Quiz 2 Stats test

SS 1023/2037 Quiz 2 Instructor: Johanna de Haan-Ward October 10 2023 SS1023/2037A: Fall 2023 Quiz 2 Version 1 Name: Student number: Section (circle): SS1023 SS2037 MULTIPLE CHOICE: 6 QUESTIONS Circle the correct answer. There is only one correct answer per question. Each question is worth one (1) point. QUESTION 1 The correlation between two variables x and y is -0.77. The R-squared is: a) 0.77 b) -0.77 c) 0.593 d) -0.593 e) 0.877 QUESTION 2 In the fall of 1973, University of California at Berkeley admitted 44% of men who applied to their graduate programs, but only 35% of women who applied to these same graduate programs. However, when these applicants were grouped by faculty, 4 of 6 faculties actually admitted a greater percent of women applicants. This is an example of: a) Simpson’s paradox b) Contingency tables c) Correlation is not causation d) Relative risk QUESTION 3 Which of the following statements is plausible: a) The correlation between x and y is 27%. b) This linear regression shows that 75% of the variation in fuel efficiency is caused by the weight of the vehicle. c) The intercept value of a simple linear regression with grade as the response and hours studied as the explanatory variable is 10, which means that for every hour studied, the expected grade increases by 10. d) The odds ratio is -0.13. e) None of the above.

SS 1023/2037 Quiz 2 Instructor: Johanna de Haan-Ward October 10 2023 QUESTION 4 Consider the following statements about the correlation, ? , between two variables ? and ? . (1) Correlation has the same sign (i.e. positive or negative) as the slope term of a linear regression with x as the explanatory variable and y as the response variable. (2) Correlation has the opposite sign the slope term of a linear regression with x as the explanatory variable and y as the response variable (3) Correlation must be between -1 and 1. (4) Correlation is never negative Which statements are true? a) Only (1) is true b) (2) and (4) are true c) (1) and (3) are true d) Only (4) is true e) (2) and (3) are true QUESTION 5 When examining the residuals from a fitted least squares regression line, you should: a) Verify that the residuals are unimodal and Normally distributed. b) Verify that the residuals are Normally distributed and that the scatterplot with fitted values on the x-axis and residuals on the y-axis shows a linear pattern. c) Verify that the residuals are Normally distributed and that the scatterplot with fitted values on the x-axis and residuals on the y-axis shows no clear pattern. d) Verify that the residuals are Normally distributed and that the scatterplot with response values on the x-axis and residuals on the y-axis shows no clear pattern. QUESTION 6 The figure on the right is from “Drivers of California’s changing wildfires: a state -of-the knowledge synthesis ” (2023) by MacDonald et al. The dark line through the points represents the least squares regression line. Consider the following statements: (1) There is a positive association between these two variables. (2) There are no outliers. (3) Area burned (ha) is the explanatory variable. (4) The correlation between Year and Area burned (ha) is 0.249. Which statements are true? a) (1) and (2) are true b) (3) and (4) are true c) Only (2) is true d) Only (1) is true e) Only (4) is true

SS 1023/2037 Quiz 2 Instructor: Johanna de Haan-Ward October 10 2023 QUESTION 3 (6 points) a) Define risk. The probability with which an event will occur. b) Define odds. The probability of the event occurring divided by the probability of the event not occurring. Consider the following contingency table, which summarizes 222 days of weather forecasts, focusing on thunderstorms. c) What is the relative risk of a thunderstorm occurring when there is a thunderstorm forecast compared to when there is not one forecast? Interpret this value. 𝑹𝑹 = ? ሺ? + ?ሻ ൗ ? ሺ? + ?ሻ ൗ = ?? ሺ?? + ??ሻ ൗ ? ሺ? + ???ሻ ൗ = ??. ?? RR > 1, so the risk of a thunderstorm is greater if one is in the forecast. d) What is the odds ratio? Interpret this value. 𝑶𝑹 = ?? ?? ൗ ? ??? ൗ = ?? OR > 1, so the odds of a thunderstorm are greater if one is in the forecast. QUESTION 4 (2 points) Suppose we have two different regression lines fit to the same set of five observations. We want to know which fits the data better. The first line results in the residuals: 0.5, 1.8, -0.8, 2.2, -5.2. The second line results in the residuals: 0.2, -1.1, 4.8, 3.3, -2. Which line fits the data better? Explain your answer. Line 1: 0.5 2 + 1.8 2 + ሺ−0.8ሻ 2 + 2.2 2 + ሺ−5.2ሻ 2 = 36.01 Line 2: 0.2 2 + ሺ−1.1ሻ 2 + 4.8 2 + 3.3 2 + ሺ−2ሻ 2 = 39.18 Line 1 has a lower sum of residual squares, and thus fits the data better. Thunderstorm occurred Yes No Thunderstorm in the forecast Yes 24 20 No 3 175

SS 1023/2037 Quiz 2 Instructor: Johanna de Haan-Ward October 10 2023 RELEVANT EQUATIONS ? ? = ? ? ? ? ? ? ? = ? ̅ − ? ? ? ̅ 𝑹𝑹 = ? ሺ? + ?ሻ ൗ ? ሺ? + ?ሻ ൗ 𝑶𝑹 = ? ? ൗ ? ? ൗ