Question

Using your own words explain the meaning of the global significance test. Show how the null and alternative hypothesis are setup, the F test and what the critical value for this test is.

Answer 1

See wit example:

The F-test of the overall significance is a specific form of the F-test. It compares a model with no predictors to the model that you specify. A regression model that contains no predictors is also known as an intercept-only model.

The hypotheses for the F-test of the overall significance are as follows:

• Null hypothesis: The fit of the intercept-only model and your model are equal.
• Alternative hypothesis: The fit of the intercept-only model is significantly reduced compared to your model.

In Minitab statistical software, you'll find the F-test for overall significance in the Analysis of Variance table.

If the P value for the F-test of overall significance test is less than your significance level, you can reject the null-hypothesis and conclude that your model provides a better fit than the intercept-only model.

Compare the p-value for the F-test to your significance level. If the p-value is less than the significance level, your sample data provide sufficient evidence to conclude that your regression model fits the data better than the model with no independent variables.

This finding is good news because it means that the independent variables in your model improve the fit!

Generally speaking, if none of your independent variables are statistically significant, the overall F-test is also not statistically significant. Occasionally, the tests can produce conflicting results. This disagreement can occur because the F-test of overall significance assesses all of the coefficients jointly whereas the t-test for each coefficient examines them individually. For example, the overall F-test can find that the coefficients are significant jointly while the t-tests can fail to find significance individually.