Inference in the linear regression context aims to draw conclusions about the true relationship in the population from the sample data. This includes tests of hypothesis about the significance of the overall relationship or the values of particular coefficients, as well as estimates of confidence intervals.
The key ingredient for statistical inference is a test statistic with a known distribution. We can use it to assume that the null hypothesis is true and compute the probability of observing the value for this statistic in the sample, familiar as the p-value. If the p-value drops below a significance threshold (typically five percent) then we reject the hypothesis because it makes the actual sample value ...
