College Political Science Quiz: Regression Interpretation
20 questions · exam conditions
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Regression InterpretationQuestion 1 of 20

A cross-sectional study of 50 nations finds a strong, statistically significant, positive correlation between the number of active civil society organizations and the country's level of press freedom. The model has a high R-squared. What is the most cautious and appropriate conclusion to draw from this finding?

An increase in the number of civil society organizations causes a country's press to become more free.
A high degree of press freedom is a necessary precondition for the development of a robust civil society.
The finding proves that civil society and press freedom are causally linked, but does not identify the direction of the effect.
Countries with more active civil society organizations tend to have greater press freedom, but this correlation does not in itself establish a causal relationship.
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College Political Science Quiz

College Political Science Quiz: Regression Interpretation

Practice Regression Interpretation in College Political Science with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Regression Interpretation, giving you a quick way to practice the rules, question types, and explanations that matter most for College Political Science.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A cross-sectional study of 50 nations finds a strong, statistically significant, positive correlation between the number of active civil society organizations and the country's level of press freedom. The model has a high R-squared. What is the most cautious and appropriate conclusion to draw from this finding?

  1. An increase in the number of civil society organizations causes a country's press to become more free.
  2. A high degree of press freedom is a necessary precondition for the development of a robust civil society.
  3. The finding proves that civil society and press freedom are causally linked, but does not identify the direction of the effect.
  4. Countries with more active civil society organizations tend to have greater press freedom, but this correlation does not in itself establish a causal relationship. (correct answer)
Explanation: Regression and correlation show association, not causation. This is especially true in cross-sectional studies where temporal order cannot be established. The relationship could be causal in either direction (A or B), or it could be spurious, with a third factor (like level of democracy) causing both. Therefore, the most appropriate conclusion is a descriptive one that acknowledges the association without making a causal claim. (A) and (B) assume a specific causal direction. (C) incorrectly uses the word 'proves' and insists on a causal link.

Question 2

A researcher tests the hypothesis that a new online voter education program increases political knowledge. After a randomized controlled trial, a regression of political knowledge scores on a 'treatment' dummy variable (1=exposed to program, 0=control) yields a coefficient of 0.50 with a p-value of 0.40. What is the most appropriate conclusion from this analysis?

  1. The study proves that the online voter education program is ineffective at increasing political knowledge.
  2. The program has a positive effect on political knowledge, but the effect is not statistically significant.
  3. The analysis does not provide sufficient statistical evidence to conclude that the program is associated with a change in political knowledge. (correct answer)
  4. The data are flawed because the results from a randomized controlled trial should always be statistically significant.
Explanation: A p-value of 0.40 indicates that the observed result is very likely to have occurred by chance if the true effect were zero. Therefore, we fail to reject the null hypothesis. The most precise conclusion is that there is insufficient evidence to support the research hypothesis. (A) is too strong; failing to find evidence of an effect is not the same as proving there is no effect. (B) is misleading because it presents the positive point estimate (0.50) as a finding, whereas the high p-value indicates this estimate cannot be distinguished from random noise. (D) is incorrect; randomization ensures internal validity but does not guarantee a significant result, especially if the treatment effect is small or the sample size is limited.

Question 3

A researcher runs a simple regression and finds a strong, positive, and statistically significant relationship between the number of public libraries per capita in a city and the city's rate of violent crime. A critic argues this result is likely due to omitted variable bias. Which of the following potential omitted variables would most plausibly explain this counterintuitive finding?

