Solutions to Healey 2/3e #13.1 (1e #15.1) Turnout by Unemployment and by Negative Campaigning

Data from Problem: Turnout x Unemployment Rate The scores on each variable are displayed in table format: –Y = % Turnout –X = Unemployment Rate CityXY A555 B860 C965 D968 E1070

1. Draw and Interpret the Scattergram: The relationship between X and Y is linear and homoscedastic. Estimate regression line: Relationship is positive and strong.

2. Make a Computational Table: XYX2X2 Y2Y2 XY ∑ X = 41 ∑Y = 318 ∑ X 2 = 351 ∑Y 2 = ∑XY = 2652

3. Next, calculate b and a…. Calculate slope: Calculate y-intercept:

Find the Regression Line*: Prediction equation: *Note: you can now substitute two values for X to solve for Y to find points to plot the actual regression line on your scattergram and to use for prediction.

Calculate and Interpret Pearson’s r An r of indicates a strong relationship between unemployment rate and voter turnout for these five cities (use the table given for gamma to estimate strength)

5. Find the Coefficient of Determination (r 2 ) and Interpret: The coefficient of determination is r 2 =.893. Unemployment rate, by itself, explains 89.3% of the variation in voter turnout.

6. Testing r for significance: Use the 5 step model from powerpoint df = n - 2 = 3, α =.05, t cr = +/ Decision: Reject H 0 Interpretation: The association between voter turnout and unemployment rate is significant (t=4.997, df=3, α =.05

Always include a brief summary of your results: There is a very strong, positive relationship between % voter turnout and unemployment rate for the five cities. As years of schooling increase, the % of voter turnout goes up. The relationship is significant (t=4.997, df=3, α =.05). Unemployment rate explains 89.3% of the variation in voter turnout.

Data from Problem: Turnout x Negative Campaigning The scores on each variable are displayed in table format: –Y = % Turnout –X = Negative campaigning CityXY A6055 B6360 C5565 D5368 E4870

1. Draw and Interpret the Scattergram: The relationship between X and Y is linear. Estimate regression line: Relationship is negative and moderately strong.

2. Make a Computational Table: XYX2X2 Y2Y2 XY ∑ X = 279 ∑Y = 318 ∑ X 2 = ∑Y 2 = ∑XY = 17619

3. Next, calculate b and a…. Calculate slope: Calculate y-intercept:

Find the Regression Line*: Prediction equation: *Note: you can now substitute two values for X to solve for Y to find points to plot the actual regression line on your scattergram and to use for prediction.

Calculate and Interpret Pearson’s r An r of indicates a strong negative relationship between negative campaigning and voter turnout for these five cities (use the table given for gamma to estimate strength)

5. Find the Coefficient of Determination (r 2 ) and Interpret: The coefficient of determination is r 2 =.759. Negative campaigning, by itself, explains 75.9% of the variation in voter turnout.

6. Testing r for significance: Use the 5 step model from powerpoint df = n - 2 = 3, α =.05, t cr = +/ Decision: Fail to reject H 0 Interpretation: The association between voter turnout and neg. campaigning is not significant.

Include a brief summary of your results: There is a strong, negative relationship between % voter turnout and negative campaigning for the five cities. As the % of negative ads increase, the % of voter turnout goes down. However, the relationship is not significant. Negative campaigning explains 75.9% of the variation in voter turnout.