Consider the two variable regression model: Y = Bo+ B,Edu + B2Exp21 + U. 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, 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 Ho: B, = B, vs. H, B, #B2. 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: Y, = Bo +Y,Edu+ B2W, + u, where y, = B,-B2 and W, = Edu, + Exp2 Since y = B, - B2, the test the researcher wants to conduct will now be Ho: y=0 vs. H,: y 0. Let y, and SE,), denote the estimated slope coefficient of Y, and the standard error of 71, respectively. If SEG,) is 1.14 and y, is 1.75, then the 95% confidence interval for the difference between the coefficients, B, - B2, denoted by y1, is ) (Round your answer to two decimal places. Enter a minus sign if your answer is negative.) v the null hypothesis Ho y=0. Based on the calculated confidence interval, we can say that at the 5% significance level, we will reject fail to reject Enter your answer in each of the answer boxes.
Consider the two variable regression model: Y = Bo+ B,Edu + B2Exp21 + U. 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, 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 Ho: B, = B, vs. H, B, #B2. 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: Y, = Bo +Y,Edu+ B2W, + u, where y, = B,-B2 and W, = Edu, + Exp2 Since y = B, - B2, the test the researcher wants to conduct will now be Ho: y=0 vs. H,: y 0. Let y, and SE,), denote the estimated slope coefficient of Y, and the standard error of 71, respectively. If SEG,) is 1.14 and y, is 1.75, then the 95% confidence interval for the difference between the coefficients, B, - B2, denoted by y1, is ) (Round your answer to two decimal places. Enter a minus sign if your answer is negative.) v the null hypothesis Ho y=0. Based on the calculated confidence interval, we can say that at the 5% significance level, we will reject fail to reject Enter your answer in each of the answer boxes.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.CR: Review Exercises
Problem 90CR
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Transcribed Image Text:Consider the two variable regression model:
Y = Bo+P,Edu+ B2EXP21 + u,
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, 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 Ho: B = 6, vs. H, f,+P2 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:
Y, Po+Y,Edu, +
B2W +u, where y, =P,-P2 and W, = Edu,, + Exp2i
%D
Since y, = B, - B2, the test the researcher wants to conduct will now be Ho: y=0 vs. H y0. Let y, and SE(y,), denote the estimated slope coefficient of y, and the
standard error of 7, respectively.
is .D
IS
If SE(y,) is 1.14 and y, is 1.75, then the 95% confidence interval for the difference between the coefficients, B,- B,, denoted by y,
(Round your answer to two decimal places. Enter a minus sign if your answer is negative.)
the null hypothesis Ho: y=0.
Based on the calculated confidence interval, we can say that at the 5% significance level, we will
reject
fail to reject
Enter your answer in each of the answer boxes.
P.
DELL
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