  1. The city's average annual temperature, because it is unrelated to both libraries and crime.
  2. The political party of the city's mayor, because it might influence library funding but is unlikely to be correlated with crime rates.
  3. The city's unemployment rate, because it is negatively correlated with library funding but positively correlated with crime.
  4. The city's population density, because it is positively correlated with the need for public services like libraries and also tends to be positively correlated with crime rates. (correct answer)
Explanation: Omitted variable bias occurs when a variable that is correlated with both the independent and dependent variables is left out of the model. To explain a positive coefficient between libraries and crime, the omitted variable must be positively correlated with both. Population density is a plausible candidate: denser areas require more services (like libraries) and also tend to have higher crime rates. (A) is incorrect because an omitted variable must be related to both X and Y. (B) is incorrect because the variable is unlikely to be related to the dependent variable (crime). (C) describes a variable that would likely induce a negative bias, not explain the positive finding.

Question 4

A cross-national study examines the relationship between economic inequality (measured by the Gini coefficient) and political instability. A key finding for the Gini coefficient variable is a p-value of 0.03. Which of the following is the most accurate conclusion that can be drawn from this specific p-value?

  1. There is a 3% chance that economic inequality has no effect on political instability.
  2. If the null hypothesis of no relationship is true, there is a 3% probability of observing a relationship at least as strong as the one found in the sample. (correct answer)
  3. The model proves that economic inequality is a significant cause of political instability, with a 97% confidence level.
  4. The relationship between economic inequality and political instability is substantively large and important for policy-making.
Explanation: The p-value is the probability of observing the current result, or a more extreme one, assuming the null hypothesis is true. A p-value of 0.03 means that there is a 3% chance of getting a result this strong or stronger by random chance if there were actually no relationship in the population. (A) is a common but incorrect interpretation of the p-value; it is not the probability that the null hypothesis is true. (C) makes a causal claim, which cannot be proven by the model, and misinterprets the meaning of the p-value as a confidence level. (D) confuses statistical significance with substantive significance; a small p-value does not necessarily mean the effect size is large or practically important.

Question 5

A political economist models the number of anti-government protests per year in various countries. To account for the wide range in economic development, the model uses the natural log of GDP per capita, ln(GDP), as an independent variable. The dependent variable is the count of protests. The coefficient for ln(GDP) is -25.0 and is statistically significant. How should this coefficient be interpreted?

  1. Each one-dollar increase in a country's GDP per capita is associated with 25 fewer protests per year.
  2. A 1% increase in a country's GDP per capita is associated with a decrease of approximately 0.25 protests per year. (correct answer)
  3. A 1% increase in a country's GDP per capita is associated with a 25% decrease in the number of protests per year.
  4. A one-unit increase in the natural log of GDP per capita is associated with 25 more protests per year.
Explanation: This is a level-log model, where the dependent variable is in its original units (level) and the independent variable is logged. The interpretation of the coefficient β is that a 1% change in the independent variable is associated with a (β/100) unit change in the dependent variable. Here, β = -25.0. So, a 1% increase in GDP per capita is associated with a (-25.0 / 100) = -0.25 change in the number of protests. (A) incorrectly interprets the logged variable as if it were linear. (C) is the interpretation for a log-log model. (D) misinterprets the sign of the coefficient.

Question 6

In a regression model, the standard error of a coefficient is a critical piece of information used to assess statistical significance. Which of the following best describes the conceptual meaning of a coefficient's standard error?

  1. It is a measure of the typical distance that the estimated coefficient is from the true, unobservable population coefficient. (correct answer)
  2. It represents the average squared difference between the observed and predicted values of the dependent variable.
  3. It is the probability that the null hypothesis is true for that specific independent variable.
  4. It indicates the change in the dependent variable for a one-standard-deviation change in the independent variable.
Explanation: When you encounter questions about regression analysis, focus on distinguishing between different measures of uncertainty and model performance. The standard error of a coefficient is fundamentally about sampling variability—how much your estimated coefficient would fluctuate if you repeated your study with different samples from the same population. The standard error captures the typical distance between your estimated coefficient and the true population parameter you're trying to estimate. Since you can never observe the true population coefficient directly, the standard error quantifies the uncertainty inherent in your estimate. This makes option A correct—it's essentially measuring how "off" your estimate might be from reality. Option B describes the residual sum of squares or mean squared error, which measures how well your model fits the observed data points, not the precision of individual coefficients. Option C confuses the standard error with a p-value; the standard error helps calculate p-values, but it's not itself a probability. Option D describes a standardized coefficient (beta coefficient), which shows the effect size in standard deviation units rather than measuring estimation uncertainty. The standard error serves as the denominator when calculating t-statistics for hypothesis testing: t=coefficient estimatestandard errort = \frac{\text{coefficient estimate}}{\text{standard error}}. A smaller standard error means more precise estimation and larger t-statistics. Study tip: Remember that standard errors always relate to sampling uncertainty—they tell you how much estimates would vary across different samples. This distinguishes them from model fit measures or effect size measures.

