Question

Consider the accompanying set of dependent and independent variables. The variable x3 is qualitative with H= High, M= Medium, and L= Low. Complete parts a and b below.

y   x1   x2   x3
70   51   73   L
60   42   64   M
63   37   80   H
52   42   50   M
40   28   42   L
43   22   45   L
35   20   37   M
10   16   18   H
4   12   13   H

a. Using​ technology, construct a regression model using all three independent variables.​ (Let variable Cond 1 be one of the dummy variables forx3. Assign a 1 to High for this variable. Let Cond 2 be another dummy variable for x3. Assign a 1 to Medium for this​ variable.) Complete the regression equation for the model​ below, where x3 represents the dummy variable Cond 1, and x4 represents the dummy variable Cond 2.

y= __ + () x1+ () x2+ () x3+ () x4

b) Interpret the meaning of each of the regression coefficients. Select the correct choice below and fill in the answer boxes to complete your choice. (Round to four decimal places)

a. Increasing x₁ by 1 unit increases y by an average of (     ) units. Increasing x₂ by 1 unit decreases y by an average of (    ) units. Females decrease y by an average of (     ) units when compared with males.

b. Increasing x₁ by 1 unit increases y by an average of (     ) units. Increasing x₂ by 1 unit decreases y by an average of (    ) units. Males increase y by an average of (     ) units when compared with females.

c. Increasing x₁ by 1 unit increases y by an average of (     ) units. Increasing x₂ by 1 unit decreases y by an average of (    ) units. Increasing x₃ by 1 unit increases y by an average of (     ) units.

Answer 1

Answer a.

The Regression Equation is given using the coefficients highlighted in Yellow in the Excel Output.

y = 1.69032 + (0.229958)x1 + (0.779396)x2 + (-.984371)x3 + (0.108229)x4

Answer b.

Increasing x₁ by 1 unit increases y by an average of ( 0.2300) units. Increasing x₂ by 1 unit increases y by an average of ( 0.7794 ) units. Increasing x₃ by 1 unit decreases y by an average of ( 0.9844 ) units.