POS3713 Exam 4

*16. If we estimate the model Yi = a + B1Xi + B2Zi, and the results show that B^1 = 1.4 and B^2 = 2.3, what (if anything) is potentially problematic with concluding that the effects of Z on Y are bigger than the effects of X on Y?* (a) Because X and Z might be measured on different metrics, it makes comparing the values of B^1 and B^2 potentially misleading. (b) Because we have not yet tested for reverse causality, it is impossible to know the true effects of either X or Z on Y. (c) Both (a) and (b) are true. (d) There isn't a problem. The effects of Z on Y are bigger than the effects of X on Y.

A

*19. Assume the following: that the true model that generates the data is Yi = a + B1Xi + B2Zi; that we nevertheless estimate the regression without including the variable Z; that B^1 is positive; that X and Z are negatively related; and that the existing literature suggests that B^2 is negative. Which statement is likely to be true?* (a) B^1 > B1 (b) B^1 = B1 (c) B^1 = B2 (d) There is not enough information to determine which of the above is likely to be true.

A

*23. Which of the following is an accurate statement about multicollinearity?* (a) Multicollinearity leads to inflated standard errors. (b) Multicollinearity is caused by correlation between an independent variable and the dependent variable. (c) Both (a) and (b) are correct. (d) Neither (a) nor (b) are correct.

A

*3. Which of the following statements are accurate?* (a) E(ui) = 0 (b) E(ui2) = 0 (c) Both (a) and (b) are correct. (d) Neither (a) nor (b) are correct.

A

*9. Which of the following statements are accurate?* (a) It is highly unlikely that we would see the relationship that we are seeing between the independent variable and the dependent variable in this model due to random chance. (b) This model explains about 90% of the variation in "Blair Feelings." (c) Both (a) and (b) are correct. (d) Neither (a) nor (b) are correct.

A

*12. The statistical problem "bias" is defined as:* (a) The problems that often result from a measure being faulty. (b) The expected value of the parameter estimate that we obtain from a sample will not be equal to the true population parameter. (c) The researcher had predetermined the "conclusions" of her or his research before beginning the analysis, thereby affecting the results. (d) The sample, despite being randomly chosen, is somehow unrepresentative of the population.

B

*15. What does it mean in multiple regression to say that there is perfect multicollinearity between X and Z?* (a) That X and Z must be drawn from independent samples. (b) That X and Z are perfectly correlated with one another. (c) That the estimated slope coefficients connecting X to Y is exactly equal to the slope connecting Z to Y. (d) That both X and Z have been measured without any detectable error.

B

*20. Examine the following table, containing three separate regression models (in columns marked A, B, and C), and then answer which of the following is not a correct interpretation of the results:* -CHART- (a) The regression models account for roughly one-quarter to one-third of the variance in Y. (b) We can conclude with at least 95% confidence, based on the results in column C, that Z positively affects Y. (c) Whereas it appeared, based on the bivariate results, that Z was related to Y, controlling for X made the relationship statistically indistinguishable from zero. (d) The relationship between X and Y remains almost unchanged between the bivariate and multiple regressions.

B

*22. If an individual is right of center, what is the impact of a one unit increase in "Iraq War Success Scale" on the dependent variable?* (a) 0.34 (b) 0.29 (c) -0.09 (d) None of the above.

B

*8. Which of the following statements are accurate?* (a) For every one-unit increase in "Blair Feelings", we can expect to see a 0.31 increase in "Iraq War Success Scale." (b) For every one-unit increase in "Iraq War Success Scale", we can expect to see a 0.31 increase in "Blair Feelings." (c) If the variable "Blair Feelings" is zero, it is highly likely that the variable "Iraq War Success Scale" will also be equal to zero. (d) None of the above.

B

*1. Which of the following statements are accurate about the population regression model?* (a) u_i is the stochastic component of Yi. (b) a^ + B^Xi is the systematic component of Yi. (c) Both (a) and (b) are correct. (d) Neither (a) nor (b) are correct.

C

*10. Which of the following statements are accurate?* (a) With these results, if we know the value of "Iraq War Success Scale" then we will be able to predict the value of "Blair Feelings." Our predictions will on average be off by 2.337. (b) Even if an individual feels very negatively about how the Iraq war is going, they are quite unlikely to have the worst possible judgment about Tony Blair's competence. (c) Both (a) and (b) are correct. (d) Neither (a) nor (b) are correct.

