Need help understanding P/T/F coeffs for simple/multiple linear regression, as well as ANOVA, VIF, etc


So I'm currently taking a stats class, and we've just gone over simple and multiple linear regressions. I get the basic idea and how to use it, yet I have a lot of trouble properly understanding the mathematical details, especially related to the different estimators and their variance, and the testing of the estimators using p t or f values. I also have trouble understanding ANOVA and VIF. I get R^2 though. I'm currently working on the next problem set, and it just shows me how little I understand everything.

This short powerpoint was one of our lectures last week:

I guess it's partly due to the super messy notation and everything having such similar names (SSE, SE, SST, Sxx, SD, etc), but as soon as the slides re-introduce the different random variables and how to convert whatever data we have about the regression into those random variables ot use them for hypothesis testing, I just lose all understanding needed.

I mainly don't understand the whole hypthesis testing of regression line coefficients thing. What does the t-value have to do with it? And on slide 8, how are we testing that b1 = 0? After all, the estimate for it is large, and the p-value small, but shouldnt we find out a large p value for the estimate being 0 instead?

Any advice or idea on what specific readings / video-watching I could do in order to understand this? Thanks a lot!
Last edited:


Active Member
Hi S,

You run the T-test for each coefficient, to check if the IV really help you to predict the DV (Y).
While the F test is for the entire model, comparing the model with all the IVs to the model without the IVs: (Y=b)

You need p-value to be small since this is the probability to reject a correct H0.

You can try to run your data in the following online calculator. If you will hover the ANOVA table I think you will get explanations for each value. You will also get some explanations to the VIF and the R squared.