Question 7

A cross-national study examines the relationship between economic inequality (measured by the Gini coefficient) and political instability. A key finding for the Gini coefficient variable is a p-value of 0.03. Which of the following is the most accurate conclusion that can be drawn from this specific p-value?

  1. There is a 3% chance that economic inequality has no effect on political instability.
  2. If the null hypothesis of no relationship is true, there is a 3% probability of observing a relationship at least as strong as the one found in the sample. (correct answer)
  3. The model proves that economic inequality is a significant cause of political instability, with a 97% confidence level.
  4. The relationship between economic inequality and political instability is substantively large and important for policy-making.
Explanation: The p-value is the probability of observing the current result, or a more extreme one, assuming the null hypothesis is true. A p-value of 0.03 means that there is a 3% chance of getting a result this strong or stronger by random chance if there were actually no relationship in the population. (A) is a common but incorrect interpretation of the p-value; it is not the probability that the null hypothesis is true. (C) makes a causal claim, which cannot be proven by the model, and misinterprets the meaning of the p-value as a confidence level. (D) confuses statistical significance with substantive significance; a small p-value does not necessarily mean the effect size is large or practically important.

Question 8

A study on the effects of foreign aid on democratic development reports a coefficient for 'Aid as % of GDP'. Instead of a p-value, it provides a 95% confidence interval for this coefficient, which is [0.05, 0.45]. Based on this confidence interval, what can be concluded?

  1. There is a 95% probability that the true effect of foreign aid is between 0.05 and 0.45.
  2. The effect of foreign aid is not statistically significant at the 0.05 level because the interval is too wide.
  3. The effect of foreign aid is statistically significant at the 0.05 level because the interval does not contain zero. (correct answer)
  4. The model's prediction for the effect of foreign aid is correct in 95% of cases.
Explanation: A confidence interval provides a range of plausible values for the true population parameter. Statistical significance at the α = 0.05 level is established if the 95% confidence interval does not contain the null hypothesis value (which is typically 0). Since the interval [0.05, 0.45] is entirely positive and does not include 0, we can reject the null hypothesis and conclude the effect is statistically significant. (A) is a common misinterpretation; in frequentist statistics, the interval is random, not the parameter. The correct phrasing is about confidence in the procedure, not probability about the parameter. (B) is incorrect; the width of the interval relates to precision, but significance is determined by whether it contains zero. (D) misinterprets the confidence level as a measure of predictive accuracy.

Question 9

An analyst is studying political participation in a small N study of 15 Western European countries. The regression model shows a positive coefficient for the effect of compulsory voting laws on voter turnout, but the p-value is 0.15. What is the most methodologically sound interpretation of this finding?

