# linear and logistic regression

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?

• 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? – whuber Jun 20 '16 at 15:29
• Consider looking at link – Kontorus Jun 20 '16 at 15:31

## 2 Answers

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.

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