# Multiple regression analysis

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 resulted in many of the large grocery store chains building 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 $5.04 $ 73.98 4

2 4.08 54.90 2

3 5.76 94.14 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 6.60 77.58 7

14 4.92 171.36 2

15 6.60 82.08 9

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 4.80 48.42 5

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

Develop a correlation matrix. Do you see any problems with multicollinearity?

Determine the regression equation. Discuss the regression equation. How much does an additional family member add to the amount spent on food?

What is the value of R2? Can we conclude that this value is greater than 0?

Would you consider deleting either of the independent variables?

Plot the residuals in a histogram. Is there any problem with the normality assumption?

Plot the fitted values against the residuals. Does this plot indicate any problems with homoscedasticity?

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#### Solution Summary

Step by step method for regression analysis is discussed here. Regression coefficients, coefficient of determination, scatter diagram and significance of regression model are explained in the solution.