In Problem 13.1, data regarding voter turnout in five cities were presented. For the sake of convenience, the data for three of the variables are presented again here along with descriptive statistics and zero-order correlations.
a. Compute the partial correlation coefficient for the relationship between turnout (Y ) and unemployment (X ) while controlling for the effect of negative advertising (Z ). What effect does this control variable have on the bivariate relationship? Is the relationship between turnout and unemployment direct?
b. Compute the partial correlation coefficient for the relationship between turnout (Y ) and negative advertising (X ) while controlling for the effect of unemployment (Z ). What effect does this have on the bivariate relationship? Is the relationship between turnout and negative advertising direct?
c. Find the unstandardized multiple regression equation with unemployment (X1) and negative ads (X2) as the independent variables. What turnout would be expected in a city in which the unemployment rate was 10% and 75% of the campaign ads were negative?
d. Compute beta-weights for each independent variable. Which has the stronger impact on turnout?
e. Compute the multiple correlation coefficient (R ) and the coefficient of multiple determination (R 2 ). How much of the variance in voter turnout is explained by the two independent variables?
f. Write a paragraph summarizing your conclusions about the relationships among these three variables.
Problem 13.1
Why does voter turnout vary from election to election? For municipal elections in five different cities, information has been gathered on the percentage of eligible voters who actually voted, unemployment rate, average years of education for the city, and the percentage of all political ads that used “negative campaigning” (personal attacks, negative portrayals of the opponent’s record, etc.). For each relationship:
a. Draw a scattergram and a freehand regression line
b. Compute the slope (b) and find the Y intercept (a).
c. State the least-squares regression line and predict the voter turnout for a city in which the unemployment rate was 12, a city in which the average years of schooling was 11, and an election in which 90% of the ads were negative.
d. Compute r and r2
.
e. Assume these cities are a random sample and conduct a test of significance for each relationship.
f. Describe the strength and direction of the relationships in a sentence or two. Which (if any) relationships were significant? Which factor had the strongest effect on turnout?