Question

Please use R to solve and explain fully

Market Planning, Inc., a marketing research firm, has obtained the prescription sales data in the table below for n = 20 independent pharmacies.

These variables can be described precisely as follows:

y = average weekly prescription sales over the past year (in units of $1000)

x₁ = floor space (in square feet)

x₂= percent of floor space allocated to the prescription department

x₃ = number of parking spaces available for the store

x₄ = monthly per capita income for the surrounding community (in units of $100)

x₅ is an independent variable that equals 1 if the pharmacy is located in a shopping center and equals 0 otherwise (x₅ is called a dummy variable)

a. Output the stepwise regression of the data in this exercise. Set, both alpha_entry and alpha_stay equal to .15. What is the final model arrived at by stepwise regression?

b. Perform a backward elimination procedure on the same data. Describe the order in which the independent variables are removed by the backward elimination procedure.

c. Is the model arrived at by backward elimination the same as the model arrived at by stepwise regression?

Pharmacy	y	x1	x2	x3	x4	x5
1	22	4900	9	40	18	1
2	19	5800	10	50	20	1
3	24	5000	11	55	17	1
4	28	4400	12	30	19	0
5	18	3850	13	42	10	0
6	21	5300	15	20	22	1
7	29	4100	20	25	8	0
8	15	4700	22	60	15	1
9	12	5600	24	45	16	1
10	14	4900	27	82	14	1
11	18	3700	28	56	12	0
12	19	3800	31	38	8	0
13	15	2400	36	35	6	0
14	22	1800	37	28	4	0
15	13	3100	40	43	6	0
16	16	2300	41	20	5	0
17	8	4400	42	46	7	1
18	6	3300	42	15	4	0
19	7	2900	45	30	9	1
20	17	2400	46	16	3	0

Answer 1

Answer for part (a) : Final model arrived by stepwise regression is in orange box in the below picture.

Answer for part (b) : Backward Elimination :

Order in which independent variables are removed is :

1st removed : x4

2nd removed : x3

3rd removed : x1

You can see this removal order in below picture(See step-2,step-3,step-4 respectively. You can see values for removed variables are not available.).Also the final regression model is in orange box.

Answer for part (c) : The model arrived by backward elimination and stepwise regression is same. (You can see orange boxes.)