Ex. 8 Blue Book

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CHAPTER 8 Correlation and Linear Regression - 185 : Name:: E-mail: Date: - Section': CHAPTER 8 EXERCISES 1. (Dataset: NES. Variables: ft_Trump_pre, ft_Police, ft_Rep, ft_Obama, ft_ HClinton_pre, nesw.) We have worked with feeling thermometer ratings several times already. As you know, feeling thermometer questions on the NES ask respondents to rate something on a scale from 0 to 100, with o being very cold/negative feelings, 50 representing neutral feelings, and 100 being very warm/positive feelings. Let’s look at the correlations among several feeling thermometers to get an idea of how people view different subjects. If people think subjects are similar, they should express similar sentiments about them. Perhaps knowing how someone feels about one subject can help us predict how they might feel about a variety of subjects. A. Usethe Analyze » Correlate » Bivariate procedure to generate a correlation matrix for the following feeling thermometers in the NES dataset: ft_Trump_pre, ft_ Police, ft_Rep, ft_Obama, and ft_HClinton_pre. Be sure to weight observations using nesw so your results are nationally representative. Fill in the missing Pearson correlation coefficients in the following table. ft_Trump_pre 1.00 ft_Police ? 1.00 #t_Hep o4 2400 ft_Obama ? ? -053 1.00 ft_HClinton_pre - 7l ipo4 g 2 100 B. According to the correlation coefficient, as feeling thermometer scores for the police increase, feeling thermometer scores for Republicans (circle one) increase. decrease. C. According to the correlation coefficient matrix, which of the following variables has the strongest correlation (either negatively or positively) with feeling thermometer scores for Donald Trump? (circle one) Police Republicans Obama H. Clinton D. According to the correlation coefficient matrix, the following two feeling thermometer scores have the strongest correlation (either negatively or positively): and 2, (Dataset: States. Variables: vep16_turnout, clinton16.) An article of faith among Democratic Party strategists (and a source of apprehension among Republican strategists) is that high voter turnouts help Democratic candidates. Why should this be the case? According to the conventional wisdom, Democratic electorates are less likely to vote than are Republican voters. Thus, low turnouts naturally favor Republican candidates. As turnouts push higher, the reasoning goes, a larger number of potential Democratic voters will go to the polls, creating a better opportunity for Democratic candidates. Therefore, as turnouts g0 up, so should the Democratic percentage of the vote.* A. Use the Analyze » Regression P Linear procedure to test this conventional wisdom. The States dataset contains vep16_turnout, the percentage of the state voting-eligible population that turned out to vote in the 2016 presidential election. This is the independent variable. Another variable, clinton16, the percentage of the vote cast for Democratic candidate Hillary Clinton, is the dependent variable. Use linear regression analysis to examine the relationship between voter turnout and Hillary Clinton’s vote share. Complete the following table. % Voter ? ? ? ? turnout Constant ? 2 122 . 0227 term ‘ 1 : N ? R-squared - P Adjusted ? R-squared 4 See Michael D. Martinez and Jeff Gill, “The Effects of Turnout on Partisan Outcomes in US Presidential Elections 1960-2000,” _ Journal of Politics 67, no. 4 (2005): 1248-1274. Martinez and Gill find that the Democratic advantage from higher turnouts has declined over time.

