These statistics describe a standard regression including the constant:

ANOVA (analysis of variance) statistics for standard regression without a constant:

**Table 6. ANOVA Statistics, Standard Regression without a Constant**

Source | Sum of Squares | Degrees of Freedom | Mean Square | F Ratio |
---|---|---|---|---|

Regression | m | MSR = SSR/m | ||

Error | n – m | MSE = SSE/(n – m – 1) | ||

Total | n | n/a | n/a |

The F statistic follows an F distribution with (m, n – m) degrees of freedom. This information is used to calculate the p-value of the F statistic.

R^{2} is the coefficient of determination. This statistic represents the proportion of error for which the regression accounts.

You can use many methods to calculate R^{2}. Predictor uses the equation:

R^{2} can be extremely large in cases when the regression constant is omitted, even when the correlation between Y and X is weak. Because it can be meaningless, many applications do not mention this statistic. Predictor provides this statistic but it is not used for stepwise regression when there is no regression constant.

Adjusted R^{2} can be calculated for regression without a constant:

Adjusted R^{2} =

where n is the number of data points and m is the number of independent variables.

Like R^{2} for regression without a constant, this is also a very large number without much meaning.

SSE (standard error of measurement) is a measure of the amount the actual values differ from the fitted values. The formula for SSE:

where n is the number of data points you have and m is the number of independent variables.

The F statistic checks the significance of the relationship between the dependent variable and the particular combination of independent variables in the regression equation. The F statistic is based on the scale of the Y values, so analyze this statistic in combination with the p–value (described in the next section). When comparing the F statistics for similar sets of data with the same scale, the higher F statistic is better.

The formula for the F statistic is given in Table 5, ANOVA Statistics, Standard Regression with a Constant.

The statistics for the p^{th} coefficient for regressions without a constant are the same as those for regressions with a constant. See Statistics for Individual Coefficients.