11.107 Predicting CO2 emissions.
The data set CO2MPG contains an SRS of 200 passenger vehicles sold in Canada in 2014. There appears to be a quadratic relationship between CO2 emissions and mile per gallon highway(MPGHWY).
co2mpg
11.107
(a)
Regression Coefficients | |||
Type | Intercept | mpg | mpg2 |
D | 267.3823 | −5.42585 | 0.04619 |
E | 160.84557 | −3.89582 | 0.30631 |
X | 235.16637 | −7.18033 | 0.12751 |
Z | 243.75987 | −7.88188 | 0.13832 |
Type X and Z are very similar and show very few differences in all of the coefficients. Types D and E are very different. Type E has a much smaller slope for MPG than all the other types, and the MPG2 effect is quite large—more than double all the rest. Type D also has a slightly smaller slope for MPG than X and, but it has an extremely small slope for MPG2.
(b)
Parameter | Estimate |
Intercept | 243.75987 |
X1 | 23.62243 |
X2 | −82.91430 |
X3 | −8.59350 |
mpg | −7.88188 |
MPGX1 | 2.45603 |
MPGX2 | 3.98607 |
MPGX3 | 0.70155 |
mpg2 | 0.13832 |
MPG2X1 | −0.09214 |
MPG2X2 | 0.16798 |
MPG2X3 | −0.01081 |
S-34
Answers will vary depending on how the indicator variables were created. Setting Z has the default type ; the parameter estimates are in the table shown. So the estimates for the Intercept, MPG, and MPG2 will match type Z’s estimates exactly. To recoup the others, we just set and for Type D, etc., yielding an intercept of , a slope for MPG of , and a slope for MPG2 of , etc. This yields the same equations as part (a).