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 $4.08 $73.98 3 2 4.08 54.90 2 3 5.76 137.48 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 6.50 77.58 7 14 5.20 99.58 7 15 6.60 38.88 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 5.24 45.23 6

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.) Food Income Income Size (a-2) Do you see any problems with multicollinearity? There is . (b-1) Determine the regression equation. (Round your answers to 3 decimal places. Leave no cells blank - be certain to enter "0" wherever required.) The regression equation is: Food = + Income + Size. (b-2) 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. (c-1) What is the value of R2? (Round your answer to 3 decimal places.) R2 (c-2) State the decision rule for 0.05 significance level. H0: β1 = β2 = 0; H1: Not all βi's are 0. (Round your answer to 2 decimal places.) Ho is rejected if F > (c-3) Complete the ANOVA (Leave no cells blank - be certain to enter "0" wherever required. Round SS, MS to 3 decimal places and F to 2 decimal places.) Source DF SS MS F p Regression Error Total (c-4) Can we conclude that this value is greater than 0? Ho. Some of the regression coefficients are . (d-1) Complete the given below table. (Leave no cells blank - be certain to enter "0" wherever required.