  1. The study fails to reject the null hypothesis of no effect, which may be due to the small sample size providing insufficient statistical power. (correct answer)
  2. The study proves that compulsory voting laws have no effect on voter turnout in Western Europe.
  3. The positive coefficient indicates that the laws do increase turnout, but the relationship is not strong enough to be meaningful.
  4. The result is inconclusive and should be disregarded entirely because the p-value is greater than 0.10.
Explanation: When analyzing statistical results in small-N comparative studies, you need to distinguish between statistical significance, practical significance, and the limitations imposed by sample size. This question tests your understanding of hypothesis testing and statistical power in political science research. Answer A correctly interprets this finding. With a p-value of 0.15, you fail to reject the null hypothesis at conventional significance levels (0.05 or 0.01), meaning you cannot conclude there's a statistically significant effect. However, the positive coefficient suggests a relationship might exist, and with only 15 countries, the study likely lacks sufficient statistical power to detect even meaningful effects. Small samples make it harder to achieve statistical significance even when real relationships exist. Answer B makes a fundamental error by claiming the study "proves" no effect exists. Failing to reject the null hypothesis never proves the null is true—it simply means you lack sufficient evidence to conclude an effect exists. This is a classic Type II error interpretation. Answer C confuses statistical significance with practical significance. The coefficient's size doesn't determine whether it's "meaningful"—statistical significance testing is about whether observed effects are likely due to chance, not about substantive importance. Answer D is too extreme and ignores the broader context. While some fields use p < 0.10, dismissing results entirely because they don't meet arbitrary thresholds wastes valuable information, especially in small-N studies where power is inherently limited. Remember: in comparative politics with small samples, always consider statistical power alongside significance tests when interpreting null findings.

Question 10

In a regression model, the standard error of a coefficient is a critical piece of information used to assess statistical significance. Which of the following best describes the conceptual meaning of a coefficient's standard error?

  1. It is a measure of the typical distance that the estimated coefficient is from the true, unobservable population coefficient. (correct answer)
  2. It represents the average squared difference between the observed and predicted values of the dependent variable.
  3. It is the probability that the null hypothesis is true for that specific independent variable.
  4. It indicates the change in the dependent variable for a one-standard-deviation change in the independent variable.
Explanation: When you encounter questions about regression analysis, focus on distinguishing between different measures of uncertainty and model performance. The standard error of a coefficient is fundamentally about sampling variability—how much your estimated coefficient would fluctuate if you repeated your study with different samples from the same population. The standard error captures the typical distance between your estimated coefficient and the true population parameter you're trying to estimate. Since you can never observe the true population coefficient directly, the standard error quantifies the uncertainty inherent in your estimate. This makes option A correct—it's essentially measuring how "off" your estimate might be from reality. Option B describes the residual sum of squares or mean squared error, which measures how well your model fits the observed data points, not the precision of individual coefficients. Option C confuses the standard error with a p-value; the standard error helps calculate p-values, but it's not itself a probability. Option D describes a standardized coefficient (beta coefficient), which shows the effect size in standard deviation units rather than measuring estimation uncertainty. The standard error serves as the denominator when calculating t-statistics for hypothesis testing: t=coefficient estimatestandard errort = \frac{\text{coefficient estimate}}{\text{standard error}}. A smaller standard error means more precise estimation and larger t-statistics. Study tip: Remember that standard errors always relate to sampling uncertainty—they tell you how much estimates would vary across different samples. This distinguishes them from model fit measures or effect size measures.

Question 11

A researcher tests the hypothesis that a new online voter education program increases political knowledge. After a randomized controlled trial, a regression of political knowledge scores on a 'treatment' dummy variable (1=exposed to program, 0=control) yields a coefficient of 0.50 with a p-value of 0.40. What is the most appropriate conclusion from this analysis?

  1. The study proves that the online voter education program is ineffective at increasing political knowledge.
  2. The program has a positive effect on political knowledge, but the effect is not statistically significant.
  3. The analysis does not provide sufficient statistical evidence to conclude that the program is associated with a change in political knowledge. (correct answer)
  4. The data are flawed because the results from a randomized controlled trial should always be statistically significant.
Explanation: A p-value of 0.40 indicates that the observed result is very likely to have occurred by chance if the true effect were zero. Therefore, we fail to reject the null hypothesis. The most precise conclusion is that there is insufficient evidence to support the research hypothesis. (A) is too strong; failing to find evidence of an effect is not the same as proving there is no effect. (B) is misleading because it presents the positive point estimate (0.50) as a finding, whereas the high p-value indicates this estimate cannot be distinguished from random noise. (D) is incorrect; randomization ensures internal validity but does not guarantee a significant result, especially if the treatment effect is small or the sample size is limited.

