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

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

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.)

rev: 11_23_2015_QC_CS-33651, 06_18_2016

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 $5.26 $73.98 5.00 2 4.08 54.90 2.00 3 5.76 59.12 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 6.45 77.58 7.00 14 4.63 172.92 6.00 15 6.60 90.98 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 4.78 60.72 4.00 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 (Click to select)multicollinearityno multicollinearity.

b-1. Determine the regression equation. (Round your answer to 3 decimal places.)   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: = 1 = 2 = 0; H1: Not all i'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?   (Click to select)Do not rejectReject H0. Some of the regression coefficients are (Click to select)zeronot zero. 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                           d-2. Would you consider deleting either of the independent variables?   There is (Click to select)no needa need to delete a variable. e. State true or false.

   

From the graph the residuals appear normally distributed. (Click to select)FalseTrue f. Choose the right option from the following graph.

   

(Click to select)There is no homoscedasticity problemThere is a homoscedasticity problem.

rev: 11_23_2015_QC_CS-33651, 06_18_2016

-0,8 -0.6 -0,4 -0.2 0.0 0.2 0.4 0.6 0.8 Residual

Explanation / Answer

Part-a-1

Correlation matrix is as follows:

Food

Income

Income

0.107

1

Size

0.867

0.132

Part-a-2

There is no multicollinearity

Part-b-1

Regression equation is Food= 3.304-0.0002 Income+0.422 Size

Part-b-2

Additional family member add to $0.422

Part-c-1

R2=0.751

Part-c-2

H0 is rejected if F>3.44

Part-c-3

ANOVA

Source

df

SS

MS

F

Significance F

Regression

2

16.512

8.256

33.24

0.000

Error

22

5.463

0.248

Total

24

21.975

Part-c-4

Reject H0. Some of he regression coefficients are not zero

Part-d-1

Coefficients

Standard Error

t Stat

P-value

Constant

3.304

0.288

11.49

0.000

Income

0.000

0.003

-0.07

0.942

Size

0.422

0.052

8.09

0.000

Part-d-2

There is need to delete a variable

Part-e

True

Part-f

No

Food

Income

Income

0.107

1

Size

0.867

0.132

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