Many regions in North and South Carolina and Georgia have experienced rapid popu

Question

Many regions 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.

5

44.83

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

2. Determine the regression equation. (Round your answer to 3 decimal places.)

The regression equation is: Food=_________+ _________income+______size

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

   Another member of the family adds ______ to the food bill.

4. What is the value of R2 ?

5. Complete the table given below. (Leave no cells blank - be certain to enter "0" wherever required. Round Coefficient, SE Coefficient, P to 4 decimal places and T to 2 decimal places.)

Family FOod Income Size 1 6.16 73.98

5

2 4.08 54.90 2 3 5.76 124.25 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 5.31 77.58 7 14 4.72 121.87 8 15 6.60 96.76 8 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 7.36

44.83

2

Explanation / Answer

1

Correlation: FOod, Income, Size

FOod Income
Income 0.093
Size 0.593 0.172

2.

Regression Analysis: FOod versus Income, Size

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Regression 2 9.5427 4.77136 5.96 0.009
Income 1 0.0022 0.00223 0.00 0.958
Size 1 9.3087 9.30875 11.62 0.003
Error 22 17.6223 0.80101
Total 24 27.1650

Model Summary

S R-sq R-sq(adj) R-sq(pred)
0.894994 35.13% 29.23% 12.41%

Regression Equation

FOod = 3.873 - 0.00027 Income + 0.2966 Size

3.

R2=35.13%

4

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant 3.873 0.513 7.55 0.000
Income -0.00027 0.00517 -0.05 0.958 1.03
Size 0.2966 0.0870 3.41 0.003 1.03

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