Many regions along the coast in North and South Carolina and Georgia have experi

Question

Many regions along the coast in North and South Carolina and Georgia have experienced rapid population growth over the last 10 years. It is expected that the growth will continue over the next 10 years. This has motivated many of the large grocery store chains to build new stores in the region. The Kelley's Super Grocery Stores Inc. chain is no exception. The director of planning for Kelley's Super Grocery Stores wants to study adding more stores in this region. He believes there are two main factors that indicate the amount families spend on groceries. The first is their income and the other is the number of people in the family. The director gathered the following sample information.

Family      Food     Income     Size

1             $5.01     $73.98       3

2             4.08       54.90        2

3             5.76       71.89       4

4             3.48       52.02       1

5            4.20       65.70        2

6            4.80       53.64         4

7            4.32        79.74         3

8            5.04        68.58          4

9            6.12       165.60         5

10          3.24        64.80          1

11         4.80        138.42         3

12        3.24        125.82          1

13         6.15         77.58           7

14        4.29        164.20          3

15        6.60          76.55          5

16       5.40         141.30         3

17        6.00         36.90           5

18        5.40        56.88            4

19       3.36         71.82            1

20       4.68         69.48            3

21       4.32         54.36            2

22       5.52        87.66             5

23       4.56        38.16             3

24      5.40        43.74             7

25       5.90       46.87             8

Food and income are reported in thousands of dollars per year, and the variable size refers to the number of people in the household.

(a-1) Develop a correlation matrix. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)

(a-2) Do you see any problems with multicollinearity?

(b-1) Determine the regression equation. (Round your answers to 3 decimal places. Leave no cells blank - be certain to enter "0" wherever required.)

(b-2) How much does an additional family member add to the amount spent on food? (Round your answer to the nearest dollar amount.)

(c) What is the value of R2? (Round your answer to 3 decimal places.)

(d-1) Complete the given below table. (Leave no cells blank - be certain to enter "0" wherever required. Do not round the intermediate calculations. Round T to 2 decimal places and all other values to 3 decimal places.)

(d-2) Would you consider deleting either of the independent variables?

Explanation / Answer

(a1) the correlation matrix is given as

bold number shows the p-value of t-test of significance of corrleation coefficient

(a2) since income and size are independent variables and correlation coefficient between them are not significant.

so there is no problem of multicollinearity.

(b1) following information has been generated using regression analysis

the regression equation is given as

Food=3.053+0.003*Income+0.437*size

(b2) if th income remains fixed the the additional family member add to the amount spent on food=0.437

(c) R2=0.7424

(d1) table is not given in the question

(d2) here level of significance is not given let it be 0.01

independent variable Income may be deleted as it is not significant at alpha=0.01

Food Income Size Food 1 0.02289 0.85225 0.9135 <.0001 Income 0.02289 1 -0.12085 0.9135 0.565 Size 0.85225 -0.12085 1 <.0001 0.565

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