Problem:
|
Price($)
|
Promotional exp(K)
|
Qualityof Service
|
City:1/Suburban:0
|
Monthly Sales(K)
|
|
904
|
5
|
9.5
|
1
|
168
|
|
909
|
4.3
|
4.5
|
0
|
168
|
|
915
|
3
|
8.5
|
1
|
162
|
|
921
|
2
|
5.5
|
0
|
160
|
|
934
|
0.75
|
6.5
|
1
|
154
|
|
941
|
4.8
|
10
|
0
|
152
|
|
949
|
3.6
|
4.25
|
1
|
150
|
|
953
|
3
|
5.5
|
1
|
146
|
|
955
|
1.5
|
7.5
|
0
|
146
|
|
962
|
0.7
|
9.5
|
0
|
144
|
|
978
|
4.7
|
9
|
1
|
134
|
|
990
|
3.5
|
7
|
0
|
130
|
|
1006
|
2.8
|
5
|
1
|
122
|
|
1014
|
1.3
|
4
|
0
|
118
|
|
1018
|
0.25
|
9
|
1
|
116
|
|
1021
|
4.5
|
6
|
1
|
114
|
|
1022
|
3.2
|
5
|
0
|
114
|
|
1038
|
2.4
|
8
|
0
|
106
|
|
1040
|
1.2
|
4
|
1
|
104
|
|
1050
|
0
|
9
|
0
|
100
|
Please consider the data presented above for the monthly sales of Ever-cool brand of refrigerators in 1,000s of dollars and answer the following questions:
Independent variables are as follows.
Price(in dollars); Promotional Expenditure (in 1,000s of dollars); Quality of service ( scale of 1-10); location (categorical variable: city area : 1; suburban area : 0) .
a. Based on 4 in 1 plot and the plots of independent variables vs. residuals, do you see any evidence of violation of assumptions?
b. State the multiple regression equation and interpret the meaning of the slopes, b1, b2, b3, and b4.
c. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. On the basis of these results, indicate the independent variables to include in this model. (Based on t - test results)
d. Construct a 95% confidence interval estimate of the population slope between price and the monthly sales ()
e. Perform the overall F- test and comment on the significance of the model.