Question

1. Use “Question1_Dataset.xlsx.” For 12 straight weeks, you have observed the sales (in number of cases) of canned tomatoes at Mr. D’s Supermarket. For each week, you have data about the following:

• If a promotional notice for canned tomatoes was placed in all shopping carts
• If a coupon for canned tomatoes was given to each customer
• If there was a price reduction of 1 cent given
• If there was a price reduction of 2 cents given
  1. Use this data to determine how these factors influence sales (determine the multiple regression equation). Make sure that your final regression results contain only statistically significant variables.
  2. What is the R square of your regression and what does it mean?

Week	Sales	Cart?	2 cents off?	1 cent off?	Coupon
1	36	1	0	0	1
2	38	1	0	1	1
3	40	1	1	0	1
4	40	1	0	0	0
5	42	1	0	1	0
6	44	1	1	0	0
7	12	0	0	0	1
8	20	0	0	1	1
9	30	0	1	0	1
10	8	0	0	0	0
11	16	0	0	1	0
12	33	0	1	0	0

Answer 1

Using Excel

data -> data analysis -> regression

y^ = 14.5 + 20.1667 cart + 12.75 * 2 cents off + 5 * 1 cent off -1.16667 coupon

we see that 1 cent off and coupon are not significant as p-value > 0.05 for these variables

we remove coupon as it is most insignificant

still 1 cent off is significant

after removing 1 cent off too

now both independent variables are signfiicant

y^ = 16.4167 + 20.1667 cart + 10.25 2 cent off

R^2 = 0.8559

hence 85.59 % variation in sales explained by these independent variables

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