e+04   2.54e+02   54.24  < 2e-16 ***
## factor(dept)95     5.10e+04   2.46e+02  206.90  < 2e-16 ***
## factor(dept)96    -3.90e+03   2.66e+02  -14.68  < 2e-16 ***
## factor(dept)97    -5.02e+03   2.48e+02  -20.24  < 2e-16 ***
## factor(dept)98    -1.30e+04   2.53e+02  -51.42  < 2e-16 ***
## factor(dept)99    -2.52e+04   5.08e+02  -49.59  < 2e-16 ***
## temperature        7.29e+01   2.01e+00   36.20  < 2e-16 ***
## cpi               -2.58e+01   6.34e-01  -40.60  < 2e-16 ***
## unemployment      -5.05e+02   1.30e+01  -38.88  < 2e-16 ***
## typeB              2.36e+03   6.89e+01   34.25  < 2e-16 ***
## typeC              3.04e+03   1.16e+02   26.17  < 2e-16 ***
## size               1.26e-01   6.25e-04  201.95  < 2e-16 ***
## season_nameSpring -2.25e+03   7.79e+01  -28.86  < 2e-16 ***
## season_nameSummer -3.50e+03   1.03e+02  -34.02  < 2e-16 ***
## season_nameAutumn -3.19e+03   8.59e+01  -37.21  < 2e-16 ***
## fuel_price        -6.65e+02   5.40e+01  -12.32  < 2e-16 ***
## superbowlTRUE     -1.18e+02   1.58e+02   -0.75  0.45224    
## christmasTRUE     -2.18e+03   2.12e+02  -10.30  < 2e-16 ***
## laborTRUE         -1.38e+02   1.58e+02   -0.88  0.38155    
## thanksgivingTRUE   6.36e+03   2.38e+02   26.74  < 2e-16 ***
## mark_down1         2.39e-02   7.26e-03    3.29  0.00101 ** 
## mark_down2         9.18e-03   5.02e-03    1.83  0.06761 .  
## mark_down3         6.67e-02   4.96e-03   13.44  < 2e-16 ***
## mark_down4        -1.65e-02   1.05e-02   -1.58  0.11383    
## mark_down5         4.95e-02   5.83e-03    8.48  < 2e-16 ***
## 
## Residual standard error: 14000 on 421470 degrees of freedom
## Multiple R-squared:  0.627,  Adjusted R-squared:  0.627 
## F-statistic: 7.15e+03 on 99 and 421470 DF,  p-value: <2e-16

vif(model_final)

##              GVIF Df GVIF^(1/(2*Df))
## factor(dept) 1.07 80            1.00
## temperature  2.98  1            1.73
## cpi          1.33  1            1.15
## unemployment 1.26  1            1.12
## type         3.38  2            1.36
## size         3.14  1            1.77
## season_name  3.60  3            1.24
## fuel_price   1.32  1            1.15
## superbowl    1.11  1            1.05
## christmas    1.34  1            1.16
## labor        1.11  1            1.05
## thanksgiving 1.70  1            1.30
## mark_down1   4.16  1            2.04
## mark_down2   1.41  1            1.19
## mark_down3   1.63  1            1.28
## mark_down4   3.58  1            1.89
## mark_down5   1.30  1            1.14

We arrive at our final model with an adjusted R square of 62.7%, i.e around 63% of the variability in weekly sales is explained by the explanatory variables incorporated in the final model. Moreover, the colinearity problem has been resolved as VIF coefficient for all variables is less than 5.

Checking for assumption of Linear Regression

library(ggfortify)
autoplot(model_final) +
theme_bw()

Residuals vs. Fitted: Residuals seem no to follow any patterns

Normal Q-Q: Apart from the two ends of the line residuals seem no to deviate from straight line

Scale-Location: The clear trend is not recognizable.

Residuals vs. Leverage: There are some outliers that could lead to biased estimated of the model.

In conclusion, given more time, more analytics should be done in order to assess whether the model meets the assumptions of the linear regression.

