Chapter 3 Review: Examining Relationships

1. Chapter 3 Review:Examining Relationships Karey Duane Deepak Jhol Sean Eikhoff Dylan Fryar

2. The Big Idea • The relationships between two variables can be strongly influenced by other variables that are lurking in the background. • Who are the individuals described by the data? • What are the variables ? • Why was the data gathered? • When, where, how, and by whom was the data produced?

3. Vocabulary You Need to Know • Response variable- measures the outcome of a study • Explanatory variable- helps explain or influence changes in a response variable • Scatterplot- shows the relationship between two quantitative variables measured on the same individuals • Outlier- an observation that lies outside the overall pattern of the other observations. • Positive Association- When the above-average values of one tend to accompany above-average values of the other, and below-average values also tend to occur together. • Negative Association- When above-average values of one tend to accompany below average values of the other, and vice versa. • Correlation- measures the direction and strength of the linear relationship between two quantitative variables, usually written as r.

4. Vocabulary You Need to Know • Regression Line- a line that describes how a response variable y changes as an explanatory variable x changes. • Extrapolation- the use of a regression line for prediction outside the range of values of the explanatory variable x used to obtain the line; often not accurate. • Least-Squares Regression Line- the line that makes the sum of the squared vertical distances of the data points from the line as small as possible. • Residuals- the differences between the observed and predicted values of y. • Coefficient of Determination- r2is the fraction of the variance of one variable that is explained by the least-squares regression on the other variable. • Lurking Variable- a variable that is not among the explanatory or response variables in a study and yet may influence the interpretation of relationships among those variables.

5. Key Topics Covered in this Chapter • Data • Recognize whether each variable is quantitative or categorical • Identify the explanatory or response variables in situations where one variable explains or influences another • Scatterplots • Make a scatterplot to display the relationship between two quantitative variables. Place the explanatory variable (if any) on the x-axis. • Describe the direction, form, and strength of the overall pattern of a scatterplot. • Correlation • Using a calculator, find the correlation r between two quantitative variables • Know the basic properties of correlation • Regression Lines • Explain what the slope b and the y intercept a mean in the equation ŷ=a + bx of a regression line. • Using a calculator, find the least-squares regression line for predicting values of a response variable y from an explanatory variable x from data. • Find the slope and intercept of the least-squares regression line from the means and standard deviations of x and y and their correlation • Use the regression line to predict y for a given x. Recognize extrapolation and be aware of its dangers. • Assessing Model Quality • Calculate the residuals and plot them against the explanatory variable x or against other variables. Recognize unusual patterns. • Use r2to describe how much of the variation in one variable can be accounted for by a straight-line relationship with another variable • Recognize outliers and potentially influential observations from a scatterplot with the regression line drawn on it. • Interpreting Correlation and Regression • Understand both r and the least-squares regression line can be strongly influenced by a few extreme observations. • Recognize possible lurking variables that may explain the correlation between two variables x and y.

6. Formulas You Should Know

7. Calculator Key Strokes Make a Scatterplot Perform a Regression

8. Helpful Hints Steps for Ch. 3 Problems: • Plot data on a scatterplot • Interpret what you see; direction, form, strength, outliers, etc. • Numerical Summary; x, y, sx ,sy, and r • Mathematical Model/Regression Line • How well does it fit? Residuals and r2