Source DF Seq SS

X1 1 4624.1

X2 1 200.4

D 1 28.6

a) The estimated regression equation is

(1)

We also can use column labeled COEF and write the estimated regression equation as

(2)

b) The coefficient of the variable gender is . It indicates that the female drivers pay, an average, $3.573 more than male drivers with similar driving experiences and the same number of driving violations.

In fact, by using dummy variable D in our regression model, we have estimated two regression models: one for male drivers, and another for the female drivers. Since for male drivers , after substituting it into the estimated regression model we find the estimated model for male drivers as

For female drivers . Substituting it in the regression model, we obtain the estimated regression model for the female drivers

We see that, the constant term for female drivers is 3.573 greater than that for the male drivers’ model. Thus, on average, female drivers pay a yearly auto insurance premium that is $3.573 more than the yearly auto insurance premium paid by male drivers with similar driving experiences and the same number of driving violations.

c) To find the predicted auto insurance premium for a male driver with 14 years of driving experience and 3 driving violations, we substitute , , and in the estimated regression model (2),

Thus, a male driver with 14 years of driving experience and 3 driving violations is expected to pay a yearly auto insurance premium of $45.765.

d) To find the predicted auto insurance premium for a female driver with 14 years of driving experience and 3 driving violations, we substitute , , and in the estimated regression model (2),

Thus, a female driver with 14 years of driving experience and 3 driving violations is expected to pay a yearly auto insurance premium of $49.338.

e) We are to make a 99% confidence interval for . From the given information and from the MINITAB solution we obtain

; ; and

So, from

a 99% confidence interval for is

Thus, the 99% confidence interval for is -$32.863 to $40.009. We can state with 99% confidence that female drivers pay somewhere between $32.863 less than to $40.009more than male drivers with similar values for the and variables.

f) We are to test whether or not the coefficient of gender in model (1) is zero. The two hypotheses are

The decision rule is

Reject if or

From MINITAB solution we find that the value of test statistic is

and

Since 0.36 is not greater than 3.707, the value of test statistic falls in the non rejection region. Consequently, we fail to reject the null hypothesis and conclude that in regression model is not different from zero. That is, the variable gender has no effect on the auto insurance premiums paid by drivers.

Remark:

The number of dummy variables used for qualitative variable in a regression model is one less than the number of categories for that variable. For example, we may want to investigate influence of quarters. Because the variable quarter is a qualitative variable, we will use dummy variables to represent it in our regression model. Since there are 4 quarters in a year, we will use 3 dummy variables. Let be the dummy variable for the first quarter, be the dummy variable for the second quarter and be the dummy variable for the third quarter. Then

for the first quarter, and zero for other quarters

for the second quarter, and zero for other quarters

for the third quarter, and zero for other quarters

If our regression model consists of two independent variables and , then we will estimate regression model as

Дата добавления: 2015-08-05