Question 4: Analysts at a major automobile company collected data on a variety of variables for a sample of 30 different cars and small trucks. Included among those data were the EPA highway mileage rating and the horsepower of each vehicle. The analysts were interested in the relationship between horsepower (x) and highway mileage (y). Given below is the Excel output from regressing starting miles per gallon (MPG) on number of horsepower for a sample of 30 students.
Note: Some of the numbers in the output are purposely erased.
Regression Statistics |
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Multiple R |
0.5493 |
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R Square |
0.3016 |
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Adjusted R Square |
0.2766 |
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Standard Error |
3.5532 |
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Observations |
30 |
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ANOVA |
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df |
SS |
MS |
F |
Significance F |
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Regression |
1 |
152.655 |
12.091 |
12.091 |
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Residual |
12.625 |
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Total |
30 |
506.167 |
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Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
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Intercept |
31.1658 |
1.9332 |
16.12 |
0.0000 |
27.2058 |
35.1258 |
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Horsepower |
-0.0286 |
0.0082 |
-3.4772 |
0.0017 |
-0.0454 |
-0.0117 |
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a) What is the estimated average change in MPG as a result of an extra unit of horsepower?
b) What is the value of the measured t-test statistic and its p-value to test whether average MPG depends linearly on Horsepower?
c) What is the error sum of squares (SSE) of the above regression? Show how you obtain your answer.
f) The 99% confidence interval for the average change in MPG as a result of increased horsepower is:
A) wider than [-0.0454, -0.0117].
B) narrower than [-0.0454, -0.0117].
C) wider than [27.2058, 35.1258].
D) narrower than [27.2058, 35.1258].
Explain your reasoning.
ANSWER::
Option:: (B) is correct......... narrower than [-0.0454, -0.0117]
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