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.

x y

5 16.3

10 9.7

15 8.1

20 4.2

45 1.9

25 3.4

60 1.3

Change y-list to resids after running a linear correlation regression – 2nd 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?

x y

0 1

-3 0.125

-4 0.0625

3 8

4 16

5 32

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