Difference between sample regression and population regression line?


A sample is a subset of a population. Usually it is impossible to test an entire population so tests are done on a sample of that population. These samples can be selected so that they are representative of the population in which cases the sample will have weights, strata, and clusters. But usually people use random samples. So it's not that the line is different, it's that the line comes from different data. In stats we have formulas that allow a sample to represent a population, if you have the entire population (again unlikely), you wouldn't need to use this sample formulas, only the population formulas.