Multiple Linear Regression Question

Question

The computer output shown below is part of the regression analysis to predict the height of the gold medal winning high jump in the Olympics based on year and gender.

 

 

Predictor          Coef              SE Coef             T                P

Constant        -9.0965                 0.4708       -19.32        0.000
Year              0.0057426       0.0002409         23.84        0.000
Gender(M=0)  -0.34761           0.01537                          0.000

Source          Df         SS           MS          F         P
Regression     2        2.0735     1.0368              0.000
Error             4        0.1015      0.0024
Total             44       2.1751

 

 

This model will give:

A. Two parallel lines

B. A curve

C. Two parallel curves

D. Two non-parallel curves

E. A straight line

 

 

 

Answer 1

The correct answer is A: Two parallel lines.

This scenario is testing for a linear relationship between height of the gold medal winning jump as the dependent variable and year and gender as independent variables. Because gender is a categorical variable, it utilizes a dummy variable for males to equal 0 and females to equal 1.

The general equation for the regression line is y = a + b1x1 + b2x2, where y = the height of the gold medal winning jump, b1 = the slope for year, and b2 = the slope for gender.

By plugging in x2 = 0 for the males, the regression equation is y = -9.0965 + 0.0057426x.

By plugging in x2 = 1 for the females, the regression equation is y = -9.44411 + 0.0057426x.

Because the lines have the same slope but different y-intercepts, they are parallel, so the answer is A.