Scatterplots and Correlation BPS 7e Chapter 4 © 2014 W. H. Freeman and Company
Explanatory and Response A researcher wants to know if taking increasing amounts of ginkgo biloba will result in increased memory capacity for different students. He administers it to the students in doses of 250 milligrams, 500 milligrams, and 1000 milligrams. What is the explanatory variable in this study? amount of ginkgo biloba given to each student change in memory ability size of the student’s brain whether the student takes the ginkgo biloba
Explanatory and Response (answer) A researcher wants to know if taking increasing amounts of ginkgo biloba will result in increased memory capacity for different students. He administers it to the students in doses of 250 milligrams, 500 milligrams, and 1000 milligrams. What is the explanatory variable in this study? amount of ginkgo biloba given to each student change in memory ability size of the student’s brain whether the student takes the ginkgo biloba
Explanatory and Response A study examines if state political repression increases the chances for popular revolution. What is the response variable in this study? state popular revolution state political repression repression
Explanatory and Response (answer) A study examines if state political repression increases the chances for popular revolution. What is the response variable in this study? state popular revolution state political repression repression
Displaying Relationships If a data set consists of two variables measured on each of 20 individuals, how many dots are in the scatterplot? 10 20 30 40
Displaying Relationships (answer) If a data set consists of two variables measured on each of 20 individuals, how many dots are in the scatterplot? 10 20 30 40
Displaying Relationships Everyone will draw the same conclusions about form, direction, and strength from a scatterplot. True False
Displaying Relationships (answer) Everyone will draw the same conclusions about form, direction, and strength from a scatterplot. True False
Interpreting Scatterplots Look at the following scatterplot. Choose which description BEST fits the plot. Direction: positive; form: linear; strength: strong Direction: negative; form: linear; strength: strong Direction: positive; form: non-linear; strength: weak Direction: negative; form: non-linear; strength: weak No relationship
Interpreting Scatterplots (answer) Look at the following scatterplot. Choose which description BEST fits the plot. Direction: positive; form: linear; strength: strong Direction: negative; form: linear; strength: strong Direction: positive; form: non-linear; strength: weak Direction: negative; form: non-linear; strength: weak No relationship
Interpreting Scatterplots Look at the following scatterplot. Choose which description BEST fits the plot. Direction: positive; form: non-linear; strength: strong Direction: negative; form: linear; strength: strong Direction: positive; form: linear; strength: weak Direction: positive; form: non-linear; strength: weak No relationship
Interpreting Scatterplots (answer) Look at the following scatterplot. Choose which description BEST fits the plot. Direction: positive; form: non-linear; strength: strong Direction: negative; form: linear; strength: strong Direction: positive; form: linear; strength: weak Direction: positive; form: non-linear; strength: weak No relationship
Interpreting Scatterplots Look at the following scatterplot. Choose which description BEST fits the plot. Direction: positive; form: non-linear; strength: strong Direction: negative; form: linear; strength: strong Direction: positive; form: linear; strength: weak Direction: positive; form: non-linear; strength: weak No relationship
Interpreting Scatterplots (answer) Look at the following scatterplot. Choose which description BEST fits the plot. Direction: positive; form: non-linear; strength: strong Direction: negative; form: linear; strength: strong Direction: positive; form: linear; strength: weak Direction: positive; form: non-linear; strength: weak No relationship
Interpreting Scatterplots Which of the following scatterplots displays the stronger linear relationship? Plot A Plot B Same for both
Interpreting Scatterplots (answer) Which of the following scatterplots displays the stronger linear relationship? Plot A Plot B Same for both
Interpreting Scatterplots Which phrase best describes the strength of this relationship? very weak moderate mod. strong strong
Interpreting Scatterplots (answer) Which phrase best describes the strength of this relationship? very weak moderate mod. strong strong
Adding Categorical Variables Look at the following scatterplot. Which variable is categorical? Height Weight Gender
Adding Categorical Variables (answer) Look at the following scatterplot. Which variable is categorical? Height Weight Gender
Adding Categorical Variables What do we learn by using different symbols for men and women in the following scatterplot of shoe size versus height? The form is positive. The form is linear. The relationship is moderately strong. Six or seven men likely didn’t record their height correctly.
Adding Categorical Variables (answer) What do we learn by using different symbols for men and women in the following scatterplot of shoe size versus height? The form is positive. The form is linear. The relationship is moderately strong. Six or seven men likely didn’t record their height correctly.
Correlation For which of the following situations would it be appropriate to calculate r, the correlation coefficient? time spent studying for statistics exam and score on the exam income for county employees and their respective counties eye color and hair color of selected participants party affiliation of senators and their vote on presidential impeachment
Correlation (answer) For which of the following situations would it be appropriate to calculate r, the correlation coefficient? time spent studying for statistics exam and score on the exam income for county employees and their respective counties eye color and hair color of selected participants party affiliation of senators and their vote on presidential impeachment
Correlation What is a FALSE statement about r, the correlation coefficient? It can range in value from –1 to 1. It measures the strength and direction of the linear relationship between X and Y. It is measured in units of the X variable.
Correlation (answer) What is a FALSE statement about r, the correlation coefficient? It can range in value from –1 to 1. It measures the strength and direction of the linear relationship between X and Y. It is measured in units of the X variable.
Correlation Which scatterplot would give a larger value for r? Plot A Plot B It would be the same for both plots. y y x x
Correlation (answer) Which scatterplot would give a larger value for r? Plot A Plot B It would be the same for both plots. y y x x
Correlation Which of the following is the correlation of understanding (of biology) with attitude for the following scatterplot? –0.75 –0.04 0.63 0.98
Correlation (answer) Which of the following is the correlation of understanding (of biology) with attitude for the following scatterplot? –0.75 –0.04 0.63 0.98
Facts about Correlation True or False: Computing r as a measure of the strength of the relationship between X and Y is appropriate for the data in the following scatterplot. True False y x
Facts about Correlation (answer) True or False: Computing r as a measure of the strength of the relationship between X and Y is appropriate for the data in the following scatterplot. True False y x
Facts about Correlation Compare the correlation coefficient, r, for the data in Plots A and B. r in Plot A is less than r in Plot B. r in Plot A is equal to r in Plot B. r in Plot A is greater than r in Plot B. Not enough information exists to compare the two r’s. y y x x
Facts about Correlation (answer) Compare the correlation coefficient, r, for the data in Plots A and B. r in Plot A is less than r in Plot B. r in Plot A is equal to r in Plot B. r in Plot A is greater than r in Plot B. Not enough information exists to compare the two r’s. y y x x
Facts about Correlation If we change the height measure (X) from inches into centimeters and weight measure (Y) from pounds into kilograms, what will happen to the correlation (r) coefficient? Correlation will increase. Correlation will decrease. Correlation will remain the same.
Facts about Correlation (answer) If we change the height measure (X) from inches into centimeters and weight measure (Y) from pounds into kilograms, what will happen to the correlation (r) coefficient? Correlation will increase. Correlation will decrease. Correlation will remain the same.
Facts about Correlation Given that the correlation between MPG (miles per gallon) and a car’s weight is –0.85; when reversed, the correlation between a car’s weight and MPG should become +0.85. True False
Facts about Correlation (answer) Given that the correlation between MPG (miles per gallon) and a car’s weight is –0.85; when reversed, the correlation between a car’s weight and MPG should become +0.85. True False