Active Learning Lecture Slides For use with Classroom Response Systems Association: Contingency, Correlation, and Regression

3.1 Below is a contingency table of the results of two questions asked during the 2006 GSS. Participants were asked if gun control should be stricter after the 9/11/01 tragedy and about their political party affiliation. Find the conditional proportion of Republicans that think that gun control laws should be stricter. Should be stricter Should be less strict Total Democrat 454 62 516 Independent 195 37 232 Republican 363 104 467 1012 203 1215 a) 363 / 1215 b) 363 / 1012 c) 363 / 467 d) 1012 / 1215 e) 467 / 1215 Copyright © 2013 Pearson Education, Inc.

3.1 Below is a contingency table of the results of two questions asked during the 2006 GSS. Participants were asked if gun control should be stricter after the 9/11/01 tragedy and about their political party affiliation. Find the conditional proportion of Republicans that think that gun control laws should be stricter. Should be stricter Should be less strict Total Democrat 454 62 516 Independent 195 37 232 Republican 363 104 467 1012 203 1215 a) 363 / 1215 b) 363 / 1012 c) 363 / 467 d) 1012 / 1215 e) 467 / 1215 Copyright © 2013 Pearson Education, Inc.

3.2 Below is a contingency table of the results of two questions asked during the 2006 GSS. Participants were asked if gun control should be stricter after the 9/11/01 tragedy and about their political party affiliation. Find the conditional proportion of Democrats think that gun control laws should be stricter. Should be stricter Should be less strict Total Democrat 454 62 516 Independent 195 37 232 Republican 363 104 467 1012 203 1215 a) 454 / 516 b) 454 / 1012 c) 454 / 1215 d) 1012 / 1215 e) 516 / 1215 Copyright © 2013 Pearson Education, Inc.

3.2 Below is a contingency table of the results of two questions asked during the 2006 GSS. Participants were asked if gun control should be stricter after the 9/11/01 tragedy and about their political party affiliation. Find the conditional proportion of Democrats think that gun control laws should be stricter. Should be stricter Should be less strict Total Democrat 454 62 516 Independent 195 37 232 Republican 363 104 467 1012 203 1215 a) 454 / 516 b) 454 / 1012 c) 454 / 1215 d) 1012 / 1215 e) 516 / 1215 Copyright © 2013 Pearson Education, Inc.

3.3 Below is a contingency table of the results of two questions asked during the 2006 GSS. Participants were asked if gun control should be stricter after the 9/11/01 tragedy and about their political party affiliation. What percentage of those surveyed think that gun control laws should be stricter? Should be stricter Should be less strict Total Democrat 454 62 516 Independent 195 37 232 Republican 363 104 467 1012 203 1215 a) 77% b) 83% c) 84% d) 88% e) 90% Copyright © 2013 Pearson Education, Inc.

3.3 Below is a contingency table of the results of two questions asked during the 2006 GSS. Participants were asked if gun control should be stricter after the 9/11/01 tragedy and about their political party affiliation. What percentage of those surveyed think that gun control laws should be stricter? Should be stricter Should be less strict Total Democrat 454 62 516 Independent 195 37 232 Republican 363 104 467 1012 203 1215 a) 77% b) 83% c) 84% d) 88% e) 90% Copyright © 2013 Pearson Education, Inc.

3.4 A personal trainer decides to track the amount of time each of her clients spends exercising and their amount of weight loss in a two month period. What are the explanatory and response variables? a) Explanatory variable: time spent exercising Response variable: weight loss b) Explanatory variable: weight loss Response variable: time spent exercising c) Cannot be determined Copyright © 2013 Pearson Education, Inc.

3.4 A personal trainer decides to track the amount of time each of her clients spends exercising and their amount of weight loss in a two month period. What are the explanatory and response variables? a) Explanatory variable: time spent exercising Response variable: weight loss b) Explanatory variable: weight loss Response variable: time spent exercising c) Cannot be determined Copyright © 2013 Pearson Education, Inc.

3.5 A psychologist believes that people who have a religious belief system are happier. She asks 10 people each of the Jewish, Christian, Islamic, Hindu and Buddhist religions as well as 10 people who claim no religion to rate their happiness on a 5 point scale. Which more naturally is the response variable and the explanatory variable? a) Explanatory variable: happiness rating Response variable: religion b) Explanatory variable: religion Response variable: happiness rating c) Cannot be determined Copyright © 2013 Pearson Education, Inc.

3.5 A psychologist believes that people who have a religious belief system are happier. She asks 10 people each of the Jewish, Christian, Islamic, Hindu and Buddhist religions as well as 10 people who claim no religion to rate their happiness on a 5 point scale. Which more naturally is the response variable and the explanatory variable? a) Explanatory variable: happiness rating Response variable: religion b) Explanatory variable: religion Response variable: happiness rating c) Cannot be determined Copyright © 2013 Pearson Education, Inc.

