Statistics, Standard Regression without Constant

These statistics describe a standard regression including the constant:

ANOVA, No Constant

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

Table 6. ANOVA Statistics, Standard Regression without a Constant

SourceSum of SquaresDegrees of FreedomMean SquareF Ratio
RegressionFormula for regression sum of squares without constantmMSR = SSR/mFormula for F ratio; F equals MSR divided by MSE
ErrorFormula for SSE, regression errorn – mMSE = SSE/(nm – 1)Formula for F ratio; F equals MSR divided by MSE
TotalFormula for total sum of squares, regression without constantnn/an/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.

R2, No Constant

R2 is the coefficient of determination. This statistic represents the proportion of error for which the regression accounts.

You can use many methods to calculate R2. Predictor uses the equation:

Formula for R2 for regression without a constant

R2 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 R2, No Constant

Adjusted R2 can be calculated for regression without a constant:

Adjusted R2 =

Formula for adjusted R squared for regression without a constant

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

Like R2 for regression without a constant, this is also a very large number without much meaning.

SSE, No Constant

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

Formula for standard error of estimate for regression without a constant

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

F, No Constant

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.

Statistics for Individual Coefficients, No Constant

The statistics for the pth coefficient for regressions without a constant are the same as those for regressions with a constant. See Statistics for Individual Coefficients.