Computer solution of multiple regressions

Usually the calculations for a multiple regression model are made by using statistical software package for computers, such as MINITAB, instead of using the formula manually. In this chapter we will analyze the multiple regression models using MINITAB statistical software. The solutions obtained using other packages can be interpreted the same way.

Remark:

To use MINITAB menu follow the following instructions

1. Select Stat>Regression

2. Select Response column

3. Select Predictors columns

4. Click OK.

Example1:

Suppose that we want to find the effect of driving experience and the number of driving violations on auto insurance premiums. A random sample of 10 drivers insured with a company and having similar auto insurance policies was selected. Table 4.1 lists the yearly auto insurance premiums (in dollars) paid by these drivers, y, their driving experience (, in years), and the number of driving violations that each of them has committed during the past five years.

Table 4.1

Use a computer package to perform a regression analysis using model

and answer the following questions:

a) Write the estimated regression equation;

b) Interpret the meaning of the estimated regression coefficients;

c) What are the values of the variance and standard deviation of errors, the coefficient of determination, and the adjusted coefficient of determination?

d) What is the predicted auto insurance premium paid per month by a driver with seven years of experience and four driving violations?

Solution:

Using MINITAB, we first enter the data of y, , in three different columns and then use the regression command. The computer executes a multiple regression analysis. We focus our attention on the principal aspects of the output as shown in Figure 4.1

Figure 4.1

The regression equation is

Y= 87.9 - 3.39 X1 + 2.33 X2

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