1. Correlation & Regression – Non Linear Emphasis Section 3.3

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

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

4. Quadratic and Exponential on Calculator…… Quadratic: Exponential:

5. 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.

6. Example……The scatter plot could possibly be linear. You must check the residual pattern. xy 516.3 109.7 158.1 204.2 451.9 253.4 601.3

7. 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.

8. This is a quadratic regression….. Equation:

9. Example 2……Is it linear? xy 01 -30.125 -40.0625 38 416 532

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

11. Here is the equation you should use for predictions:

12. Practice Assignment…… Worksheet