Good day, XValidators. This is my 1st question in the community.
I'm at my wit's end here. Nowhere in the interwebz nor in youtoubeland can I find an answer to the following:
Assume you have this model on the well-known
mtcars R dataset:
lm(mpg ~ factor(am) * wt + qsec, data=mtcars) where:
- mpg = fuel efficiency
- am = automatic (0) or manual (1)
- wt = weight (1000lbs)
- qsec = quarter-mile second (secs)
With the following coeffs:
Estimate Std. Error t value Pr(>|t|) (Intercept) 9.723 5.899 1.648 0.110893 factor(am)1 14.079 3.435 4.099 0.000341 *** wt -2.937 0.666 -4.409 0.000149 *** qsec 1.017 0.252 4.035 0.000403 *** factor(am)1:wt -4.141 1.197 -3.460 0.001809 **
Are the following interpretations correct?
- All coeffs will be given with respect to am=0 (meaning cars with automatic transmission), right?
- If so, then
factor(am)1is the mpg difference from an automatic car, right?
- And the coeff for wt will be the change in mpg for each 1000lb weight added FOR AUTOMATIC cars, right?
- And if we want to know the same but for MANUAL cars we just look at the coeff for the interaction term
- And if we want to obtain just the wt coeff regardless of type of car, we just add
wt + factor(am)1:wt, right?
- Now, what about qsec? Is it also given with respect to am=0 (AUTOMATIC cars)? If so, how can we know the qsec for MANUAL cars? Or since it doesn't have an interaction, is it given for all types of car?
Could someone shed some light here, plz?
Thank you all in advance.