Question

After running a regression on 60 monthly observations of a fund's returns on the returns of a stock market index, you find the estimate of the slope coefficient of 0.73 with a standard error of 0.27. You are interested in testing the hypothesis of whether the slope is equal to 1. What is the t-statistic for this hypothesis test?

(Bonus thinking question: can you reject the null hypothesis that the slope = 1 at a 5% confidence level?)

The answer is -1

Please show how to get there

Answer 1

Provided n=60

,

At 5% level of significance, we want to test the claim that the slope is equal to 1.

The null and alternative hypothesis are:

The test statistic is:

There are total n=60 observations, therefore, the degrees of freedom for the test are n-2=58

Thus the t critical value at 5% level of significance for two tail test is:

    ### By using t table. Since the critical value for 58 degrees of freedom is not in the table, we used for 60 degrees of freedom

Since, , We are unable to reject the null hypothesis at 5% level of significance.

Therefore, we do not have enough evidence to reject the claim that the slope is equal to 1.