Similar to this question: How to translate the results from lm() to an equation? in which the top voted answer said how to get the form of an equation from lm(y ~ x) and equivalently for lm(z ~ y + x) and other sums, I'm wondering: how can the equation be obtained from the form of lm(z ~ y*x)?
I have:
> summary(lm(log(z) ~ x*y)) Call: lm(formula = log(z) ~ x * y) Residuals: Min 1Q Median 3Q Max -0.181142 -0.073755 0.000481 0.082088 0.200902 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -9.85368 0.09304 -105.906 < 2e-16 *** x -97.41166 6.28269 -15.505 < 2e-16 *** y -2.26398 0.14243 -15.895 < 2e-16 *** x:y 91.69016 9.77390 9.381 6.95e-14 *** It returns 4 coefficients — (Intercept), x, y, and x:y — but I'm not sure how to put them together to get the final equation.
Is it simply that x:y term multiplied by x*y plus the intercept? That is, in this case $log z = 91.69 xy -9.853$?
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Best Answer
The equation is $widehat{log z} = -9.853 -97.41166x -2.26398y + 91.69xy$ where $widehat{log z}$ is the estimated value of $log z$.
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