Question 12

A researcher runs a simple regression and finds a strong, positive, and statistically significant relationship between the number of public libraries per capita in a city and the city's rate of violent crime. A critic argues this result is likely due to omitted variable bias. Which of the following potential omitted variables would most plausibly explain this counterintuitive finding?

  1. The city's average annual temperature, because it is unrelated to both libraries and crime.
  2. The political party of the city's mayor, because it might influence library funding but is unlikely to be correlated with crime rates.
  3. The city's unemployment rate, because it is negatively correlated with library funding but positively correlated with crime.
  4. The city's population density, because it is positively correlated with the need for public services like libraries and also tends to be positively correlated with crime rates. (correct answer)
Explanation: Omitted variable bias occurs when a variable that is correlated with both the independent and dependent variables is left out of the model. To explain a positive coefficient between libraries and crime, the omitted variable must be positively correlated with both. Population density is a plausible candidate: denser areas require more services (like libraries) and also tend to have higher crime rates. (A) is incorrect because an omitted variable must be related to both X and Y. (B) is incorrect because the variable is unlikely to be related to the dependent variable (crime). (C) describes a variable that would likely induce a negative bias, not explain the positive finding.

Question 13

A political economist models the number of anti-government protests per year in various countries. To account for the wide range in economic development, the model uses the natural log of GDP per capita, ln(GDP), as an independent variable. The dependent variable is the count of protests. The coefficient for ln(GDP) is -25.0 and is statistically significant. How should this coefficient be interpreted?

  1. Each one-dollar increase in a country's GDP per capita is associated with 25 fewer protests per year.
  2. A 1% increase in a country's GDP per capita is associated with a decrease of approximately 0.25 protests per year. (correct answer)
  3. A 1% increase in a country's GDP per capita is associated with a 25% decrease in the number of protests per year.
  4. A one-unit increase in the natural log of GDP per capita is associated with 25 more protests per year.
Explanation: This is a level-log model, where the dependent variable is in its original units (level) and the independent variable is logged. The interpretation of the coefficient β is that a 1% change in the independent variable is associated with a (β/100) unit change in the dependent variable. Here, β = -25.0. So, a 1% increase in GDP per capita is associated with a (-25.0 / 100) = -0.25 change in the number of protests. (A) incorrectly interprets the logged variable as if it were linear. (C) is the interpretation for a log-log model. (D) misinterprets the sign of the coefficient.

Question 14

A cross-sectional study of 50 nations finds a strong, statistically significant, positive correlation between the number of active civil society organizations and the country's level of press freedom. The model has a high R-squared. What is the most cautious and appropriate conclusion to draw from this finding?

  1. An increase in the number of civil society organizations causes a country's press to become more free.
  2. A high degree of press freedom is a necessary precondition for the development of a robust civil society.
  3. The finding proves that civil society and press freedom are causally linked, but does not identify the direction of the effect.
  4. Countries with more active civil society organizations tend to have greater press freedom, but this correlation does not in itself establish a causal relationship. (correct answer)
Explanation: Regression and correlation show association, not causation. This is especially true in cross-sectional studies where temporal order cannot be established. The relationship could be causal in either direction (A or B), or it could be spurious, with a third factor (like level of democracy) causing both. Therefore, the most appropriate conclusion is a descriptive one that acknowledges the association without making a causal claim. (A) and (B) assume a specific causal direction. (C) incorrectly uses the word 'proves' and insists on a causal link.

