### AP Review Questions for Regression

(chapter 3) Countries are measured according to per capita income. They are also measured according to an index of political corruption, with 0 meaning no corruption and 100 being extremely high corruption. The mean of the corruption index is 50, with a standard deviation of 14. The mean of per capita income is \$8700 with a standard deviation of \$2800. The correlation coefficient between corruption and income is -0.7

1. What is the value of R-squared?
2. What is the slope of the least-squares regression line for the relationship between corruption and income?
3. Predict the value of per capita income for a country with a corruption index of 80.

(chapter 14) A study was conducted of the relationship between corruption and the number of violent regime changes over the past 40 years. The theory is that where there are frequent violent regime changes, a country tends to be very corrupt, because the rulers try to steal as much as they can as quickly as they can, with little concern for the future of the country. Thus, the dependent variable is the corruption index and the independent variable is the frequency of violent regime changes. 82 countries were in the study. The results were:

variablecoefficientstandard error
Constant22.410.1
Violent coups11.55.1

1. If a country had 4 coups over the past 40 years, what is its predicted level of corruption?
2. What does the constant term tell us?
3. What is the p-value for the null hypothesis that violent coups have no effect on corruption vs. the alternative hypothesis that violent coups and corruption are positively related?
4. (chapter 5) Explain why this result does not establish that frequent violent coups cause corruption. State one or more alternative hypotheses that are consistent with these results.