Imagine the two variable regression model:

Upper Y Subscript i equals beta 0 plus beta 1 Edu Subscript 1 i Baseline plus beta 2 Exp Subscript 2 i Baseline plus u Subscript i,where Y denotes the average monthly income, Edu denotes the number of years of education, Exp denotes the number of years of experience, and u Subscript i denotes the error term.

Suppose the researcher wants to test whether the effect of education on average monthly income and the effect of experience on the average monthly income of an individual are the same or not. So, the test the researcher wants to conduct is

Upper H 0 : beta 1 equals beta 2 vs. Upper H 1 : beta 1 not equals beta 2.

The hypotheses can be tested by modifying the original regression equation to turn the restriction into a restriction on a single regression coefficient.

Suppose the regression function is modified in the following way:

Upper Y Subscript i Baseline equals beta 0 plus gamma 1 Edu Subscript 1 i Baseline plus beta 2 Upper W Subscript 1 i Baseline plus u Subscript i comma where gamma 1 equals beta 1 minus beta 2 and Upper W Subscript i Baseline equals Edu Subscript 1 i Baseline plus Exp Subscript 2 i Baseline nbsp.Since

gamma 1 equals beta 1 minus beta 2, the test the researcher wants to conduct will now be

Upper H 0 : gamma equals 0 vs. Upper H 1 : gamma not equals 0.

Let

ModifyingAbove gamma with caret 1 and SE(ModifyingAbove gamma with caret 1), denote the estimated slope coefficient of gamma 1 and the standard error of ModifyingAbove gamma with caret 1, respectively.If SE(ModifyingAbove gamma with caret 1) is 1.14 and ModifyingAbove gamma with caret 1 is 0.67, then the 95% confidence interval for the difference between the coefficients,

beta 1 minus beta 2, denoted by gamma 1, is (?, ?).

Based on the calculated confidence interval, we can say that at the 5% significance level, we will

the null hypothesis

Upper H 0 : gamma equals 0