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 $log z = 91.69 xy -9.853$?

**Contents**hide

#### 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 $log z$.

### Similar Posts:

- Solved – Formulate equation after fitting to log(y)~x) using lm()
- Solved – How to interpret the j-test result in this result from ‘gmm’ command from ‘gmm’ package
- Solved – How to interpret the j-test result in this result from ‘gmm’ command from ‘gmm’ package
- Solved – How is the intercept calculated in a regression model with two independent factor variables
- Solved – Interpretation of Square of Logarithm-transformed term in linear regression