ESM 206 Problem Set 3
MicroExam will be due Tuesday, Feb. 5 at 4 PM.
A. For this section use the Cars_1993.xls data on the course website.
1)
Use regression to answer the following question: “All else being equal, how
would a 100 pound reduction in a car’s weight affect its highway fuel mileage?”
2)
Write down the equation corresponding to the analysis you just did, and identify
the variables, the parameters, and the residuals.
What was your estimate of each
parameter and of the residual variance?
What was the 95% confidence interval
for each of your parameter estimates?
3)
I ran a model in which the dependent variable was highway mileage and the
independent variables were weight and the interaction between weight and engine
size, and got the output shown below (it is from JMP, but you should be able to
find the key elements of the output).
Explain in words the meaning of the
interaction term and what the results suggest about how engine size affects fuel
economy.
Response HighwayMPG
Whole Model
Summary of Fit
RSquare
0.676073
RSquare Adj
0.668794
Root Mean Square Error
3.075279
Mean of Response
29.13043
Observations (or Sum Wgts)
92
Analysis of Variance
Source
DF
Sum of Squares
Mean Square
F Ratio
Model
2
1756.7316
878.366
92.8766
Error
89
841.7031
9.457
Prob > F
C. Total
91
2598.4348
<.0001
Lack Of Fit
Source
DF
Sum of Squares
Mean Square
F Ratio
Lack Of Fit
82
808.70315
9.86223
2.0920
Pure Error
7
33.00000
4.71429
Prob > F
Total Error
89
841.70315
0.1521
Max RSq
0.9873
Parameter Estimates
Term
Estimate
Std Error
t Ratio
Prob>t
Intercept
56.472278
2.660277
21.23
<.0001
Weight
0.009941
0.001224
8.12
<.0001
EngineSize*Weight
0.0003637
0.000152
2.40
0.0187
Effect Tests
Source
Nparm
DF
Sum of Squares
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 Spring '08
 KENDALL,BERKLEY
 Environmental Science, Regression Analysis, Standard Deviation, Mean, Fuel economy in automobiles, Parameter Estimates

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