I'm fitting a linear model to a dataset. I've reduced the model from 7 variables to 3 and as part of that I've transformed one of my variables (wt) in order to get a better fit.
For my final model, the summary is:
summary(lm22)
Call:
lm(formula = mpg ~ poly(wt, 2) + year + origin, data = redautoi)
Residuals:
Min 1Q Median 3Q Max
-6.4126 -1.5029 -0.0003 1.5994 7.6032
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -33.94088 2.84630 -11.925 < 2e-16 ***
poly(wt, 2)1 -100.09492 3.14080 -31.869 < 2e-16 ***
poly(wt, 2)2 27.18431 2.61085 10.412 < 2e-16 ***
year 0.74125 0.03736 19.839 < 2e-16 ***
origin 0.55447 0.20314 2.729 0.00665 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 2.477 on 367 degrees of freedom
Multiple R-squared: 0.8842, Adjusted R-squared: 0.883
F-statistic: 700.7 on 4 and 367 DF, p-value: < 2.2e-16
My question is how do I interpret these estimates? Especially poly(wt,2)1 and poly(wt,2)2
Substituting values from the original dataset using the above estimates gives a wild fitted value. (but using fitted(lm22) appears to give reasonable estimates)
