# Question in fitting regression

Consider the plot attached as the histogram of the outcome ($Y$) that is going to be the outcome in a linear regression. Clearly, the histogram shows the outcome is not normally distributed. How can I come up with a transformation that makes the data be normal so that I can fit a linear regression?

My goal is to compare the effect of TRT (treatment) vs. CTRL (control). One obvious regression is:

$Y = \mathrm{TRT} + \text{other covariates}$

Since $Y$ is not normal, do you think I can assess the TRT effect by considering $Y$ as a coefficient and TRT as outcome and fit a logistic regression?

• $Y$ (the outcome) does not have to be normally distributed to fit a linear regression. The residuals of the regression are assumed to be normally distributed (see here, for example). Could you explain what the outcome is? – COOLSerdash Sep 29 '13 at 22:22
• Using TRT as the DV makes no sense. Treatment isn't a dependent variable. – Peter Flom - Reinstate Monica Sep 29 '13 at 22:37
• The Linear Regression Model does NOT need any kind of distributional assumptions. If a normality assumption is made, then we have the Normal Linear Regression Model, which is a special case of the former. – Alecos Papadopoulos Sep 29 '13 at 22:45
• @COOLSerdash Actually, it's the random errors that are assumed normal (and then only when using normality to produce inferences such as hypothesis tests or intervals). The residuals should approximate the errors, though, so they are useful for seeing if the assumptions that were made are at least reasonable. – Glen_b Sep 29 '13 at 23:25
• @COOLSerdash Sorry, correction: If we take the other assumptions as satisfied, then when $I-H$ is too far from $I$, $e$ will generally be a poor approximation for $ε$; we can adjust for the differences in variance, but they're still dependent and in some cases, highly so – Glen_b Sep 30 '13 at 0:04

COOLSerdash is right that only the residuals need to be normally distributed. However, When the $Y$ is skewed, the residuals will often be skewed in the same direction. So look at the residual plot before doing any transformations. For right skewed distributions like this one, you can use a $\log_{10}(x), 1/x$, or $\sqrt{x}$ transformation.