Scatterplots and Correlation BPS chapter 4 © 2010 W.H. Freeman and Company

Explanatory variables A researcher wants to know if taking increasing amounts of ginkgo biloba will result in increased capacities of memory ability 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 variables (answer) A researcher wants to know if taking increasing amounts of ginkgo biloba will result in increased capacities of memory ability 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.

Numeric bivariate data The first step in analyzing numeric bivariate data is to Measure strength of linear relationship. Create a scatterplot. Model linear relationship with regression line.

Numeric bivariate data (answer) The first step in analyzing numeric bivariate data is to Measure strength of linear relationship. Create a scatterplot. Model linear relationship with regression line.

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

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

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

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

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

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

Scatterplots Which of the following scatterplots displays the stronger linear relationship? Plot A Plot B Same for both

Scatterplots (answer) Which of the following scatterplots displays the stronger linear relationship? Plot A Plot B Same for both

Scatterplots Look at the following scatterplot. Which variable is categorical? Height Weight Gender

Scatterplots (answer) Look at the following scatterplot. Which variable is categorical? Height Weight Gender

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 is a product of z-scores of X and Y. 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 is a product of z-scores of X and Y. 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.

Correlation (answer) Which scatterplot would give a larger value for r? Plot A Plot B It would be the same for both plots.

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

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

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.

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.