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.

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

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

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

Correlation: Food., Income., Size,

Food. Income.
Income. 0.093
Size, 0.593 0.172

Cell Contents: Pearson correlation

Correation matrix .

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

Regression Analysis: Food. versus Size,, Income.

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Regression 2 9.5427 4.77136 5.96 0.009
Size, 1 9.3087 9.30875 11.62 0.003
Income. 1 0.0022 0.00223 0.00 0.958
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%

Coefficients

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

Regression Equation

Food. = 3.873 + 0.2966 Size, - 0.00027 Income.

Comment - 0.2966 ammount  additional family member add to the amount spent on food.

Food Income Income 0.093 Size 0.593 0.172

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