T-stat vs. F-stat

The t-stat is used to test the significance of the individual independent variables.
E.g. intercept = 0 v intercept <> 0, or b1 = 1 v b1 <> 1
F-test is used to test if at least one of the independent variablesis significantly different from 0.
The null hypothesis is b1 = b2 = … = bn = 0. The alternative hypothesis is that at least one of them differs from 0.
 
You use a t-statistic when you’re trying to determine whether a particular regression coefficient – the intercept or a slope coefficient – could equal a particular value; in the case of slope coefficients, the most common value against which you are testing them is zero. If your sample size is large (≥ 30), you can use a z-statistic if you like.
You use an F-statistic when you’re trying to determine whether all of the slope coefficients (taken together, as a group) could be zero.
So:
  • Intercept: use a t-statistic
  • Single slope: use a t-statistic
  • All slopes (together): use an F-statistic
 
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