Many regions along the coast in North and South Carolina and Georgia have experi

ID: 3259715 • Letter: M

Question

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.

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

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

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

State the decision rule for 0.05 significance level. H0: = 1 = 2 = 0; H1: Not all i's = 0. (Round your answer to 2 decimal places.)

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.)

Excel Data File:

Explanation / Answer

(a) Using MINITAB the entire analysis is done

(a-1) The correlation matrix is given by

Food Income
Income 0.126
Size 0.872 -0.016

(a-2) Now correlation between food and family size is high 0.872

so there may be strong linear relationship

To know that we calculate the p-value (given along with the correlation matrix in MINITAB)

p-value is 0.00 <0.05so it is highly significant !

So there is multicollinearity!

(b-1)Using the multiple regression analysis we get the following MINITAB output

Regression Analysis: Food versus Income, Size

The regression equation is
Food = 2.93 + 0.00410 Income + 0.464 Size

Predictor Coef SE Coef T P
Constant 2.9313 0.3100 9.46 0.000
Income 0.004098 0.002915 1.41 0.174
Size 0.46352 0.05294 8.76 0.000

S = 0.474182 R-Sq = 78.1% R-Sq(adj) = 76.1%

So the regression equation is: Food = 2.93 + 0.004 *Income + 0.464 *Size

(b-2) For a unit change in family size the expenditure on food increases by 0.464*1000=464 dollar!

(c-1) R2 value was reported earlier in the output

R2= 78.1%

(c-2) Decision rule: We reject the null hypothesis at 5% level of significance if F_cal > F_tab; F_cal: calculated value of the test statistic and F_tab is the tabulated value at 5% level of significance

Here, we can also check the p-values, if p_value <0.05 ,we reject the null hypothesis at 5% level of significance!

(c-3) The ANOVA test output by MINITAB is

Analysis of Variance

Source DF SS MS F P
Regression 2 17.5955 8.7978 39.13 0.000
Residual Error 22 4.9467 0.2248
Total 24 22.5422

Source DF Seq SS
Income 1 0.3603
Size 1 17.2352

(c-4) Since the F_cal = 39.13 is greater than F_tab = F.05,2,22 = 3.44

So we reject Ho at 5% level of significance. Thus the value is greater than 0.

(d) Consider the table question (b-1)

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