I'm currently playing around with linear regression in R, and I've come up with a regression that fits data quite well. I'm just having some problems with interpreting the coefficients of my model. I know how to interpret log-log models in a simpler form, but when I have interactions I'm not quite sure how to interpret them.
Here's my output from R:
Call:
lm(formula = log(y) ~ log(x1) + x2 * log(x1) + x3 * log(x1) +
I(x3^2), data = Data)
Residuals:
Min 1Q Median 3Q Max
-0.56943 -0.12082 0.00012 0.11123 0.54579
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2.393889950 0.545879641 -4.385 0.000025149470154 ***
log(x1) 0.497477722 0.056113496 8.866 0.000000000000009 ***
x2 -0.000264760 0.000055476 -4.773 0.000005220020368 ***
x3 0.041126987 0.017930934 2.294 0.02357 *
I(x3^2) -0.000688879 0.000231778 -2.972 0.00358 **
log(x1):x2 0.000031580 0.000006691 4.720 0.000006494076511 ***
log(x1):x3 0.003145219 0.001277909 2.461 0.01528 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.1932 on 119 degrees of freedom
Multiple R-squared: 0.9865, Adjusted R-squared: 0.9859
F-statistic: 1454 on 6 and 119 DF, p-value: < 2.2e-16
I've been Googling for the past hour, but I can only find answers to some simpler models like the answer given here: Interpretation of log transformed predictor or http://www.ats.ucla.edu/stat/sas/faq/sas_interpret_log.htm
I hope someone out there can help me with interpreting the interaction terms and the polynomial term in my model.