2. In his analysis of California's Proposition 103 (see Illustration 4.2), Benjamin Zycher notes that one of the most im

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2 In His Analysis Of California S Proposition 103 See Illustration 4 2 Benjamin Zycher Notes That One Of The Most Im 1 (277.98 KiB) Viewed 27 times

2. In his analysis of California's Proposition 103 (see Illustration 4.2), Benjamin Zycher notes that one of the most important provisions of this proposition is eliminating the practice by insurance companies of basing premiums (in part) on the geographic location of driv- ers. Prohibiting the use of geographic location to assess the risk of a driver creates 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) is inversely related to the average) percentage change in auto premiums (P) that the proposition confers upon the drivers of that county. The data in the table below were presented by Zycher to support his contention that Vand Pare inversely related: Percent for Change in Proposition 103 average premium County ( IP) ] Los Angeles 62.8 - 21.4 Orange 51.7 -82 San Francisca 65.2 -0.9 Alameda 58.9 +8.0 Marin 53.5 +9.1 51.0 +118 52.8 +126 129 Santa Cruz + 13.0 Ventura +1.4 San Diego Monterey +15.3 Sacramento 39.3 + 16.0 Tulare 28.7 +233 Sutter 323 +37.1 Lassen +46.5 Siskiyou 29.9 +49 8 Moder 23.2 +576 Sources: California Department of Insurance and Office of the California Secretary of State Using the data in the table, we estimated the regression equation V V = a +bP to see if voting behavior is related to the change in auto insurance premiums in a statis- tically significant way. Here is the regression output from the computer: Santa Clara San Mateo 542 44.8 44.1 + 10.7 41.5 29.9 DEPENDENT VARIABLE: V R-SQUARE F-RATIO P-VALUE ON F 0.0001 OBSERVATIONS: 17 0.7399 42.674 PARAMETER STANDARD VARIABLE ESTIMATE ERROR T-RATIO T INTERCEPT 53.682 2.112 25.42 P -0.528 0.081 -6.52 P-VALUE P 0.0001 0.0001 156 CHAPTER 4 Basic Estimation Techniques a. Does this regression equation provide evidence of a statistically significant rela- tion between voter support for Proposition 103 in a county and changes in average auto premiums affected by Proposition 103 in that county? Perform an F-test at the 95 percent level of confidence. b. Test the intercept estimate for significance at the 95 percent confidence 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 vote for Proposition 103 decline?