1. Question 1: The Public Utility Commission is interested in describing the relationship between household monthly utility bills and the size of the house. A recent study of 30 randomly selected household resulted in the following regression results: SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.149769088 0.02243078 -0.012482407 16.72762259 30 ANOVA df SS MS 179.7725274 179.7725 0.642473 7834.774007 279.8134 1 Regression Residual Total 28 29 8014.546534 Standard Eror 13.44691911 4.941135 3.26E-05 0.006560753 0.801544 0.429567 Coefficients t Stat P-value Intercept Square Feet 66.44304169 0.005258733 (a) Based on the information provided, indicate what, if any, conclusions can be reached about the relationship between utility bill and the size of the house in square feet. (b) Construct a 95% confidence interval for the true regression coefficient of Square Feet. How do you interpret this confidence interval? (c) What is the F-test? In view of the F-test reported in this table, is the model significant? Please give a reason.

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1. Question 1: The Public Utility Commission is interested in describing the relationship between
household monthly utility bills and the size of the house. A recent study of 30 randomly
selected household resulted in the following regression results:
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
0.149769088
0.02243078
-0.012482407
16.72762259
Observations
30
ANOVA
df
SS
MS
1
179.7725274 179.7725 0.642473
Regression
Residual
28
7834.774007 279.8134
Total
29
8014.546534
t Stat
13.44691911 4.941135 3.26E-05
0.006560753 0.801544 0.429567
P-value
Coefficients
66.44304169
0.005258733
Standard Eror
Intercept
Square Feet
(a) Based on the information provided, indicate what, if any, conclusions can be reached
about the relationship between utility bill and the size of the house in square feet.
(b) Construct a 95% confidence interval for the true regression coefficient of Square Feet.
How do you interpret this confidence interval?
(c) What is the F-test? In view of the F-test reported in this table, is the model significant?
Please give a reason.
Transcribed Image Text:1. Question 1: The Public Utility Commission is interested in describing the relationship between household monthly utility bills and the size of the house. A recent study of 30 randomly selected household resulted in the following regression results: SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error 0.149769088 0.02243078 -0.012482407 16.72762259 Observations 30 ANOVA df SS MS 1 179.7725274 179.7725 0.642473 Regression Residual 28 7834.774007 279.8134 Total 29 8014.546534 t Stat 13.44691911 4.941135 3.26E-05 0.006560753 0.801544 0.429567 P-value Coefficients 66.44304169 0.005258733 Standard Eror Intercept Square Feet (a) Based on the information provided, indicate what, if any, conclusions can be reached about the relationship between utility bill and the size of the house in square feet. (b) Construct a 95% confidence interval for the true regression coefficient of Square Feet. How do you interpret this confidence interval? (c) What is the F-test? In view of the F-test reported in this table, is the model significant? Please give a reason.
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