Scatterplots, Association, and Correlation Chapter 7 Scatterplots, Association, and Correlation

Goals Understand Association Understand Correlation Work with and interpret scatterplots Distinguish between association and causation

Car Weight v. Gas Mileage

Questions What is the general pattern of the data? Does there appear to be a association between car weight and gas mileage? What type of function would best fit the data? Any unusual data values?

Marriage Ages

Marriage Ages ctd. Association type? Strength: Center: Spread:

Variable Roles Response variable The dependent variable (frequently y). Explanatory variable or predictor variable The independent variable (frequently x). used to predict or explain the values of the response variable.

Sketch a plot Drug dosage and degree of pain relief. Calories consumed and weight loss. Hours of sleep and score on a test. Shoe size and grade point average. Time for a mile run and age.

Correlation Correlation measures the strength of the linear relationship between two quantitative variables. A correlation is a specific type of association between two variables.

Car data From the course webpage, select Car Data from Fathom Data Files.

Correlation Coefficient ctd. The correlation coefficient is known as r. What is the biggest value of r? What is the smallest value of r? What value(s) correspond to a strong association between two variables? What value(s) correspond to a weak association between two variables?

Correlation Coefficient Formula

Unusual data points There are 3 types of unusual data points you will find in a scatterplot. Each can have a dramatic effect on the correlation value. Outlier Influential Observation High Leverage Point

Outlier

Influential Observation

High Leverage Point

Standardized Graph From the course webpage, select Bird Data from Fathom Data Files.

Association v. Causation The following examples all have a strong association indicated by r. Which of these are likely to have causation? Drug dosage and degree of pain relief. Calories consumed and weight loss. Ice cream consumption and number of drownings. Number of fire trucks that respond to a call and the cost of the damage.

Chapter 7 Objectives Understand and distinguish between the terms association, correlation, and causation. Know how to make a scatterplot Know how to find a correlation between two variables.