# 8.4 - Estimating the standard deviation of the error term

8.4 - Estimating the standard deviation of the error termOur simple linear regression model is:

\(Y=\beta_0+\beta_1X+\epsilon\)

The errors for the \(n\) observations are denoted as \(\epsilon_i\), for \(i=1, …, n\). One of our assumptions is that the errors have equal variance (or equal standard deviation). We can estimate the standard deviation of the error by finding the standard deviation of the residuals, \(\hat{\epsilon}_i=\hat{y}_i-y_i\). Minitab also provides the estimate for us, denoted as \(S\), under the Model Summary. We can also calculate it by:

\(s=\sqrt{\text{MSE}}\)

Find the MSE in the ANOVA table, under the Adj MS column and the Error row. The value of 1.12 represents the average squared error. This becomes the denominator for the F test.

##### Analysis of Variance

Source | DF | Adj SS | Adj MS | F-Value | P-Value |
---|---|---|---|---|---|

Regression | 1 | 9281.7 | 9281.72 | 8267.30 | 0.000 |

Critical Areas | 1 | 9287.7 | 9281.72 | 8267.30 | 0.000 |

Error | 93 | 104.4 | 1.12 | ||

Total | 94 | 9386.1 |