1. STAT 1301 Chapter 8 Scatter Plots, Correlation

2. For Regression Unit You Should Know n How to plot points n Equation of a line Y = mX + b m = slope b = Y-intercept n Plotting line from equation Y = 3X + 2

3. Data Set X Y 1 5 3 9 4 7 5 1 7 13 1 2 3 4 5 6 7 8 121086420 Y X

4. 121086420 Y X X Y X Y 0 2 0 2 3 11 3 11 Y = 3X + 2 Y = 3X + 2..

5. For Regression Unit You Should Know n How to plot points n Equation of a line Y = mX + b m = slope b = Y-intercept n Plotting line from equation Y = 3X + 2 n Chapter 7 - Good Review if needed

6. Histogram n displays distribution of 1 variable Scatter Diagram Scatter Diagram n displays joint distribution of 2 variables n plots data as “points” in the“x-y plane.”

9. Association Between Two Variables indicates that knowing one helps in predicting the otherindicates that knowing one helps in predicting the other n Linear Association our interest in this courseour interest in this course points “swarm” about a linepoints “swarm” about a line n Correlation Analysis measures the strength of linear associationmeasures the strength of linear association

10. Hypothetical Father-Son Data

11. (association)

12. Regression Analysis n we want to predict the dependent variable using the independent variable DependentVariable(Y) Independent Variable (X)

13. Correlation Coefficient - measures linear association -1 0 +1 -1 0 +1 perfect no perfect perfect no perfect negative linear positive relationship relationship relationship n We use the letter “ r ” to denote the correlation coefficient.

14. Positive Correlation - - high values of one variable are associated with high values of the other Examples: n Father’s height, son’s height n daily grade, final grade n r = 0.93 for plot on the left 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 3210

16. Negative Correlation - - high with low, low with high Examples: n Car weight, miles per gallon n Days absent, final grade n r = - 0.89 for plot shown here 1 2 3 4 5 6 7 1 2 3 4 5 6 7 43210

18. Zero Correlation - - no linear relationship Examples: n height, IQ score n r = 0.0 for plot here 1 2 3 4 5 6 7 1 2 3 4 5 6 7 543210

19. -.75, 0,.5,.99

21. r = 0.00

22. r = 0.40

23. r = - 0.60

24. r = 0.8

25. r = 0.95