Comparing all models

huxreg(model1, model2, 
       model3, model_final,
       statistics = c('#observations' = 'nobs', 
                      'R squared' = 'r.squared', 
                      'Adj. R Squared' = 'adj.r.squared', 
                      'Residual SE' = 'sigma'), 
       bold_signif = 0.05, 
       stars = NULL
) %>% 
  set_caption('Comparison of models')

Comparison of models
	(1)	(2)	(3)	(4)
(Intercept)	26402.925	261.270	30095.562	10009.413
	(3279.520)	(595.617)	(2608.255)	(328.500)
store	-142.187	-137.237
	(3.103)	(3.145)
dept	111.041	111.046
	(1.103)	(1.102)
date	-1.376
	(0.237)
is_holidayTRUE	651.533	228.658
	(141.668)	(145.850)
temperature	15.872	44.780	4.364	72.914
	(2.012)	(3.174)	(2.879)	(2.014)
fuel_price	50.519	2550.268	-433.504	-665.377
	(130.229)	(181.123)	(80.912)	(54.001)
mark_down1	0.028	0.071	0.005	0.024
	(0.012)	(0.012)	(0.007)	(0.007)
mark_down2	-0.000	-0.012	-0.029	0.009
	(0.007)	(0.007)	(0.005)	(0.005)
mark_down3	0.117	0.134	0.043	0.067
	(0.006)	(0.006)	(0.005)	(0.005)
mark_down4	-0.002	-0.037	-0.038	-0.017
	(0.016)	(0.016)	(0.010)	(0.010)
mark_down5	0.106	0.104	0.034	0.049
	(0.009)	(0.009)	(0.006)	(0.006)
cpi	-25.887	-22.842	7.969	-25.752
	(0.991)	(1.070)	(12.172)	(0.634)
unemployment	-262.948	-410.937	-371.165	-504.709
	(20.625)	(21.125)	(45.561)	(12.981)
typeB	-347.400	-313.618		2359.473
	(108.415)	(109.668)		(68.899)
typeC	5812.229	5712.684		3039.403
	(185.008)	(185.120)		(116.126)
size	0.098	0.097		0.126
	(0.001)	(0.001)		(0.001)
year2011		-2664.309
		(163.037)
year2012		-4095.732
		(200.194)
season_nameSpring		-2467.574	-1247.136	-2249.424
		(128.969)	(84.012)	(77.933)
season_nameSummer		-2693.031	-1028.243	-3495.199
		(161.091)	(127.646)	(102.752)
season_nameAutumn		-2762.360	-1806.772	-3194.682
		(133.147)	(95.553)	(85.862)
factor(dept)2			24550.460	24550.460
			(235.662)	(246.364)
factor(dept)3			-7464.951	-7464.951
			(235.662)	(246.364)
factor(dept)4			6807.887	6807.887
			(235.662)	(246.364)
factor(dept)5			2044.060	2000.986
			(236.483)	(247.218)
factor(dept)6			-15369.094	-15360.873
			(240.112)	(250.977)
factor(dept)7			4966.376	4966.376
			(235.662)	(246.364)
factor(dept)8			11048.673	11048.673
			(235.662)	(246.364)
factor(dept)9			836.523	840.894
			(236.417)	(247.151)
factor(dept)10			-901.882	-901.882
			(235.662)	(246.364)
factor(dept)11			-4746.484	-4746.689
			(235.671)	(246.374)
factor(dept)12			-15198.006	-15195.109
			(235.901)	(246.614)
factor(dept)13			11528.060	11528.060
			(235.662)	(246.364)
factor(dept)14			-4369.432	-4369.432
			(235.662)	(246.364)
factor(dept)16			-5003.584	-5003.584
			(235.662)	(246.364)
factor(dept)17			-9129.862	-9127.402
			(235.874)	(246.585)
factor(dept)18			-12651.841	-12594.189
			(251.705)	(263.127)
factor(dept)19			-20556.063	-20204.112
			(267.134)	(279.083)
factor(dept)20			-14423.773	-14419.751
			(239.601)	(250.481)
factor(dept)21			-14330.502	-14330.502
			(235.662)	(246.364)
factor(dept)22			-10176.644	-10148.775
