To calculate the F-statistic in a simple linear regression study, follow these steps to create the ANOVA table:
- Calculate the regression sum of squares (RSS) by summing the squared differences between the predicted values and the mean of the dependent variable.
- Calculate the sum of squared errors (SSE) by summing the squared differences between the observed values and the predicted values of the dependent variable.
- Calculate the degrees of freedom for the model.
- Calculate the mean squared error (MSE) by dividing the SSE by the DF for the error.
- Calculate the regression mean squared error (MSR) by dividing the SSR by the DF for the model.
- 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.