An IBM® SPSS® Companion to Political Analysis B. Based on your results, the regression equation for estimating the percentage voting for Hillary Clinton is (fil in the blanks, put the constant, _cons, in the last blank) Clinton Voter Percentage = x Percentage Turnout + C. Consider your findifigs in parts A and B. One may conclude that (complete one option) 1 The conventional wisdom is correct because 03 The conventional wisdom is incorrect because 3. (Dataset: States, Variables: abortlaw2017, prochoice_ percent.) As you are no doubt aware, in its momentous decision in Roe v. Wade (1973), the U.S. Supreme Court declared that states may not outlaw abortion. Even so, many state legislatures have enacted restrictions and regulations that, while not banning abortion, make an abortion more difficult to obtain. Other states, however, have few or no restrictions. What factors might explain these differences in abortion laws among the states? We know that the public remains divided on this issue. Public opinion in some states is more favorable toward permitting abortion, whereas public opinion is less favorable in other states. Does public opinion guide state policy on this issue? The States dataset contains abortlaw2017, which measures the number of abortion restrictions a state has enacted into law. Values on abortlaw2017 range from 0 (least restrictive) t0 19 (most restrictive). This is the dependent variable. The dataset also has the variable, prochoice_percent, the percentage of the mass public that is pro-choice (thus opposed to putting restrictions on abortion access). This is the independent variable. A. Ifyou were to use regression analysis to test the idea that public opinion on abortion affects state abortion policy, you would expect to find (check one) (7 anegative sign on prochoice_percent’s regression coefficient. 0 apositive sign on prochoice_percent’s regression _ coefficient. B. Using SPSS’s Analyze » Regression > Linear procedure, analyze the relationship between abortlaw2017 and prochoice_percent. Complete the following table. 9% Pro-choice Constant term ? 2.30 ? ? N ? R-squared ? Adjusted ? R-squared C. According to the results, the regression equation for estimating the number of abortion restrictions is (fill in the blanks, put the constant, _cons, in the last blank) Number of Restrictions = X Percentage Pro-choice + D. According to the data, 70 percent of Virginia residents are pro-choice. In Tennessee, by contrast, only 40 percent of the public holds this view. Based on the regression equation (fil} in the blanks), You would estimate that Virginia would have abortion restrictions. You would estimate that Tennessee would have abortion restrictions. E. Adjusted R-squared is equal to . This means that F. Runthe Graphs » Legacy Dialogs » Scatter/Dot procedure to obtain a scatterplot with a linear prediction overlay. Make sure the x-axis and y-axis are appropriately labeled. Also, change the color and pattern of the linear prediction line. If you prefer, make other enhancements to the graph’s appearance. Print the graphic. 4. (Dataset: States. Variables: abortlaw2017, prochoice_ percent, womleg_2017.) Suppose that a critic, upon examining the variables in the States dataset and viewing your results in Exercise 3, expresses skepticism about the relationship between mass-level abortion attitudes and the . number of st_ate~level restrictions on abortion: “There is a key aspect of state governance that you have not taken into account: the percentage of state legislators who are women (womleg_2017). If you were to examine the correlation coefficients among abortlaw2017, prochoice_percent, and womleg_2017, you will find two things. First, the correlation between abortlaw2017 and womleg_2017 will be negative and pretty strong. . . say, at least —0.50. Second, the correlation

CHAPTER 8 Correlation and Linear Regression o 187 ‘ between prochoice_percent and womleg_2017 will be positive A. Use the Analyze P Correlate b Bivariate procedure and fairly strong—at least +0.50. Third, when you perform a to obtain a correlation matrix for abortlaw2017, multiple regression analysis of abortlaw2017, using prochoice__ prochoice_percent, and womleg_2017. Write the percent and womleg 2017 as independent variables, you correlation coefficients next to the question marks in will find that womleg 2017 is statistically significant, while the following table. prochoice_percent will fade to statistical insignificance.” No. of abortion restrictions (abortlaw2017) 1.00 Percent mass public pro-choice {prochoice_percent) ? 1.00 ? ? 1.00 Percent female legislators (womleg_2017) B. Consider the skeptical critic’s first claim regarding the relationship between womleg_2017 and abortlawz017. According to the correlation coefficient, this claim is . . R-squared ? (circle one and explain your answer) Adjusted R- ? correct incorrect squared because E. Based on the evidence in part D, is the critic’s third claim regarding the multiple regression analysis correct? (circle one and explain your answer): C. Consider the skeptical critic’s second claim regarding Correct Incorrect the relationship between womleg 2017 and prochoice_ because percent. According to the correlation coefficient, this claim is (circle one and explain your answer) correct incorrect because F. Create a bubble plot that depicts the relationship between abortlaw2017 (y-axis) and prochoice_percent (x-axis), weighted by womleg_2017. This is a special graphing procedure demonstrated in a screencast video. Print the graph. D. Use the Analyze > Regression b Linear procedure to 5. (Dataset: GSS. Variables: tolerance, educ, age, polviews, estimate the multiple regression model suggested by wtss,) What factors affect a person’s level of tolerance of the critic. Write the correct values next to the question unpopular groups? Consider three hypotheses: marks in the following table. Hypothesis 1: In a comparison of individuals, older people will be less tolerant than younger people. Hypothests 2: In a comparison of individuals, those with higher levels of education will have higher levels of tolerance % Pro-choice ? ? ? ? . : than those with lower levels of education. % Women ? ? ? ? legislators Hypothesis 3: In a comparison of individuals, conservatives . will be less tolerant than liberals. GConstant term ? 2.14 8.30 ? N . . : The GSS dataset includes the following variables, as ) described in the table below.

