F-ratio: Statistical Significance of the Overall Regression Model

The F-ratio, which follows the F-distribution, is the test statistic to assess the statistical significance of the overall model. It tests the hypothesis that the variation explained by regression model is more than the variation explained by the average value (ȳ).

$$ F =\frac{SS_{reg}/df_{reg}}{SS_{res}/df_{res}} $$ $$ = \frac{R^2/k}{(1-R^2)/(n-k-1)}$$


k is the number of explanatory variables, and n is sample size.

SSreg: Explained sum of squared deviation.

SSres: Residual (error) sum of squares.

dfreg: Degrees of freedom (regression) = number of estimated coefficients including intercept − 1 = number of explanatory variables (k).

dfres: Degrees of freedom (residual) = sample size (n) − (k+1).

R2: Coefficient of Determination (R2) is the proportion of the variance in the dependent variable that is predictable from the independent variable.

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