F test and t test are performed in regression models.
In linear model output in R, we get fitted values and expected values of response variable. Suppose I have height as explanatory variable and body weight as response variable for 100 data points.
Each variable (explanatory or independent variable, if we have multiple regression model) coefficient in linear model is associated with a t-value (along with its p value)? How is this t-value computed?
Also there is one F test at the end; again I am curious to know about its computation?
Also in ANOVA after linear model, I have seen a F-test.
Although I am new statistics learner and not from statistical background, I have gone through with lots of tutorials on this. Please do not suggest for going me with basic tutorials as i have already done that. I am only curious to know about the T and F test computation using some basic example.
Best Answer
The misunderstanding is your first premise "F test and $t$-test are performed between two populations", this is incorrect or at least incomplete. The $t$-test that is next to a coefficient tests the null hypothesis that that coefficient equals 0. If the corresponding variable is binary, for example 0 = male, 1 = female, then that describes the two populations but with the added complication that you also adjust for the other covariates in your model. If that variable is continuous, for example years of education, you can think of comparing someone with 0 years of education with someone with 1 years of education, and comparing someone with 1 years of education with someone with 2 years of education, etc, with the constraint that each step has the same effect on the expected outcome and again with the complication that you adjust for the other covariates in your model.
An F-test after linear regression tests the null hypothesis that all coefficients in your model except the constant are equal to 0. So the groups that you are comparing is even more complex.