Correlation

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
ExampleThe 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
7

• 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.

8
This is a quadratic regression..

• Equation

9
Example 2Is it linear?
x y
0 1
-3 0.125
-4 0.0625
3 8
4 16
5 32
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