Lecture 12 Cautions in Analyzing Associations

Transcription

1 Lecture 12 Cautions in Analyzing Associations MA Stephen Sawin Fairfield University August 8, 2017

2 Cautions in Linear Regression Three things to be careful when doing linear regression we have already talked about: If the relationship is not linear, then r, r 2 and the least squares line are not telling you much useful. There is no reason to think the least squares line or r tell you anything useful about values of x outside the range in which you have data. Correlation does not imply Causation: Lurking variables can make unrelated variables appear related and vice versa.

3 Cautions in Linear Regression Three things to be careful when doing linear regression we have already talked about: If the relationship is not linear, then r, r 2 and the least squares line are not telling you much useful. There is no reason to think the least squares line or r tell you anything useful about values of x outside the range in which you have data. Correlation does not imply Causation: Lurking variables can make unrelated variables appear related and vice versa.

4 Cautions in Linear Regression Three things to be careful when doing linear regression we have already talked about: If the relationship is not linear, then r, r 2 and the least squares line are not telling you much useful. There is no reason to think the least squares line or r tell you anything useful about values of x outside the range in which you have data. Correlation does not imply Causation: Lurking variables can make unrelated variables appear related and vice versa.

5 Types of Outliers Outlier in the x direction - an unusual x value. Outlier in the y direction - an unusual y value. Regression Outlier - a point with an unusually large residual. Noninfluential Outlier - A regression outlier whose x is near the x mean. Influential Outlier - A regression outlier whose x is far from the mean.

6 Types of Outliers Outlier in the x direction - an unusual x value. Outlier in the y direction - an unusual y value. Regression Outlier - a point with an unusually large residual. Noninfluential Outlier - A regression outlier whose x is near the x mean. Influential Outlier - A regression outlier whose x is far from the mean.

7 Types of Outliers Outlier in the x direction - an unusual x value. Outlier in the y direction - an unusual y value. Regression Outlier - a point with an unusually large residual. Noninfluential Outlier - A regression outlier whose x is near the x mean. Influential Outlier - A regression outlier whose x is far from the mean.

8 Types of Outliers Outlier in the x direction - an unusual x value. Outlier in the y direction - an unusual y value. Regression Outlier - a point with an unusually large residual. Noninfluential Outlier - A regression outlier whose x is near the x mean. Influential Outlier - A regression outlier whose x is far from the mean.

9 Types of Outliers Outlier in the x direction - an unusual x value. Outlier in the y direction - an unusual y value. Regression Outlier - a point with an unusually large residual. Noninfluential Outlier - A regression outlier whose x is near the x mean. Influential Outlier - A regression outlier whose x is far from the mean.

10 Influential/Noninfluential Outliers The GPA data without any outliers:

11 Influential/Noninfluential Outliers The GPA data with an influential outlier:

12 Influential/Noninfluential Outliers The GPA data without any outliers:

13 Influential/Noninfluential Outliers The GPA data with a noninfluential outlier:

14 Residual Regardless of its influence a regression outlier, a point with with an unusually large residual, has a response variable that is way above or below what you would expect just based on the value of their explanatory variable. Thus there is something else strongly affecting it, and it is always worth figuring out what that something is.

15 Lecture 12 Key Points After this lecture you should be able to Not draw conclusions for x values outside the range of your data. Know that causation does not imply correlation. After processing this lecture you should be able to Recognize the different types of outliers (outliers in x and y direction, regression outliers and influential outliers) and their effect on the last squares line.