How Do You Perform a Test of the Overall Significance

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The Answer is You perform a test of the overall significance of the regression function by comparing the p-value for the overall regression (the significance F)to the chosen significance level.The null and alternative hypothesis for the test are

H _ { 0 } : \beta _ { 0 } = \beta _ { 1 } = \beta _ { 2 } = \ldots = \beta _ { k } = 0

H _ { A } :

at least one of

\beta _ { 0 } , \beta _ { 1 } , \beta _ { 2 } , \ldots , \beta _ { k } eq 0

The rejection rule for the 5 percent significance level is:

ext { Reject } H _ { 0 } ext { if

This test works for the following reason.By definition,the significance F is the probability of observing the estimated sample regression function that we actually observed if the true value of all of the population coefficients are 0.A very small value therefore indicates that it is very unlikely to observe the results that we actually observed if H₀ were actually true.Hence,if we observe a very small,the fact that we observed the results that we did observe provides statistical evidence that H₀ is likely not true.

How Do You Perform a Test of the Overall Significance

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