Question 15

An analyst is studying political participation in a small N study of 15 Western European countries. The regression model shows a positive coefficient for the effect of compulsory voting laws on voter turnout, but the p-value is 0.15. What is the most methodologically sound interpretation of this finding?

  1. The study fails to reject the null hypothesis of no effect, which may be due to the small sample size providing insufficient statistical power. (correct answer)
  2. The study proves that compulsory voting laws have no effect on voter turnout in Western Europe.
  3. The positive coefficient indicates that the laws do increase turnout, but the relationship is not strong enough to be meaningful.
  4. The result is inconclusive and should be disregarded entirely because the p-value is greater than 0.10.
Explanation: When analyzing statistical results in small-N comparative studies, you need to distinguish between statistical significance, practical significance, and the limitations imposed by sample size. This question tests your understanding of hypothesis testing and statistical power in political science research. Answer A correctly interprets this finding. With a p-value of 0.15, you fail to reject the null hypothesis at conventional significance levels (0.05 or 0.01), meaning you cannot conclude there's a statistically significant effect. However, the positive coefficient suggests a relationship might exist, and with only 15 countries, the study likely lacks sufficient statistical power to detect even meaningful effects. Small samples make it harder to achieve statistical significance even when real relationships exist. Answer B makes a fundamental error by claiming the study "proves" no effect exists. Failing to reject the null hypothesis never proves the null is true—it simply means you lack sufficient evidence to conclude an effect exists. This is a classic Type II error interpretation. Answer C confuses statistical significance with practical significance. The coefficient's size doesn't determine whether it's "meaningful"—statistical significance testing is about whether observed effects are likely due to chance, not about substantive importance. Answer D is too extreme and ignores the broader context. While some fields use p < 0.10, dismissing results entirely because they don't meet arbitrary thresholds wastes valuable information, especially in small-N studies where power is inherently limited. Remember: in comparative politics with small samples, always consider statistical power alongside significance tests when interpreting null findings.

Question 16

A political scientist develops a model to explain variation in voter turnout across different precincts in a city. The model includes variables for average income, percentage of residents with a college degree, and average age. The model produces an R-squared value of 0.18. Which of the following is the correct interpretation of this R-squared value?

  1. The independent variables in the model cause 18% of the voter turnout in the city's precincts.
  2. For any given precinct, the model can predict the exact voter turnout with 18% accuracy.
  3. Eighteen percent of the variation in voter turnout across precincts is explained by the variation in the model's independent variables. (correct answer)
  4. The model is a poor fit for the data because the R-squared value is significantly less than 0.50.
Explanation: R-squared, or the coefficient of determination, measures the proportion of the variance in the dependent variable that is predictable from the independent variables. An R-squared of 0.18 means that 18% of the variance in voter turnout is accounted for by the model. (A) is incorrect because R-squared does not establish causality. (B) misinterprets R-squared as a measure of individual prediction accuracy. (D) is a subjective judgment; in social sciences, an R-squared of 0.18 can be quite meaningful, and there is no universal threshold for what constitutes a 'good' fit.

Question 17

A political scientist develops a model to explain variation in voter turnout across different precincts in a city. The model includes variables for average income, percentage of residents with a college degree, and average age. The model produces an R-squared value of 0.18. Which of the following is the correct interpretation of this R-squared value?

  1. The independent variables in the model cause 18% of the voter turnout in the city's precincts.
  2. For any given precinct, the model can predict the exact voter turnout with 18% accuracy.
  3. Eighteen percent of the variation in voter turnout across precincts is explained by the variation in the model's independent variables. (correct answer)
  4. The model is a poor fit for the data because the R-squared value is significantly less than 0.50.
Explanation: R-squared, or the coefficient of determination, measures the proportion of the variance in the dependent variable that is predictable from the independent variables. An R-squared of 0.18 means that 18% of the variance in voter turnout is accounted for by the model. (A) is incorrect because R-squared does not establish causality. (B) misinterprets R-squared as a measure of individual prediction accuracy. (D) is a subjective judgment; in social sciences, an R-squared of 0.18 can be quite meaningful, and there is no universal threshold for what constitutes a 'good' fit.

