Question

Exercise 14-26 (LO14-1, LO14-2, LO14-4) 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 $4.20 $73.98 3.00 2 4.08 54.90 2.00 3 5.76 90.67 4.00 4 3.48 52.02 1.00 5 4.20 65.70 2.00 6 4.80 53.64 4.00 7 4.32 79.74 3.00 8 5.04 68.58 4.00 9 6.12 165.60 5.00 10 3.24 64.80 1.00 11 4.80 138.42 3.00 12 3.24 125.82 1.00 13 5.76 77.58 7.00 14 4.23 100.16 4.00 15 6.60 169.35 8.00 16 5.40 141.30 3.00 17 6.00 36.90 5.00 18 5.40 56.88 4.00 19 3.36 71.82 1.00 20 4.68 69.48 3.00 21 4.32 54.36 2.00 22 5.52 87.66 5.00 23 4.56 38.16 3.00 24 5.40 43.74 7.00 25 8.20 48.82 8.00 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 0.159 Size 0.890 0.136

a-2. Do you see any problems with multicollinearity? There is .

b-1. Determine the regression equation. (Round your answer to 3 decimal places.) The regression equation is: Food = 2.999 + 0.001 Income + 0.488 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 $ 488 to the food bill.

c-1. What is the value of R2? (Round your answer to 3 decimal places.) R2 0.793

c-2. State the decision rule for 0.05 significance level. H0: = β1 = β2 = 0; H1: Not all βi's = 0. (Round your answer to 2 decimal places.)

H0 is rejected if F >

c-3. Complete the ANOVA (Leave no cells blank - be certain to enter "0" wherever required. Round SS, MS, P 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? H0. Some of the regression coefficients are .

d-1. Complete the given below table. (Leave no cells blank - be certain to enter "0" wherever required. Round Coef, SE Coef, P to 3 decimal places and T to 2 decimal places.) Predictor Coef SE Coef T P Constant Income Size

Answer 1

a)

Correlation: Food, Income, Size

Correlations

	Food	Income
Income	0.159
Size	0.890	0.136

Cell Contents
      Pearson correlation coefficient.

a2) Multi collinearity is not present.

b1)

Regression Analysis: Food versus Income, Size

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Regression	2	25.3543	12.6771	42.17	0.000
Income	1	0.0467	0.0467	0.16	0.697
Size	1	24.5490	24.5490	81.67	0.000
Error	22	6.6129	0.3006
Total	24	31.9671

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
0.548257	79.31%	77.43%	68.58%

Coefficients

Term	Coef	SE Coef	T-Value	P-Value	VIF
Constant	2.999	0.311	9.64	0.000
Income	0.00116	0.00295	0.39	0.697	1.02
Size	0.4880	0.0540	9.04	0.000	1.02

Regression Equation

Food

=

2.999 + 0.00116 Income + 0.4880 Size

b2)

Another member of the family adds $ 488 to the food bill.

c1) R² = 0.731

c2) H0 is rejected if F > 3.44 for overall regression and F>4.30 for individual predictors.

we fail to reject null hypothesis for b1 (slpoe of income) which signifies that there is no linear relation associated with the income and food.

c3)

Fits and Diagnostics for Unusual Observations

Obs	Food	Fit	Resid	Std Resid
15	6.600	7.099	-0.499	-1.17		X
24	5.400	6.465	-1.065	-2.18	R
25	8.200	6.959	1.241	2.65	R

R Large residual
X Unusual X