Many regions along the coast in North and South Carolina and Georgia have experi
ID: 3365149 • 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.)
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.
Explanation / Answer
a-1. CORRELATION MATRIX ( Obtained in Excel by choosing Correlation from the Data Analysis Toolpack ) :
Food
Income
Size
Food
1
Income
0.308918
1
Size
0.884277
0.255363
1
a-2. Income and size are not that highly correlated. So, multicollinearity may not arise.
b-1. Regression output from Excel :
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.888445
R Square
0.789334
Adjusted R Square
0.770183
Standard Error
0.530246
Observations
25
ANOVA
df
SS
MS
F
Significance F
Regression
2
23.17632
11.58816
41.21535
3.63E-08
Residual
22
6.185547
0.281161
Total
24
29.36186
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
2.965917
0.291805
10.16403
8.97E-10
2.36075
3.571084
2.36075
3.571084
Income
0.002405
0.002738
0.878399
0.38922
-0.00327
0.008082
-0.00327
0.008082
Size
0.484005
0.056857
8.51263
2.07E-08
0.36609
0.601919
0.36609
0.601919
Regression Equation :
Food = 2.966 + 0.0024*Income + 0.484*Size
b-2. The amount spent for an additional family member is 0.484$.
c-1. R2 = 0.789.
Food
Income
Size
Food
1
Income
0.308918
1
Size
0.884277
0.255363
1
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