a. Does this regression equation provide evidence of statistically significant r

Question

a. Does this regression equation provide evidence of statistically significant relation between voter support for Proposition 103 in a country and changes in average auto premiums affected by Proposition 103 in the country? Perform an F-test at the 95%level of confidence
b. test the intercept estimate for significance at the 95 percent confide ce level. If Proposition 103 has no impact on auto insurance premiums in any given county, what percent of voters do you expect will vote for the proposition.
c. test the slope estimate for significance at the 95 percent confidence level. If P increases by 10 percent, by what percent does the vltw for Proposition 103 decline

CHAPTER 4 Basic Estimation Techniques 155 2. In his analysis of California's Proposition 103 (see llustration that one of the most important provisions of this proposition is eliminating the practice by insurance companies of basing premiums (in p geographic location of driv ers. Prohibiting the use of geographic location to assess th risk of a driver ereates a sub- stantial implicit subsidy from low-loss counties to high-loss counties, such as Los Angeles, orange, and San Francisco counties Zycher hypothesizes that the percent of voters favor. ing Proposition 103 in a given county (V) isinversely related to the (average) peroentage change in auto premiums that the propositionconfersupon the drivers of that aunty V The data in the table below were presented by Zycher to support his contention that and p inversely related: Percent for Change in Proposition 103 average premium 628 652 53 Using the data in thetable, we ehtimated the regn equation to see if voting behavior is bo the in aub premiur tically significant way.Here is the on output from the computer DEPENDENT VARIABLE: A-SouARE F-RATIo P-VALUE ONF 42674 0001 oBSERVATIONS 17 0.7309 STANDARD TRATIo ESTIMATE ERROR 0.0B1

Explanation / Answer

Solution:

Part a

Here, we have to test the significance of the statistical relationship between the two variables by using the regression model. We have to test whether there is a significant relationship between the voter support for Proposition 103 in a country and changes in average auto premiums affected by Proposition 103 in the country. From the given regression output, the F test statistic value is given as 42.674 with the P-value of 0.0001.

We are given a confidence level = c = 95% = 0.95

Level of significance = alpha = 1 – 0.95 = 0.05

P-value = 0.0001 < Alpha = 0.05

So, according to decision rule, we reject the null hypothesis that there is no any significant statistical relationship exists between the voter support for Proposition 103 in a country and changes in average auto premiums affected by Proposition 103 in the country.

This means we conclude that there is sufficient evidence that there is statistically significant relationship exists between the voter support for Proposition 103 in a country and changes in average auto premiums affected by Proposition 103 in the country.

Part b

Here, we have to test the intercept estimate for significance at the 95% confidence level.

We are given a confidence level = c = 95% = 0.95

Level of significance = alpha = 1 – 0.95 = 0.05

The test statistic value t for this test is given as 25.42 with the P-value of 0.0001.

P-value = 0.0001 < Alpha = 0.05

So, according to decision rule, we reject the null hypothesis that the intercept for the given regression equation is not statistically significant. This means we conclude that the intercept for the given regression model is statistically significant.

If Proposition 103 has no impact on auto insurance premiums in any given country, then we expect that approximately 54 percent of voters will vote for the proposition.

Part c

Here, we have to test the slope of the given regression model.

The slope for this regression model is given as -0.528 with test statistic value -6.52. we are given

P-value = 0.0001

Alpha value = 0.05

P-value < Alpha value

Reject the null hypothesis

We reject the null hypothesis that the given slope for the regression model is not statistically significant.

We conclude that the given slope for the regression model is statistically significant.

If P increases by 10 percent, then about 5.28 percent vltw for proposition 103 declines.

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