			(245.105)	(256.215)
factor(dept)23			3556.142	3540.483
			(242.405)	(253.380)
factor(dept)24			-14917.200	-14904.947
			(246.817)	(257.996)
factor(dept)25			-10459.859	-10441.416
			(236.416)	(247.151)
factor(dept)26			-12783.636	-12815.385
			(242.814)	(253.838)
factor(dept)27			-19310.808	-19292.940
			(244.203)	(255.251)
factor(dept)28			-19363.452	-19332.807
			(238.697)	(249.508)
factor(dept)29			-15874.748	-15830.505
			(248.095)	(259.327)
factor(dept)30			-17464.132	-17417.897
			(248.321)	(259.564)
factor(dept)31			-17716.658	-17657.853
			(239.249)	(250.095)
factor(dept)32			-13329.371	-13371.186
			(240.422)	(251.304)
factor(dept)33			-14840.893	-14821.944
			(247.023)	(258.209)
factor(dept)34			-5788.604	-5748.264
			(247.856)	(259.080)
factor(dept)35			-18651.178	-18607.912
			(248.241)	(259.481)
factor(dept)36			-19562.499	-19516.895
			(248.267)	(259.508)
factor(dept)37			-22578.155	-22339.107
			(312.644)	(326.403)
factor(dept)38			42176.789	42176.789
			(235.662)	(246.364)
factor(dept)39			-27324.214	-26638.886
			(3347.119)	(3498.144)
factor(dept)40			25886.272	25886.272
			(235.662)	(246.364)
factor(dept)41			-19319.282	-19316.990
			(246.980)	(258.172)
factor(dept)42			-14191.136	-14181.353
			(235.975)	(246.691)
factor(dept)43			-18503.328	-20749.800
			(3863.258)	(4038.031)
factor(dept)44			-16510.076	-16469.636
			(245.993)	(257.136)
factor(dept)45			-22393.035	-21643.719
			(346.975)	(362.485)
factor(dept)46			743.113	743.113
			(235.662)	(246.364)
factor(dept)47			-22697.506	-22028.384
			(551.932)	(576.924)
factor(dept)48			-23895.165	-21828.941
			(362.239)	(377.759)
factor(dept)49			-14429.437	-14285.038
			(260.346)	(272.100)
factor(dept)50			-23445.327	-21499.487
			(378.698)	(394.774)
factor(dept)51			-21474.110	-21175.914
			(395.681)	(413.342)
factor(dept)52			-17744.784	-17736.132
			(237.248)	(248.011)
factor(dept)54			-22002.839	-21788.399
			(255.701)	(267.280)
factor(dept)55			-10005.113	-10016.155
			(244.486)	(255.588)
factor(dept)56			-16538.714	-16497.927
			(241.312)	(252.246)
factor(dept)58			-19339.767	-18907.165
			(262.032)	(273.836)
factor(dept)59			-19186.577	-19176.543
			(238.834)	(249.673)
factor(dept)60			-18873.231	-18734.786
			(242.374)	(253.360)
factor(dept)65			27676.312	23993.362
			(1137.862)	(1182.307)
factor(dept)67			-11853.442	-11853.442
			(235.662)	(246.364)
factor(dept)71			-15805.499	-15758.581
			(248.081)	(259.314)
factor(dept)72			30840.713	30872.114
			(239.494)	(250.332)
factor(dept)74			-5447.499	-5447.707
			(235.708)	(246.412)
factor(dept)77			-24641.477	-24808.642
			(1106.216)	(1156.378)
factor(dept)78			-23238.203	-23081.829
			(888.087)	(928.339)
factor(dept)79			2775.514	2775.514
			(235.662)	(246.364)
factor(dept)80			-7734.455	-7568.909
			(241.100)	(252.014)
factor(dept)81			-3769.705	-3769.705
			(235.662)	(246.364)
factor(dept)82			-3774.982	-3774.982
			(235.662)	(246.364)
factor(dept)83			-16672.741	-16576.438
