I just wanted to follow up on my last post about Regression without Intercepts.
Regression through the Origin means that you purposely drop the intercept from the model. When X=0, Y must = 0.
The thing to be careful about in choosing any regression model is that it fit the data well. Pretty much the only time that a regression through the origin will fit better than a model with an intercept is if the point X=0, Y=0 is required by the data.
Yes, leaving out the intercept will increase your df by 1, since you’re not estimating one parameter. But unless your sample size is really, really small, it won’t matter. So it really has no advantages.
Is it appropriate to use regression through the origin when both the dependent and independent variables are relative frequencies (i.e. percent of time observed) for paired categories, i.e. 16 compass directions last year vs. this year? if the goal is to predict current/future wind direction frequencies from past data, wouldn’t it be expected that there is no intercept?
If this is the case, what would then the test statistic for the slope be? Is it still t distribution with n-2 df?
If you’re dropping the intercept, the test statistic for the slope is still a t, but the df change to n-1. Dropping the intercept frees up one df.