# Multiple Regression

Thompson Machine Works purchased several new, highly sophisticated machines. The production department needed some guidance with respect to qualifications needed by an operator. Four variables were listed.

X1 = Length of time employee was a machinist

X2 = Mechanical aptitude test score

X3 = Prior on -the-job rating

X4 = Age

Performance on the machine is designated Y

The following are the results of the regression analysis;

Independent

Variable Coefficient t-stat

Intercept 11.600 2.95

X1 0.400 1.23

X2 0.286 3.71

X3 0.112 4.10

X4 0.002 1.86

a. Write out the multiple regression equation.

b. How many independent variables are there?

c. Would you consider eliminating any of the independent variables?

Assume a very large sample size with the degrees of freedom being greater than 60.

2. Suppose the regression equation that has been used to estimate the value of existing homes is as follows;

Value = 10,000 + 50X1 + 5X2 + 10,000X3

Where;

X1 is square feet of livable area

X2 is the size of the lot measured in square feet

X3 is an indicator variable for the presence of a pool (1 if yes, 0 if no)

a. Interpret the meaning of the slopes of this equation.

b. Estimate the value of a home with 2,000 square feet of livable area, 10,000 square foot lot, and a pool.

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#### Solution Preview

1.a. Write out the multiple regression equation.

The multiple regression equation is

Y = 11.6 + 0.4 X1 + 0.286 X2 + 0.112 X3 + 0.002 X4

b. How many independent variables are there?

There are four independent variables and they are X1, X2, X3 and X4.

c. Would you consider eliminating any of the independent variables?

Assume a very large sample size with the degrees of freedom being greater than 60.

Since the sample size is large we can approximate the distribution of the test statistic for testing the significance of the coefficient of the independent variable to a Standard Normal distribution. ...

#### Solution Summary

The explanation of the output of a multiple regression analysis is discussed in the solution.