#6 - Correlation and Regression ________________ For multiple choice questions, highlight your answer. Otherwise, type your answers in bold. Explain your reasoning and show your work so we can give you partial credit. This exam is worth a total of 25 points. Questions 1 - 9 are 2 points each (total of 18 points) 1. Select the correct statement(s) concerning correlation and regression: a. Linear regression estimates the equation that best fits the data. b. The correlation of X on Y is not the same as the correlation of Y on X. c. One should reject the null hypothesis if the Pearson's Correlation Coefficient (r) = 0. d. The regression line in simple linear regression is a positive slope. 2. The reason the computed chi-square is positive is because the difference between the observed and expected frequencies is: a. always positive b. uniform c. squared d. linear 3. Correlation and regression are concerned with: a. the relationship between two qualitative variables b. the relationship between two quantitative variables c. the relationship between a qualitative and quantitative variable d. none of the above e. all of the above 4. Which of the following statements involving correlation is possible and reasonable? a. The correlation between hair color and eye color is -0.80 b. The correlation between height of a father and the height of his first son is 0.6. c. The correlation between left foot length and right foot length is 2.35. d. The correlation between hair color and age is positive. 5. The correlation between two variables is given by r = 0.0. This means: a. the best straight line through the data is horizontal b. there is a perfect positive relationship between the two variables c. there is a perfect negative relationship between the two variables d. all the points must fall exactly on a horizontal straight line 6. A regression was done with the following results: a. b. c. d. e. . If x = 10, equals 46.27 52.53 55.66 -46.27 none of the above 7. The coefficient for x2 in the regression model a. for every 1 unit change in x2, b. for every 1 unit increase in x2, means: increases by 0.78 units decreases by 0.78 units c. not enough information to answer the question d. none of the above 8. In the plot below, crime by %metropolitan in the 50 states, would you expect the regression coefficent, a. b. c. d. , to be: positive negative =0 none of the above 9. In linear regression, the null hypothesis of the test of the betas is H0: i = 0 (i.e. Xi does not statistically significantly contribute to the explanation of the variation of Y). If the CI for the test of i results in (-2.506, 0.851), I would conclude that: a. Xi does not belong in the model b. Xi does belong in the model c. neither of the above 10. The follow are the results from a data set - 2005 Statewide Crime - compiled by Agresti.* The variables are: crime: # violent crimes per 100,000 population pctmetro: % metropolitan area poverty: percent below the poverty level; single single: % families headed by a single parent The first five observations of the dataset were: crime pctmetro poverty single 761 780 593 715 1078 41.8 67.4 44.7 84.7 96.7 9.1 17.4 20.0 15.4 18.2 14.3 11.5 10.7 12.1 12.5 Pearson Correlation Coefficients, N = 50 Prob > |r| under H0: Rho=0 crime crime pctmetro poverty 1.00000 0.59396 0.36875 0.64868 <.0001 0.0084 <.0001 pctmetro 0.59396 <.0001 poverty 0.36875 -0.15562 0.0084 0.2805 single single 0.64868 <.0001 1.00000 -0.15562 0.15749 0.2805 0.2747 1.00000 0.43031 0.0018 0.15749 0.2747 0.43031 0.0018 1.00000 The REG Procedure Dependent Variable: crime Parameter Estimates Variable Parameter Standard DF Estimate Error Intercept 1 -1666.43592 pctmetro 1 7.82893 poverty 1 17.68024 single 1 132.40805 t Value Pr > |t| 147.85196 -11.27 <.0001 1.25470 6.24 <.0001 6.94093 2.55 0.0142 15.50322 8.54 <.0001 a. (1) What is the measurement scale of the variable crime? b. (1) What is the measurement scale of the variable pcmetro? c. (3) Are pctmetro and crime correlated? Explain how you came to that conclusion. If yes, what is the Pearson Correlation Coefficient? d. (2) What do you think is the most important predictor of number of violent crimes per 100,000 population in the model above? Support your