Many regions along the coast in North and South Carolina and Georgia have experi
ID: 3151809 • 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 4 decimal places and T to 2 decimal places.)
Family Food Income Size 1 $4.14 $73.98 4.00 2 4.08 54.90 2.00 3 5.76 138.86 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 7.17 77.58 7.00 14 5.94 146.51 6.00 15 6.60 162.69 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 6.71 59.83 5.00Explanation / Answer
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.)
Correlation Matrix
Food
Income
Size
Food
1.000
Income
.309
1.000
Size
.884
.255
1.000
a-2.
Do you see any problems with multicollinearity?
There is ()no multicollinearity.
b-1.
Determine the regression equation. (Round your answer to 3 decimal places.)
The regression equation is: Food = 2.966 + 0.002*Income + 0.484*Size.
Regression Analysis
R²
0.789
Adjusted R²
0.770
n
25
R
0.888
k
2
Std. Error
0.530
Dep. Var.
Food
ANOVA table
Source
SS
df
MS
F
p-value
Regression
23.1763
2
11.5882
41.22
3.63E-08
Residual
6.1855
22
0.2812
Total
29.3619
24
Regression output
confidence interval
variables
coefficients
std. error
t (df=22)
p-value
95% lower
95% upper
Intercept
2.966
0.2918
10.164
8.97E-10
2.3608
3.5711
Income
0.002
0.0027
0.878
.3892
-0.0033
0.0081
Size
0.484
0.0569
8.513
2.07E-08
0.3661
0.6019
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. $0.48
c-1.
What is the value of R2? (Round your answer to 3 decimal places.)
R2 = 0.789
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 >
3.44
c-3.
Complete the ANOVA (Leave no cells blank - be certain to enter "0" wherever required. Round SS, MS to 4 decimal places and F to 2 decimal places.)
ANOVA table
Source
SS
df
MS
F
p-value
Regression
23.1763
2
11.5882
41.22
0.0000
Residual
6.1855
22
0.2812
Total
29.3619
24
c-4.
Can we conclude that this value is greater than 0?
(Click to select)Reject Ho . Some of the regression coefficients are (Click to select)not 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 4 decimal places and T to 2 decimal places.)
Regression output
variables
coefficients
std. error
t (df=22)
p-value
Intercept
2.9659
0.2918
10.16
0.0000
Income
0.0024
0.0027
0.88
.3892
Size
0.4840
0.0569
8.51
0.0000
d-2.
Would you consider deleting either of the independent variables?
There is (Click to select)a need to delete a variable.
Income is not significant.
We can delete this variable.
Food and income are reported in thousands of dollars per year, and the variable size refers to the number of people in the household.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.