Question 18

A study on the effects of foreign aid on democratic development reports a coefficient for 'Aid as % of GDP'. Instead of a p-value, it provides a 95% confidence interval for this coefficient, which is [0.05, 0.45]. Based on this confidence interval, what can be concluded?

  1. There is a 95% probability that the true effect of foreign aid is between 0.05 and 0.45.
  2. The effect of foreign aid is not statistically significant at the 0.05 level because the interval is too wide.
  3. The effect of foreign aid is statistically significant at the 0.05 level because the interval does not contain zero. (correct answer)
  4. The model's prediction for the effect of foreign aid is correct in 95% of cases.
Explanation: A confidence interval provides a range of plausible values for the true population parameter. Statistical significance at the α = 0.05 level is established if the 95% confidence interval does not contain the null hypothesis value (which is typically 0). Since the interval [0.05, 0.45] is entirely positive and does not include 0, we can reject the null hypothesis and conclude the effect is statistically significant. (A) is a common misinterpretation; in frequentist statistics, the interval is random, not the parameter. The correct phrasing is about confidence in the procedure, not probability about the parameter. (B) is incorrect; the width of the interval relates to precision, but significance is determined by whether it contains zero. (D) misinterprets the confidence level as a measure of predictive accuracy.

Question 19

A political scientist models the effect of campaign spending on electoral outcomes. The dependent variable is a candidate's vote share (from 0 to 100), and the key independent variable is campaign spending, measured in units of $100,000. The regression output is shown below. Based on the table, which of the following is the most accurate interpretation of the coefficient for campaign spending?

  1. A $100,000 increase in campaign spending is associated with a 0.5 percentage point increase in the candidate's vote share, on average. (correct answer)
  2. A $1 increase in campaign spending is associated with a 0.5 percentage point increase in the candidate's vote share, on average.
  3. Higher campaign spending causes a candidate's vote share to increase by 0.5 percentage points, holding all else constant.
  4. For every $100,000 spent, a candidate can expect to receive 0.5% of the total votes cast in the election.
Explanation: The coefficient of 0.50 represents the change in the dependent variable (Vote Share in %) for a one-unit change in the independent variable. Since the independent variable is measured in units of $100,000, a one-unit change corresponds to a $100,000 increase, which is associated with a 0.5 percentage point increase in vote share. (B) is incorrect because it misunderstands the units of the independent variable. (C) is incorrect because regression analysis shows association, not causation. (D) misinterprets the coefficient as a direct share of total votes rather than a marginal change in the percentage share.

Question 20

A researcher investigates factors influencing judicial confirmations in the U.S. Senate. The model predicts the number of 'nay' votes a judicial nominee receives. One key independent variable is Nominee_Ideology, a scale from -1 (most liberal) to +1 (most conservative). A second is Divided_Government, a dummy variable coded 1 if the presidency and Senate are controlled by different parties, and 0 otherwise. Given the results in the table, what is the predicted number of 'nay' votes for a ideologically moderate nominee (score of 0) under a divided government?

  1. 15 votes
  2. 18 votes
  3. 25 votes
  4. 33 votes (correct answer)
Explanation: To find the predicted value, one must sum the intercept and the product of each coefficient and its corresponding variable value. For an ideologically moderate nominee (Nominee_Ideology = 0) under a divided government (Divided_Government = 1): Predicted Nay Votes = Intercept + (β₁ * Nominee_Ideology) + (β₂ * Divided_Government) = 18 + (10 * 0) + (15 * 1) = 18 + 0 + 15 = 33. (A) incorrectly uses only the Divided_Government coefficient. (B) incorrectly uses only the intercept. (C) is the sum of the Divided_Government coefficient and the Nominee_Ideology coefficient, ignoring the intercept.