			(240.934)	(251.828)
factor(dept)85			-17793.930	-17801.316
			(239.400)	(250.236)
factor(dept)87			-5895.587	-5911.375
			(236.068)	(246.788)
factor(dept)90			26178.239	26178.239
			(235.662)	(246.364)
factor(dept)91			14577.031	14577.031
			(235.662)	(246.364)
factor(dept)92			56363.489	56363.489
			(235.662)	(246.364)
factor(dept)93			7125.448	7220.329
			(240.880)	(251.772)
factor(dept)94			13801.812	13798.958
			(243.347)	(254.388)
factor(dept)95			50972.276	50972.276
			(235.662)	(246.364)
factor(dept)96			-3796.627	-3900.554
			(254.366)	(265.751)
factor(dept)97			-5173.814	-5017.316
			(237.150)	(247.902)
factor(dept)98			-13055.080	-12989.591
			(241.687)	(252.634)
factor(dept)99			-25141.474	-25179.899
			(485.755)	(507.748)
factor(store)2			5190.972
			(186.999)
factor(store)3			-16678.397
			(198.822)
factor(store)4			7615.901
			(1103.753)
factor(store)5			-18403.192
			(202.609)
factor(store)6			-254.896
			(192.025)
factor(store)7			-13472.387
			(334.200)
factor(store)8			-9646.926
			(201.684)
factor(store)9			-14803.724
			(207.568)
factor(store)10			6038.412
			(1089.953)
factor(store)11			-3014.971
			(192.191)
factor(store)12			-4562.588
			(1062.030)
factor(store)13			6596.793
			(1094.199)
factor(store)14			7697.932
			(411.974)
factor(store)15			-12214.417
			(1015.861)
factor(store)16			-14900.642
			(352.787)
factor(store)17			-8631.184
			(1097.539)
factor(store)18			-5127.144
			(1001.247)
factor(store)19			-505.983
			(1019.108)
factor(store)20			8131.028
			(216.037)
factor(store)21			-11205.881
			(190.139)
factor(store)22			-6264.581
			(964.415)
factor(store)23			-2309.614
			(1057.018)
factor(store)24			-1642.241
			(1013.883)
factor(store)25			-11771.681
			(218.384)
factor(store)26			-6955.942
			(1012.793)
factor(store)27			4028.338
			(972.613)
factor(store)28			-433.747
			(1061.787)
factor(store)29			-12916.640
			(990.678)
factor(store)30			-17902.910
			(206.739)
factor(store)31			-2312.131
			(187.546)
factor(store)32			-4900.433
			(327.155)
factor(store)33			-20634.136
			(1087.104)
factor(store)34			-7410.359
			(1053.410)
factor(store)35			-7582.403
			(955.137)
factor(store)36			-19384.388
			(216.124)
factor(store)37			-16254.347
			(206.692)
factor(store)38			-16088.749
			(1057.228)
factor(store)39			-1495.484
			(192.578)
factor(store)40			-8567.425
			(1057.185)
factor(store)41			-4014.737
			(343.959)
factor(store)42			-13896.678
			(1087.644)
factor(store)43			-13058.958
			(240.883)
factor(store)44			-20335.066
			(1093.721)
factor(store)45			-10128.505
			(410.300)
superbowlTRUE			-396.348	-118.404
			(150.922)	(157.516)
christmasTRUE			-1707.703	-2180.540
			(202.575)	(211.608)
laborTRUE			674.462	-138.230
			(153.240)	(157.968)
thanksgivingTRUE			6071.727	6356.345
			(229.451)	(237.744)
#observations	421570	421570	421570	421570
R squared	0.090	0.091	0.659	0.627
Adj. R Squared	0.090	0.091	0.658	0.627
Residual SE	21821.319	21803.689	13367.442	13974.515

