In his analysis of California's Proposition 103 (see Illustration 4.3), 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 drivers. Prohibiting the use of geographic location to assess the risk of a driver creates a substantial 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 favoring 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 V and P are inversely related:
DEPENDENT VARIABLE: S R-SQUARE F-RATIO P-VALUE ON F
OBSERVATIONS: 36 0.2247 4.781 0.0150
PARAMETER STANDARD
VARIABLE ESTIMATE ERROR T-RATIO P-VALUE
INTERCEPT 175086.0 63821.0 2.74 0.0098
A 0.8550 0.3250 2.63 0.0128
R 0.284 0.164 1.73 0.0927
158 PA R T I Some Preliminaries
Percent for Change in
Proposition 103 average premium
County (V) (P )
Los Angeles 62.8 21.4
Orange 51.7 8.2
San Francisco 65.2 0.9
Alameda 58.9 8.0
Marin 53.5 9.1
Santa Clara 51.0 11.8
San Mateo 52.8 12.6
Santa Cruz 54.2 13.0
Ventura 44.8 1.4
San Diego 44.1 10.7
Monterey 41.6 15.3
Sacramento 39.3 16.0
Tulare 28.7 23.3
Sutter 32.3 37.1
Lassen 29.9 46.5
Siskiyou 29.9 49.8
Modoc 23.2 57.6
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 a bP to see if voting behavior is related to the change in auto insurance premiums in a statistically significant way. Here is the regression output from the computer:
a. Does this regression equation provide evidence of a statistically significant relation 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?