Question

A researcher is trying to decide whether or not to use a regression model to forecast future values of the dependant variable Y, based on the behaviour of 3 independent variables X. With a sample size of n = 64, the researcher has calculated the value of SSR = 30 and SSE = 10.

What would be your advice to this researcher at 5% level of significance? How much of the variation in Y is accounted for the regression equation? Would you change your answers for a higher level of significance? Is each of the independent variables X significant? (20 points)

Answer 1

Solution:

Since there are three independent variables so degree of freedom of regression is

And degree of freedom of residual is

Now

So F test statistics for model is

The p-value for F= 60.24, df1=3,df2=60 is 0.0000.

Since p-value is less than 0.05 so model is signficant at 5% level of signficance.

Since p-value is less than 0.01 so model is signficant at 1% level of signficance.

No answer will not change for lower signfcance level becuase p-value is zero.

It cannot find from the given information that each variable is signficant or not.

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