Question 1

On average, change in one unit of temperature is associated with an increase of weekly sales by $72.9. Whereas, the change in fuel price by $1 is associated with decrease in weekly sales of $665.

Question 2

Based on estimated statistics, the impact of both Labor Day and Super Bowl weeks is not different from zero. Therefore, there is no significant difference in weekly sales during those weeks and non-holiday weeks. Probably, our retailer is not selling product widely purchased during Super Bowl and Labor Day.

store	dept_count
13	79
15	79
19	79
2	78
4	78
11	78
18	78
20	78
27	78
34	78
1	77
6	77
10	77
14	77
21	77
23	77
24	77
25	77
28	77
29	77
32	77
40	77
41	77
7	76
8	76
16	76
17	76
22	76
26	76
31	76
12	75
39	75
35	74
45	74
9	73
3	72
5	72
30	64
33	63
36	63
38	63
37	62
42	62
44	62
43	61

store	anomaly_flag
30	1
36	1
37	1
38	1
44	1
1	0
2	0
3	0
4	0
5	0
6	0
7	0
8	0
9	0
10	0
11	0
12	0
13	0
14	0
15	0
16	0
17	0
18	0
19	0
20	0
21	0
22	0
23	0
24	0
25	0
26	0
27	0
28	0
29	0
31	0
32	0
33	0
34	0
35	0
39	0
40	0
41	0
42	0
43	0
45	0

store	anomaly_flag
25	1
32	1
36	1
38	1
1	0
2	0
3	0
4	0
5	0
6	0
7	0
8	0
9	0
10	0
11	0
12	0
13	0
14	0
15	0
16	0
17	0
18	0
19	0
20	0
21	0
22	0
23	0
24	0
26	0
27	0
28	0
29	0
30	0
31	0
33	0
34	0
35	0
37	0
39	0
40	0
41	0
42	0
43	0
44	0
45	0

store	dept_count
13	79
15	79
19	79
2	78
4	78
11	78
18	78
20	78
27	78
34	78
1	77
6	77
10	77
14	77
21	77
23	77
24	77
25	77
28	77
29	77
32	77
40	77
41	77
7	76
8	76
16	76
17	76
22	76
26	76
31	76
12	75
39	75
35	74
45	74
9	73
3	72
5	72
30	64
33	63
36	63
38	63
37	62
42	62
44	62
43	61

store	anomaly_flag
30	1
36	1
37	1
38	1
44	1
1	0
2	0
3	0
4	0
5	0
6	0
7	0
8	0
9	0
10	0
11	0
12	0
13	0
14	0
15	0
16	0
17	0
18	0
19	0
20	0
21	0
22	0
23	0
24	0
25	0
26	0
27	0
28	0
29	0
31	0
32	0
33	0
34	0
35	0
39	0
40	0
41	0
42	0
43	0
45	0

store	anomaly_flag
25	1
32	1
36	1
38	1
1	0
2	0
3	0
4	0
5	0
6	0
7	0
8	0
9	0
10	0
11	0
12	0
13	0
14	0
15	0
16	0
17	0
18	0
19	0
20	0
21	0
22	0
23	0
24	0
26	0
27	0
28	0
29	0
30	0
31	0
33	0
34	0
35	0
37	0
39	0
40	0
41	0
42	0
43	0
44	0
45	0

store	dept_count
13	79
15	79
19	79
2	78
4	78
11	78
18	78
20	78
27	78
34	78
1	77
6	77
10	77
14	77
21	77
23	77
24	77
25	77
28	77
29	77
32	77
40	77
41	77
7	76
8	76
16	76
17	76
22	76
26	76
31	76
12	75
39	75
35	74
45	74
9	73
3	72
5	72
30	64
33	63
36	63
38	63
37	62
42	62
44	62
43	61

store	anomaly_flag
30	1
36	1
37	1
38	1
44	1
1	0
2	0
3	0
4	0
5	0
6	0
7	0
8	0
9	0
10	0
11	0
12	0
13	0
14	0
15	0
16	0
17	0
18	0
19	0
20	0
21	0
22	0
23	0
24	0
25	0
26	0
27	0
28	0
29	0
31	0
32	0
33	0
34	0
35	0
39	0
40	0
41	0
42	0
43	0
45	0

store	anomaly_flag
25	1
32	1
36	1
38	1
1	0
2	0
3	0
4	0
5	0
6	0
7	0
8	0
9	0
10	0
11	0
12	0
13	0
14	0
15	0
16	0
17	0
18	0
19	0
20	0
21	0
22	0
23	0
24	0
26	0
27	0
28	0
29	0
30	0
31	0
33	0
34	0
35	0
37	0
39	0
40	0
41	0
42	0
43	0
44	0
45	0