C

*13. Which of the following best characterizes the nature of omitted-variables bias in a situation where we estimate a regression that includes X and Y but improperly excludes Z?* (a) The estimated effect of X on Y will be equal to the true effect of X on Y, so long as the sample was chosen randomly. (b) The estimated effect of X on Y will be equal to the effect of Z on Y times the effect of Z on X. (c) The estimated effect of X on Y will be equal to the true effect of X on Y plus the product of the effect of Z on Y and the bivariate association between X and Z. (d) The estimated effect of X on Y will be equal to the true effect of X on Y plus the absolute value of the effect of Z on Y.

C

*18. What is the relationship between statistical significance and substantive significance?* (a) Statistical significance is more scientifically worthwhile than substantive significance. (b) Statistical significance and substantive significance are nearly synonymous; it is almost impossible to have a statistically significant relationship that is not also substantively significant. (c) Because of the effects of sample size on statistical significance, there is no logical connection between statistical significance and substantive significance. (d) None of the above is true.

C

*2. Which of the following statements are accurate?* (a) u^i is an estimate of ui. (b) X_i is assumed to be measured without error. (c) Both (a) and (b) are correct. (d) Neither (a) nor (b) are correct.

C

*21. Which of the following statements are accurate?* (a) The effect of the variable "Iraq War Success Scale" on feelings toward Tony Blair depends on the value of the variable "Right of Center." (b) The effect of the variable "Right of Center" on feelings toward Tony Blair depends on the value of the variable "Iraq War Success Scale." (c) Both (a) and (b). (d) Neither (a) nor (b).

C

*24. Which of the following is an accurate statement about multicollinearity?* (a) The problems of multicollinearity can be overcome by increasing the sample size. (b) Multicollinearity cannot occur in a bivariate regression model. (c) Both (a) and (b) are correct. (d) Neither (a) nor (b) are correct.

C

*25. Which of the following is an accurate statement about influential observations in a multivariate OLS model?* (a) The influence of a single case depends on whether it has an unusual value for at least one independent variable ("leverage") and large residual values. (b) Influential cases can impact a model's R2 statistic. (c) Both (a) and (b) are correct. (d) Neither (a) nor (b) are correct.

C

*4. Which of the statements are accurate?* (a) By specifying a bivariate regression model we are assuming that the impact of a one unit increase in X_i will always be β. (b) By specifying a bivariate regression model we are assuming that there are no other variables that cause Y_i. (c) Both (a) and (b) are correct. (d) Neither (a) nor (b) are correct.

C

*7. In this example, if an individual has judged that Iraq war is a complete failure, meaning that they have a value of 0 for the independent variable, what would be their expected value for "Blair Feelings?"* (a) 0 (b) 5.00 (c) 4.70 (d) 0.31

C

*11. What is the principal goal of multiple regression in social-scientific research?* (a) To validate the results of an experiment by applying it to a separate sample of data. (b) To attempt to cross the second causal hurdle - that is, to see if Y might cause X. (c) To maximize the likelihood that our sample is representative of the population as a whole, thus making our findings statistically significant. (d) To test whether X causes Y in observational research while controlling for other causes of Y.

D

*14. What is the proper interpretation of B^2 in the following regression equation: Yi = a + B1Xi + B2Zi* (a) The estimated effect of X on Y. (b) The estimated effect of X on Y while controlling for the effects of Z. (c) The estimated effect of Z on Y. (d) The estimated effect of Z on Y while controlling for the effects of X.

D

*17. Which of the following is true about standardized coefficients in a multiple regression model?* (a) The standardized coefficients represent the expected standard deviation change in the dependent variable given a one-standard-deviation increase in the independent variables, controlling for the other independent variables in the model. (b) The variable whose standardized coefficient has the largest absolute value has the largest effect on the dependent variable. (c) Standardized coefficients control for the possibility of reverse causality. (d) Both (a) and (b) are true.

D

*5. Which of the following statements are accurate?* (a) In order to estimate a bivariate regression model, you must have at least two cases. (b) If X_i=4 for all observed X_i you can estimate a bivariate regression model. (c) Both (a) and (b) are correct. (d) Neither (a) nor (b) are correct.

D

*6. Which of the following statements are accurate?* (a) In hypothesis testing from a bivariate regression model, our conclusions do not depend on whether or not we have a directional hypothesis. (b) The null hypothesis for any hypothesis test about β will be that β=0. (c) Both (a) and (b) are correct. (d) Neither (a) nor (b) are correct.

D