Many regions along coast in North and South Carolina and Georgia have experienced fast growth over the last 10 years. It is anticipated the growth will continue over the upcoming 10 years. This has resulted in many of the large grocery store chains building new stores in region. The Kelley's super grocery stores chain is no exception. The director of planning For Kellys wants to study adding more stores in region. He thinks there are 2 main factors which indicate the amount families spend on groceries. The first is their income and other is the number of people in family. The director collected the following sample.
Food and income are reported in thousands of dollars for each year, and the variable size refers to number of people in household.
a. Make a correlation matrix. Do you see any problem with the multicollinearity?
b. Find out the regression equation. Describe the regression equation. How much does the additional family member add to amount spent on food?
c. Find out the value of R square? Can we conclude the value is greater than o?
d. Would you consider deleting wither of independent variables?
e. Plot the residuals in the histogram. Is there any problem with normality assumption?
f. Plot the fitted values against residuals. Does this plot point out any problems with homoscedasticity?
| Family |
Food |
Income |
Size |
|
Family |
Food |
Income |
Size |
| 1 |
5.04 |
73.98 |
4 |
|
14 |
4.92 |
171.36 |
2 |
| 2 |
4.08 |
54.9 |
2 |
|
15 |
6.6 |
82.08 |
9 |
| 3 |
5.76 |
94.14 |
4 |
|
16 |
5.4 |
141.3 |
3 |
| 4 |
3.48 |
52.02 |
1 |
|
17 |
6 |
36.9 |
5 |
| 5 |
4.2 |
65.7 |
2 |
|
18 |
5.4 |
56.88 |
4 |
| 6 |
4.8 |
53.64 |
4 |
|
19 |
3.36 |
71.82 |
1 |
| 7 |
4.32 |
79.74 |
3 |
|
20 |
4.68 |
69.48 |
3 |
| 8 |
5.04 |
68.58 |
4 |
|
21 |
4.32 |
54.36 |
2 |
| 9 |
6.12 |
165.6 |
5 |
|
22 |
5.52 |
87.66 |
5 |
| 10 |
3.24 |
64.8 |
1 |
|
23 |
4.56 |
38.16 |
3 |
| 11 |
4.8 |
138.42 |
3 |
|
24 |
5.4 |
43.74 |
7 |
| 12 |
3.24 |
125.82 |
1 |
|
25 |
4.8 |
48.42 |
5 |
| 13 |
6.6 |
77.58 |
7 |
|
|
|
|
|