Chapter 13, Problem 13.1P

The data sets in the first three problems are unrealistically small to allow you to practice the computational routines presented in this chapter. Most problems use SPSS.

In problem 12.1, data regarding voter turnout in five cities was presented. For the sake of convenience, the data for three of the variables arc presented again here along with descriptive statistics and zero order correlations.

City		Turnout	Unemployment Rate	% Negative Ads
A		55	5	60
B		60	8	63
C		65	9	55
D		68	9	53
E		70	10	48
$\text{Mean}=$		63.6	8.2	55.8
$s=$		5.5	1.7	5.3
		Unemployment Rate	Negative Ads
Turnout		0.95	$-0.87$
Unemployment rate			$-0.70$

a. Compute the partial correlation coefficient for the relationship between turnout $\left(Y\right)$ and unemployment $\left(X\right)$ while controlling for the effect of negative advertising $\left(Z\right)$. What effect does this control variable have on the bivariate relationship? Is the relationship between turnout and unemployment direct? (HINT: Use Formula 13.1)

b. Compute the partial correlation coefficient for the relationship between turnout $\left(Y\right)$ and negative advertising $\left(X\right)$ while controlling for the effect of unemployment $\left(Z\right)$. What effect does this have on the bivariate relationship? Is the relationship between turnout and negative advertising direct? (HINT: Use Formula 13. 1 You will need this partial correlation to compute the multiple correlation coefficient.)

c. Find the unstandardized multiple regression equation with unemployment $\left(X_1\right)$ and negative ads $\left(X_2\right)$ 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? (HINT: Use Formulas 13.4 and 13.5 to compute the partial slopes and then use Formula 13.6 to find $a$, the $Y$ intercept. The regression line is stated in formula 13.3. Substitute 10 for $X_1$ and 75 for $X_2$, 10 compute predicted $Y$.)

d. Compute beta-weights for each independent variable. Which has the stronger impact on turnout? (HINT: Use Formulas 13. 7 and 13.8 to calculate the beta-weights.)

e. Compute the coefficient of multiple determination $\left(R^2\right)$. How much of the variance in voter turnout is explained by the two independent variables combined? (HINT: Use Formula 13. 11. You calculated $r_{y2.1}^2$. in part b of this problem.)

f. Write a paragraph summarizing your conclusions about the relationships among these three variables.