Correlation & Regression – Non Linear Emphasis Section 3.3

Non Linear Regression Shapes…… Positive Quadratic Regression: Negative Quadratic Regression:

Non Linear Regression Shapes…… Positive Exponential Regression: Negative Exponential Regression:

Quadratic and Exponential on Calculator…… Quadratic: Exponential:

What should you look for to tell if it is not linear? Sometimes a high “r” value for linear regression is deceptive. You must look at the scatter plot AND you must look at the residual pattern it makes. Residuals – positive and negative deviations from the least squares line. Each residual is the difference between the observed y value and the corresponding predicted y value. If the residuals have a curved pattern then it is NOT linear.

Example……The scatter plot could possibly be linear. You must check the residual pattern. xy

Change y-list to resids after running a linear correlation regression – 2 nd stat resid: Notice the curved pattern in the residuals. It is either quadratic or exponential.

This is a quadratic regression….. Equation:

Example 2……Is it linear? xy

Look at the residuals…… There is a curved pattern in the residuals. It is NOT linear – we will see that it is exponential. (Positive)

Here is the equation you should use for predictions:

Practice Assignment…… Worksheet