7.12 Looking ahead

The next unit takes the first step described above: measuring the variables that create the bias, and comparing observations that are alike in those respects.

Remarkably little new machinery is required. The same least squares criterion, the same normal equations, the same \(t\) statistics, the same standard errors — all of it carries over with an extra column of data attached.

What changes is the meaning of a coefficient. In a simple regression \(\hat{\beta}_1\) answered “how does average \(y\) differ across values of \(x\)?” With more than one explanatory variable it answers something considerably more useful, and considerably easier to misread.