The following model with three regressors (including the constant, so k = 3) is estimated over fifteen observations (4.13)
and the following data have been calculated from the original xs Calculate the coefficient estimates and their standard errors.
(4.14)
To calculate the standard errors, an estimate of σ
2 is required (4.15)
The variance–covariance matrix of is given by (4.16)
The coefficient variances are on the diagonals, and the standard errors are found by taking the square roots of each of the coefficient variances (4.17)
(4.18)
(4.19)

The estimated equation would be written (4.20)
Fortunately, in practice all econometrics software packages will estimate the coefficient values and their standard errors. Clearly, though, it is still useful to understand where these estimates came from.