1
$\begingroup$

how are relationship between coefficient of linear regression and logistic regression (or odds ratio)? I want compare coefficient of linear regression with odds ratios of logistic regression. Is there a relationship between these two coefficent?

$\endgroup$
  • 2
    $\begingroup$ Could you be more specific about what you mean by "linear regression"? How, exactly, is it being performed (there are many different ways to apply least-squares regression to a binary response variable) and what precisely is its relationship to the logistic regression you are doing? $\endgroup$ – whuber Jun 20 '16 at 15:29
  • $\begingroup$ Consider looking at link $\endgroup$ – Kontorus Jun 20 '16 at 15:31
1
$\begingroup$

The two coefficients should be very different numerically (after all, linear and logistic models are very different).

$Y = ax_1 + b$

$a$ = the change in $Y$ correlated with a one-unit change in $x_1$, given that all else is held constant.

$Y = \frac{1}{1+e^{-\beta_0+\beta_1x}}$

$\beta_1$ = the change in the log-odds correlated with a one-unit change in $x_1$, given that all else is held constant.

$\endgroup$
0
$\begingroup$

Yes coefficients will be numerically different but I think coefficient estimates between linear regression and logistic regression should be interpreted relatively in a similar way. I believe the main difference is that coefficients from logistic regression would be on a different scale. For example, if you used a log link then your coefficient estimates will be on a log scale. To get estimates on their original scale you can use information found here https://stats.stackexchange.com/a/14639/108922

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.