Many regions along the coast in North and South Carolina and Georgia have experi
ID: 3150779 • 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.
2
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.)
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 32
4.08 54.90 2 3 5.76 90.67 4 4 3.48 52.02 1 5 4.20 65.70 2 6 4.80 53.64 4 7 4.32 79.49 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 5.76 77.58 7 14 4.23 100.16 4 15 6.60 169.35 8 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 8.20 48.82 8Food 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 (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. RoundSS, MS to 4 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? (Do not reject or Reject H0). Some of the regression coefficients are (zero or not zero).Explanation / Answer
answer a1) correaltion matrix is given and in bold digit in small paranthesis is the p-value of the correlation
answer a2) there is not multicollinearity problem as the correlation between independent variables income and size is not signifiant at 5% level
answer b1)The regression equation food=2.999+0.001*income+0.488*size
answer b2) the partial regression coefficient of size is 0.488 so an additional family member add to the amount spent on food is 0.488
answer c1) R2=0.793
ansewer c2) H0 is rejected if F >3.443 (the critical F-value at alpha=0.05 and df=2,22)
answer c3)
answer c4) as p-value is less than 0.05 significance level so
Reject H0 and Some of the regression coefficients are not zero
Food Income Size Food 1 0.15885 0.88976 (0.4482) (<.0001) Income 0.15885 1 0.13593 (0.4482) (0.5171) Size 0.88976 0.13593 1 (<.0001) (0.5171)Related Questions
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