Active Learning Lecture Slides For use with Classroom Response Systems

Chapter 3: Association: Contingency, Correlation, and Regression

Statistics: The Art and Science of Learning from

Data

Second Edition

by Agresti/Franklin

3.1.1) 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.

a) 363 / 1215

b) 363 / 1012

c) 363 / 467

d) 1012 / 1215

e) 467 / 1215

Should be stricter

Should be less strict

Total

Democrat 454 62 516

Independent 195 37 232

Republican 363 104 467

Total 1012 203 1215

3.1.1) 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.

a) 363 / 1215

b) 363 / 1012

c) 363 / 467

d) 1012 / 1215

e) 467 / 1215

Should be stricter

Should be less strict

Total

Democrat 454 62 516

Independent 195 37 232

Republican 363 104 467

Total 1012 203 1215

3.1.2) 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.

a) 454 / 516

b) 454 / 1012

c) 454 / 1215

d) 1012 / 1215

e) 516 / 1215

Should be stricter

Should be less strict

Total

Democrat 454 62 516

Independent 195 37 232

Republican 363 104 467

Total 1012 203 1215

3.1.2) 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.

a) 454 / 516

b) 454 / 1012

c) 454 / 1215

d) 1012 / 1215

e) 516 / 1215

Should be stricter

Should be less strict

Total

Democrat 454 62 516

Independent 195 37 232

Republican 363 104 467

Total 1012 203 1215

3.1.3) 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 proportion of those surveyed think that gun control laws should be stricter?

a) 77%

b) 83%

c) 84%

d) 88%

e) 90%

Should be stricter

Should be less strict

Total

Democrat 454 62 516

Independent 195 37 232

Republican 363 104 467

Total 1012 203 1215

3.1.3) 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 proportion of those surveyed think that gun control laws should be stricter?

a) 77%

b) 83%

c) 84%

d) 88%

e) 90%

Should be stricter

Should be less strict

Total

Democrat 454 62 516

Independent 195 37 232

Republican 363 104 467

Total 1012 203 1215

3.1.4) 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

3.1.4) 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

3.1.5) 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

3.1.5) 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

3.2.1) 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

3.2.1) 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

3.2.2) 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

3.2.2) 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

3.2.3) 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 = 1, the data falls in a perfectly straight line.

e) It is not resistant to outliers.

3.2.3) 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 = 1, the data falls in a perfectly straight line.

e) It is not resistant to outliers.

3.2.4) What value of “r” below best describes the scatterplot below?

a) 0.9

b) -0.9

c) 0.3

d) -0.3

e) 0

3.2.4) What value of “r” below best describes the scatterplot below?

a) 0.9

b) -0.9

c) 0.3

d) -0.3

e) 0

3.2.5) 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

3.2.5) 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

3.3.1) 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:

a) 69.70

b) 79.89

c) 85.53

d) 89.33

e) 90.53

xy 4845.057.50ˆ

Predict the score on Exam 3 for a student that scored an 80 on Exam 1.

3.3.1) 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:

a) 69.70

b) 79.89

c) 85.53

d) 89.33

e) 90.53

xy 4845.057.50ˆ

Predict the score on Exam 3 for a student that scored an 80 on Exam 1.

3.3.2) 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: xy 500,2000,20ˆ Interpret the y-intercept.

a) 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 expected amount of salt needed when the temperature is 0° C.

d) 2,500 tons is the expected amount of salt needed when the temperatures is 0° C.

3.3.2) 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: xy 500,2000,20ˆ Interpret the y-intercept.

a) 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 expected amount of salt needed when the temperature is 0° C.

d) 2,500 tons is the expected amount of salt needed when the temperatures is 0° C.

3.3.3) 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: xy 500,2000,20ˆ

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 needed for a 1 degree increase in temperature.

c) 20,000 is the average increase in the amount of salt needed for a 1 degree increase in temperature.

3.3.3) 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: xy 500,2000,20ˆ

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 needed for a 1 degree increase in temperature.

c) 20,000 is the average increase in the amount of salt needed for a 1 degree increase in temperature.

3.3.4) 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” based on the year.

ˆ 759.0 0.3502

ˆ 2098 11.79

ˆ 629.3 0.3502

ˆ 1866 1.790

y x

y x

y x

y x

a)b)c)d)

792.0

419.2

47.5

845.64

1.1982

r

s

s

y

x

y

x

3.3.4) 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” based on the year.

ˆ 759.0 0.3502

ˆ 2098 11.79

ˆ 629.3 0.3502

ˆ 1866 1.790

y x

y x

y x

y x

a)b)c)d)

792.0

419.2

47.5

845.64

1.1982

r

s

s

y

x

y

x

3.3.5) 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: xy 4845.057.50ˆ

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

3.3.5) 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: xy 4845.057.50ˆ

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

3.4.1) 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

3.4.1) 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

3.4.2) 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?

xy 174.02.408ˆ

a) Simpson’s Paradox

b) Interpolation

c) Extrapolation

d) Confounding

e) No error has been made

3.4.2) 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?

xy 174.02.408ˆ

a) Simpson’s Paradox

b) Interpolation

c) Extrapolation

d) Confounding

e) No error has been made

3.4.3) 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

3.4.3) 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

3.4.4) True or False: If two variables have a correlation equal to 0.99, x must cause y.

a) True

b) False

3.4.4) True or False: If two variables have a correlation equal to 0.99, x must cause y.

a) True

b) False