F-statistic

PrepNuggets

F = MSR / MSE

To calculate the F-statistic in a simple linear regression study, follow these steps to create the ANOVA table:

  1. Calculate the regression sum of squares (RSS) by summing the squared differences between the predicted values and the mean of the dependent variable.
  2. Calculate the sum of squared errors (SSE) by summing the squared differences between the observed values and the predicted values of the dependent variable.
  3. Calculate the degrees of freedom for the model.
  4. Calculate the mean squared error (MSE) by dividing the SSE by the DF for the error.
  5. Calculate the regression mean squared error (MSR) by dividing the SSR by the DF for the model.
  6. Calculate the F-statistic by dividing the MSR by the MSE.

To interpret the F-statistic, compare it to a critical value from an F-table or a p-value from a statistical software package. If the F-statistic is significantly large, it indicates that the regression model is significantly better than just predicting the mean of the dependent variable. If the F-statistic is not significantly large, it indicates that the regression model is not significantly better than just predicting the mean.

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