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.

FamilyFoodIncomeSize1$6.06$73.982.0024.0854.902.0035.7666.274.0043.4852.021.0054.2065.702.0064.8053.644.0074.3279.743.0085.0468.584.0096.12165.605.00103.2464.801.00114.80138.423.00123.24125.821.00135.5877.587.00145.78100.525.00156.60161.026.00165.40141.303.00176.0036.905.00185.4056.884.00193.3671.821.00204.6869.483.00214.3254.362.00225.5287.665.00234.5638.163.00245.4043.747.00254.4143.397.00

Click here for the Excel Data File

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.)

Link in comments

FoodIncomeIncomeSize

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

There is(Click to select)

multicollinearity

no 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 ofR²?(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.)

H₀is rejected ifF>

c-3.Complete the ANOVA(Leave no cells blank - be certain to enter "0" wherever required. RoundSS,MS, P to 3 decimal places andFto 2 decimal places.)

SourceDFSSMSFpRegressionError

Total

c-4.Can we conclude that this value is greater than 0?

(Click to select)

Do not reject

Reject

H₀. Some of the regression coefficients are(Click to select)

not zero

zero

.

d-1.Complete the given below table.(Leave no cells blank - be certain to enter "0" wherever required. Round Coef, SE Coef,Pto 3 decimal places andTto 2 decimal places.)

PredictorCoefSE CoefTPConstantIncomeSize