Question

Perform hypothesis tests and confidence intervals for one coefficient

Answer 1

Hypothesis test for one coefficient

For the null hypothesis , assume we take as the true coefficient on ith regressor which takes value . This would form the null hypothesis . Here for generality , we are assuming a two tailed test

Null hypothesis = H₀ :   =  .

Alternative hypothesis = H_a:

Steps to perform hypothesis test

1) Define null and alternative hypothesiis which is done above

2) Determine the level of significance to be used

3) Calculate t statistic by first finding the standard error of the coefficient

The formula for t statistic is

z=

where n is the number of obervations

is the standard error of mean

4) Determine critical values.

5) Find whether to reject or not reject null hypothesis

6)State the conclusion

The confidence interval for one coefficient

For 95% confidence interval

95% CI=

Rearranging it for solving for we get

So the confidence interval would be