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~ AnIBM® SPSS® Companion to Political Analysis tolerance Tolerance age " R's Age (years) educ Highest Year of School polviews : ldeological Self-Placement A. Use the Analyze b Regression P Linear procedure to run a multiple regression analysis with the dependent variable and independent variables specified above. (Don’t forget to weight observations using wtss.) After you run the model, run the script to obtain adjusted R-squared. Fill in the following table. Age ? ? ? ? Education . 9 2 2 2 Political -0.12 ? R ? ideology Constant 7 ? 871 ? term ’ o N ? ? R-squared B. Based on the evidence in part A, does it appear that Hypothesis 1 has merit? (circle one and explain your answer) ' Yes No because 0 (low) to 6 (high) Dependent variable 181 1089 Independent variable 0to20 independent variable 1 (ExtrmLib) to 7 (ExtrmCons} ' Independent variable because E. The adjusted R-squared statistic for the multiple regression model you estimated in part A equals Use the regression eqilation to estimate the tolerance score for the typical respondent, which we will define as a person having the median values of all the independent variables. Run Analyze ¥ Descriptive Statistics » Frequencies with the statistics option (for medians) to obtain the median values for each independent variable. Write the medians in the following table (the median of polviews already appears in the table). age educ polviews Median 4 G. When you use the median values to estimate the tolerance score for the typical person, you obtain an estimate equal to (fill in the blank) 6. (Dataset: States. Variables: HR_conservi1, Conserv_public.) Two congressional scholars are discussing the extent to which members of the U.S. House of Representatives stay in touch with the voters in their states. Scholar 1: “When members of Congress vote on important public policies, they are closely attuned to the ideological makeups of their states. Members from states having lots of liberals will tend to cast votes in the liberal direction. Representatives from states with mostly conservative constituencies, by contrast, will take conservative positions on important policies.” Scholar 2: “You certainly have a naive view of congressional C. Based on the evidence in part A, does it appear that Hypothesis 2 has merit? (circle one and explain your answer) Yes No because D. Based on the evidence in part A, does it appear that Hypothesis 3 has merit? (circle one and explain your answer) behavior. Once they get elected, members of congress adopt a “‘Washington, D.C., state of mind,’ perhaps voting in the liberal direction on one policy and in the conservative direction on another. One thing is certain: The way members vote has little to do with the ideological composition of their states.”

Conservative Rating of U.S. House Delegation CHAPTER 8 Correlation and Linear Regression - - 189 Think about an independent variable that measures the percentage of self-described “conservatives” among the mass public in a state, with low values denoting low percentages of conservatives and high values denoting high percentages of conservatives. And consider a dependent variable that gauges the degree to which the state’s House delegation- votes in a conservative direction on public policies. Low scores on this dependent variable tell you that the delegation tends to vote in a liberal direction, and high scores say that the delegation votes in a conservative direction. A. Below is an empty graphic shell showing the relationship between the independent variable and the dependent variable. Draw a regression line inside the shell that depicts what the relationship should look like if Scholar 11is correct. Relationship Between Public Ideology and Voling in Congress 100 60 80 40 20 Conservative Rating of U.S. House Delegation 0 L 40 60 Percent Mass Public Canservative B. Belowis another graphic shell showing the relationship between the independent variable and the dependent variable. Draw a regression line inside the shell that depicts what the relationship should look like if Scholar 2 is correct. Relationship Between Public Ideology and Voting in Congress 60 80 100 ) f . 1 40 20 0 L T T T T T 0 20 80 100 40 60 Percent Mass Public Conservative C. The States dataset contains the va;'iable Conserv_public, the percentage of the mass public calling themselves conservative, This is the independent variable. The dataset also contains HR_conservii, a measure of conservative votes by states’ House members. Scores on this variable can range from o (low conservatism) to 100 (high conservatism). This is the dependent variable. Use the Analyze » Regression ¥ Linear procedure to estimate the relationship between the variables. According to the regression equation, a 1-percentage- point increase in conservatives in the mass public is associated with (check one) O about a 27-point decrease in House conservatism scores. Q about a 2-point increase in House conservatism scores. 0 about an 8-point increase in House conservatism scores. If you were to use this regression to estimate the mean House conservatism score for states having 30 percent conservatives, your estimate would be (circle the closest estimate) 30 35 40 45 50 The adjusted R-squared for this relationship is equal to . This tells you that about percent of the variation in HR_ conservi1 is explained by Conserv_public. Use the Graphs » Legacy Dialogs ¥ Scatter/Dot procedure to obtain a scatterplot with a linear prediction overlay. Remember that HR_conservii is the y-axis variable, and Conserv_public is the x-axis variable. Make sure the y-axis and x-axis are appropriately labeled and change the pattern of the linear prediction line, If you prefer, make other enhancements to the graph’s appearance. Print the graph. Based on your inspection of the regression results, the scatterplot and linear prediction line, and adjusted R- squared, which congressional scholar is more correct? O Scholar 1 is more correct because 00 Scholar 2 is more correct because That concludes the exercises for this chapter.