3.6 What type of graphic would you use to explore the association between two quantitative variables? a) Contingency Table b) Side-by-Side Boxplots c) Scatterplots d) All of the above Copyright © 2013 Pearson Education, Inc.

3.6 What type of graphic would you use to explore the association between two quantitative variables? a) Contingency Table b) Side-by-Side Boxplots c) Scatterplots d) All of the above Copyright © 2013 Pearson Education, Inc.

3.7 The scatterplot below shows a graph of median family incomes per state as determined by the US Census for 1969 versus 1989. In general, what can be said about the straight line association between the variables? a) Strong, negative b) Strong, positive c) Weak, negative d) Weak, positive http://www.census.gov/hhes/www/income/histinc/state/state2.html Copyright © 2013 Pearson Education, Inc.

3.7 The scatterplot below shows a graph of median family incomes per state as determined by the US Census for 1969 versus 1989. In general, what can be said about the straight line association between the variables? a) Strong, negative b) Strong, positive c) Weak, negative d) Weak, positive http://www.census.gov/hhes/www/income/histinc/state/state2.html Copyright © 2013 Pearson Education, Inc.

3.8 Which of the following properties is NOT a property of correlation (r)? a) It is unitless. b) It ranges from –1 to 1. c) It measures the strength of any type of relationship between x and y. d) If r = 0.9, the data exhibits a positive linear relationship. e) It is not resistant to outliers. Copyright © 2013 Pearson Education, Inc.

3.8 Which of the following properties is NOT a property of correlation (r)? a) It is unitless. b) It ranges from –1 to 1. c) It measures the strength of any type of relationship between x and y. d) If r = 0.9, the data exhibits a positive linear relationship. e) It is not resistant to outliers. Copyright © 2013 Pearson Education, Inc.

3.9 What value of “r” below best describes the scatterplot below? Copyright © 2013 Pearson Education, Inc.

3.9 What value of “r” below best describes the scatterplot below? Copyright © 2013 Pearson Education, Inc.

3.10 What value of “r” below would you expect if you were comparing the number of hours that students spend studying versus their GPA? a) 0.99 b) 0.70 c) 0.00 d) -0.70 Copyright © 2013 Pearson Education, Inc.

3.10 What value of “r” below would you expect if you were comparing the number of hours that students spend studying versus their GPA? a) 0.99 b) 0.70 c) 0.00 d) -0.70 Copyright © 2013 Pearson Education, Inc.

3.11 A least squares regression equation was created from last year’s students data to predict Exam 3 scores based on Exam 1 scores. The equation was: Predict the score on Exam 3 for a student that scored an 80 on Exam 1. a) 69.70 b) 79.89 c) 85.53 d) 89.33 e) 90.53 Copyright © 2013 Pearson Education, Inc.

3.11 A least squares regression equation was created from last year’s students data to predict Exam 3 scores based on Exam 1 scores. The equation was: Predict the score on Exam 3 for a student that scored an 80 on Exam 1. a) 69.70 b) 79.89 c) 85.53 d) 89.33 e) 90.53 Copyright © 2013 Pearson Education, Inc.

3.12 In northern cities roads are salted to keep ice from freezing on the roadways between 0 and -9.5° C. Suppose that a small city was trying to determine what was the average amount of salt (in tons) needed per night at certain temperatures. They found the following LSR equation: Interpret the y-intercept. 2,500 tons is the average decrease in the amount of salt needed for a 1 degree increase in temperature. b) Do not interpret. There is no data around x= 0° C. c) 20,000 tons is the predicted amount of salt needed when the temperature is 0° C. d) 2,500 tons is the predicted amount of salt needed when the temperatures is 0° C. Copyright © 2013 Pearson Education, Inc.

3.12 In northern cities roads are salted to keep ice from freezing on the roadways between 0 and -9.5° C. Suppose that a small city was trying to determine what was the average amount of salt (in tons) needed per night at certain temperatures. They found the following LSR equation: Interpret the y-intercept. 2,500 tons is the average decrease in the amount of salt needed for a 1 degree increase in temperature. b) Do not interpret. There is no data around x= 0° C. c) 20,000 tons is the predicted amount of salt needed when the temperature is 0° C. d) 2,500 tons is the predicted amount of salt needed when the temperatures is 0° C. Copyright © 2013 Pearson Education, Inc.

3.13 In northern cities roads are salted to keep ice from freezing on the roadways between 0 and -9.5° C. Suppose that a small city was trying to determine what was the average amount of salt (in tons) needed per night at certain temperatures. They found the following LSR equation: Interpret the slope. a) 2,500 tons is the average decrease in the amount of salt needed for a 1 degree increase in temperature. b) 2,500 tons is the average increase in the amount of salt c) 20,000 is the average increase in the amount of salt needed for a 1 degree increase in temperature. Copyright © 2013 Pearson Education, Inc.

