1 Chapter 9. Section 9-1 and 9-2. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Correlation and Regression

2 Chapter 9. Section 9-1 and 9-2. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Overview Paired Data  is there a relationship  if so, what is the equation  use the equation for prediction

3 Chapter 9. Section 9-1 and 9-2. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Definition  Correlation exists between two variables when one of them is related to the other in some way

4 Chapter 9. Section 9-1 and 9-2. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Definition  Scatterplot (or scatter diagram) is a graph in which the paired ( x,y ) sample data are plotted with a horizontal x axis and a vertical y axis. Each individual ( x,y ) pair is plotted as a single point.

5 Chapter 9. Section 9-1 and 9-2. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Scatter Diagram of Paired Data Many times the independent and dependent variables could be interchangeable

6 Chapter 9. Section 9-1 and 9-2. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Scatter Diagram of Paired Data

7 Chapter 9. Section 9-1 and 9-2. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Positive Linear Correlation x x y yy x Scatter Plots (a) Positive (b) Strong positive (c) Perfect positive

8 Chapter 9. Section 9-1 and 9-2. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Negative Linear Correlation x x y yy x (d) Negative (e) Strong negative (f) Perfect negative Scatter Plots

9 Chapter 9. Section 9-1 and 9-2. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman No Linear Correlation x x y y (g) No Correlation (h) Nonlinear Correlation Scatter Plots

10 Chapter 9. Section 9-1 and 9-2. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Descriptions of Correlation Strong, moderate, weak (no) correlation Positive or negative correlation When you are asked to describe you must use both descriptors. For example strong positive correlation.

11 Chapter 9. Section 9-1 and 9-2. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Important Correlation DOES NOT imply causation. One variable does not necessarily cause the other one to occur. Examples:Arm length versus running speed Examples: Amount of a medicine that you take versus happiness ratings.

12 Chapter 9. Section 9-1 and 9-2. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Common Errors Linearity: There may be some relationship between x and y even when there is no significant linear correlation.

13 Chapter 9. Section 9-1 and 9-2. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Distance (feet) Time (seconds) FIGURE 9-2 Common Errors Involving Correlation Scatterplot of Distance above Ground and Time for Object Thrown Upward