Stat 301
Lab 5: Due October 13
Fall 2014
1. Data on new vehicles for the 2014 model year are available from the Environmental
Protection Agency. A random sample of 200 vehicles was selected. Using these data
we wish to predict the CO2 emissions of the vehicles in city driving. The explanatory
variables are listed below. The JMP data set is posted on the course web site.
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Engine – displacement of the engine in liters (Min = 1, Max = 6.8)
Cylinder – number of cylinders (Min = 3, Max = 12)
City MPG – Fuel economy in city driving (MPG) (Min = 11, Max = 40)
Gears – number of gears (Min = 1, Max = 9)
Intake – Number of intake valves per cylinder (Min = 1, Max = 2)
Exhaust – Number of exhaust valves per cylinder (Min = 1, Max = 2)
The data are on the class web page
http://www.public.iastate.edu/~wrstephe/stat301.html
a) Use JMP’s Fit Model to fit a multiple regression model with City CO2 as the
response variable and Engine, Cylinder, City MPG, Gears, Intake and Exhaust as
six explanatory variables. Use the JMP output to answer the following questions.
Attach the JMP output at the end of your lab assignment.
b) Give the multiple regression equation.
c) Give the value of the estimate of the error standard deviation, σ.
d) Give the value and an interpretation of R2.
e) What is the value of the adjusted R2?
f) Test the hypothesis H 0 : β1 = β 2 = β 3 = β 4 = β 5 = β 6 = 0 versus the alternative that
at least one slope parameter is not zero. What does this test tell you about the
relationship between the City CO2 and the six explanatory variables?
g) Look at the plot of residuals versus City MPG. What does this plot tell you about
the adequacy of the linear model?
h) Describe what you see in the analysis of residuals; histogram, box plot and normal
quantile plot. What does this indicate about the conditions necessary for multiple
regression analysis?
2. Use JMP’s Fit Model to fit the models necessary to answer the following questions.
Be sure to support your answers with the appropriate test statistic and P-value from
the appropriate JMP output. For all tests use α = 0.05 as your level of significance.
Attach the JMP output at the end of your lab assignment.
a) Is there a statistically significant relationship between City CO2 and the
displacement of the engine?
b) Does fuel economy in city driving add significantly to the model that already
contains the displacement of the engine? How much does adding fuel economy in
city driving to the model with engine displacement add to explaining variation in
City CO2? Give either the additional sum of squares or the change in R2.
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c) Does the number of gears add significantly to the model that already contains fuel
economy in city driving? How much does adding the number of gears to the
model with fuel economy in city driving add to explaining variation in City CO2?
Give either the additional sum of squares or the change in R2.
d) Does the displacement of the engine add significantly to the model that already
contains the two variables number of cylinders and city fuel economy? How
much does adding displacement of the engine to the model with number of
cylinders and city fuel economy add to explaining variation in City CO2? Give
either the additional sum of squares or the change in R2.
e) Does displacement of the engine add significantly to the model that already
contains the three variables fuel economy in city driving, number of cylinders and
number of gears? How much does adding displacement of the engine to the
model that already contains the three variables add to explaining variation in City
CO2? Give either the additional sum of squares or the change in R2.
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