Dick Engstrom and Mike MacDonald are interested in the relationship between African-American representation on city councils and the structure of the electoral system. Their independent variable is the percentage of African Americans in the population; their dependent variable is the percentage of seats on the city council that are held by African Americans. Engstrom and MacDonald want to compare representation under single- member district election systems and under at-large election systems. They get the following results:
At-Large Systems
 = .348 + .495X
r2 = .34 n = 128 sb = .061 Sy|x = 2.4 X = 15 sx = 5.1
Single-Member District Systems
 = 2.832 + .994X
r2 = .816 n = 36 sb = .075 Sy|x = 2.1 X = 20 sx = 8
For each equation, interpret the slope, intercept, and coefficient of determination. Test the slope to see whether it could be zero. Get the predicted city council representation of a city with 25% African-American population under both systems. Place a 95% confidence limit around your estimates. Present a hypothesis about the relative impact of electoral systems. What can you say about the relative representation of African Americans under each type of system?

  • CreatedNovember 11, 2015
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