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?
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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 ♦Commented Jun 20, 2016 at 15:29
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$\begingroup$ Consider looking at link $\endgroup$– KontorusCommented Jun 20, 2016 at 15:31
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2 Answers
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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.
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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
answered Jun 20, 2016 at 15:46