3.13 In northern cities roads are salted to keep ice from freezing on the roadways between 0 and -9.5° C. Suppose that a small city was trying to determine what was the average amount of salt (in tons) needed per night at certain temperatures. They found the following LSR equation: Interpret the slope. a) 2,500 tons is the average decrease in the amount of salt needed for a 1 degree increase in temperature. b) 2,500 tons is the average increase in the amount of salt c) 20,000 is the average increase in the amount of salt needed for a 1 degree increase in temperature. Copyright © 2013 Pearson Education, Inc.

3.14 From 1974 to 1990 the GSS asked how happy people were in their marriage. The percentage of people that said “very happy” was plotted over time. Use the summary statistics below to compute the least squares regression line to predict the percent of those that are “very happy” in their marriage based on the year. a) b) c) d) Copyright © 2013 Pearson Education, Inc.

3.14 From 1974 to 1990 the GSS asked how happy people were in their marriage. The percentage of people that said “very happy” was plotted over time. Use the summary statistics below to compute the least squares regression line to predict the percent of those that are “very happy” in their marriage based on the year. a) b) c) d) Copyright © 2013 Pearson Education, Inc.

e) Cannot be determined 3.15 A least squares regression equation was created from last year’s students data to predict Exam 3 scores based on Exam 1 scores. The equation was: Suppose that a student made a 60 on Exam 1 and an 80 on Exam 3. Find the residual. a) 0.36 b) 0.54 c) -0.36 d) -0.54 e) Cannot be determined Copyright © 2013 Pearson Education, Inc.

e) Cannot be determined 3.15 A least squares regression equation was created from last year’s students data to predict Exam 3 scores based on Exam 1 scores. The equation was: Suppose that a student made a 60 on Exam 1 and an 80 on Exam 3. Find the residual. a) 0.36 b) 0.54 c) -0.36 d) -0.54 e) Cannot be determined Copyright © 2013 Pearson Education, Inc.

3.16 An experimenter wants to determine if a particular type of diet cat food (brand A or B) tends to have the most weight loss for Abyssinian and Siamese cats. In order to make the experiment easier to run he gives brand A to only Abyssinian cats and brand B to only Siamese cats. What type of error has been made? a) Simpson’s Paradox b) Interpolation c) Extrapolation d) Confounding e) No error has been made Copyright © 2013 Pearson Education, Inc.

3.16 An experimenter wants to determine if a particular type of diet cat food (brand A or B) tends to have the most weight loss for Abyssinian and Siamese cats. In order to make the experiment easier to run he gives brand A to only Abyssinian cats and brand B to only Siamese cats. What type of error has been made? a) Simpson’s Paradox b) Interpolation c) Extrapolation d) Confounding e) No error has been made Copyright © 2013 Pearson Education, Inc.

e) No error has been made 3.17 The GSS survey asked married men from 1974 to 2006 how happy they were in their marriage. According to this formula, in 2050 only 51.5% of married men will be very happy. What type of error has been made here? a) Simpson’s Paradox b) Interpolation c) Extrapolation d) Confounding e) No error has been made Copyright © 2013 Pearson Education, Inc.

e) No error has been made 3.17 The GSS survey asked married men from 1974 to 2006 how happy they were in their marriage. According to this formula, in 2050 only 51.5% of married men will be very happy. What type of error has been made here? a) Simpson’s Paradox b) Interpolation c) Extrapolation d) Confounding e) No error has been made Copyright © 2013 Pearson Education, Inc.

3.18 From 1980 to 2002, Americans were asked if they would feel safe traveling on a commercial airplane. A plot of the year versus the percentage that would feel safe is shown below. Comment on what is happening in the plot. a) Evidence of extrapolation b) Evidence of a regression outlier c) Evidence of confounding d) Evidence of nonresponse Copyright © 2013 Pearson Education, Inc.

3.18 From 1980 to 2002, Americans were asked if they would feel safe traveling on a commercial airplane. A plot of the year versus the percentage that would feel safe is shown below. Comment on what is happening in the plot. a) Evidence of extrapolation b) Evidence of a regression outlier c) Evidence of confounding d) Evidence of nonresponse Copyright © 2013 Pearson Education, Inc.

3.19 True or False: If two variables have a correlation equal to 0.99, x must cause y. a) True b) False Copyright © 2013 Pearson Education, Inc.

3.19 True or False: If two variables have a correlation equal to 0.99, x must cause y. a) True b) False Copyright © 2013 Pearson Education, Inc.