More on data transformations No recipes, but some advice.

If the primary problem is non-linearity, look at a scatter plot of the data to suggest plausible transformations. It is possible to use transformations other than ln(x) and ln(y).

Try fitting if the trend in your data follows either of these patterns.

Try fitting if the trend in your data follows either of these patterns.

Try fitting if the trend in your data follows either of these patterns.

Try fitting if the trend in your data follows either of these patterns.

Try fitting if the trend in your data follows any of these patterns.

If the variances are unequal and/or error terms are not normal, try a “power transformation” on y.

Family of power transformations A power transformation on y involves transforming the response by taking it to some power λ. That is: Most commonly, for interpretation reasons, λ is a number between -1 and 2, such as -1, -0.5, 0, 0.5, (1), 1.5, and 2. When λ = 0, the transformation is taken to be the natural log transformation. That is:

If the variances are unequal, try “stabilizing the variance” by transforming y.

If the response y is a Poisson count… A common (now archaic?) recommendation is to transform the response using the square root transformation: and stay within the linear regression framework. Perhaps, now, the advice should be to use Poisson regression.

If the response y is a binomial proportion... A common (now archaic?) recommendation is to transform the response using the arcsine transformation: and stay within the linear regression framework. Perhaps, now, the advice should be to use a form of logistic regression.

If the response y isn’t anything special… A common recommendation is to try the natural log transformation: Or the reciprocal transformation:

It’s okay to remove some data points to make the transformation work better. Just make sure you report the scope of the model.

It’s better to give up some model fit than to lose clear interpretations. Just make sure you report that that’s what you did.