Most analysts’ primary focus is to check the distributional assumptions with regards to residuals. They must be independent and identically distributed (i.i.d.) with a mean of zero and constant variance.
Residuals can also give us insight into the quality of our models.
In this webinar, we’ll review and compare what residuals are in linear regression, ANOVA, and generalized linear models. Jeff will cover:
- Which residuals — standardized, studentized, Pearson, deviance, etc. — we use and why
- How to determine if distributional assumptions have been met
- How to use graphs to discover issues like non-linearity, omitted variables, and heteroskedasticity
Knowing how to piece this information together will improve your statistical modeling skills.
Note: This training is an exclusive benefit to members of the Statistically Speaking Membership Program and part of the Stat’s Amore Trainings Series. Each Stat’s Amore Training is approximately 90 minutes long.
I was recently asked about whether centering (subtracting the mean) a predictor variable in a regression model has the same effect as standardizing (converting it to a Z score). My response:
They are similar but not the same.
In centering, you are changing the values but not the scale. So a predictor that is centered at the mean has new values–the entire scale has shifted so that the mean now has a value of 0, but one unit is still one unit. The intercept will change, but the regression coefficient for that variable will not. Since the regression coefficient is interpreted as the effect on the mean of Y for each one unit difference in X, it doesn’t change when X is centered.
And incidentally, despite the name, you don’t have to center at the mean. It is often convenient, but there can be advantages of choosing a more meaningful value that is also toward the center of the scale.
But a Z-score also changes the scale. A one-unit difference now means a one-standard deviation difference. You will interpret the coefficient differently. This is usually done so you can compare coefficients for predictors that were measured on different scales. I can’t think of an advantage for doing this for an interaction.