Correlation & Regression – Non Linear Emphasis

1. Correlation & Regression – Non Linear Emphasis Section 3.3

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

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

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

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.

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

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

9. Example 2……Is it linear?

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

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

12. Practice Assignment…… • Worksheet