2. 4.2 Introduction to Correlation Objective: By the end of this section, I will be able to… Calculate and interpret the value of the correlation coefficient.

3. Correlation Equation

4. CORRELATION COEFFICIENT MMMMeasures the strength and direction of a relationship between two variables IIIIs denoted by the letter r TTTThe range is from -1 to +1

5. EXAMPLES  r = + 1  r = + 0.75  r = + 0.5  r = +0.25  r = 0  r = - 0.25  r = - 0.5  r = - 0.75  r = - 1 STRONG + Slightly strong + Moderate + Weak + No Association Weak - Moderate - Slightly Strong - STRONG -

6. EXAMPLES  r = + 1  r = + 0.7  r = - 0.5  r = 0  r = + 0.3  r = - 1 Strong Positive Association Slightly Strong Positive Association Moderate Negative Association No Association Weak Positive Association Strong Negative Association

7. 4.3 Introduction to Regression Objectives: By the end of this section, I will be able to… 1) Calculate the value and understand the meaning of the slope and the y intercept of the regression line. 2) Predict values of y for given values of x.

8. Algebra Days  Remember the formula:  y = mx + b  y and x are the variables  m is the slope of the line  b is the y-intercept

9. Algebra Days  Then – linear equation  NOW – linear regression

10. NEW SYMBOLS  y and x are the variables  m = b 1 is the slope  b = b o = a is the y-intercept

11. Using data to predict the future Once we have graphed the data and determined the association, we can fit a regression line which best fits or models the data. Line of Best Fit

12. Select DiagnosticOn from Catalog to get r 2 and r values with LinReg. For LinReg ALWAYS use Choice #8 NOT #4. http://www.keymath.com/documents/sia2/CalculatorNotes_Ch03_SIA2.pdf

13. LINE OF BEST FIT REGRESSION LINE

15. Regression Lines  The Regression Line is sensitive to Outliers.

16. Actual vs. Predicted Values

17. Example In BMX dirt-bike racing, jumping high or “getting air” depends on many factors: the rider’s skill, the angle of the jump, and the weight of the bike. Here are data about the maximum height for various bike weights.