1. Concepts Scatter Plot Correlation: positive, negative, none; weak, strong, perfect, significant Regression Rank correlation Prediction interval

2. Skills Creating and interpreting a scatter plot Finding and interpreting the regression coefficient –Determining if the regression coefficient is significant Writing and using the regression equation –Deciding when to use the mean and when to use the regression equation for as a point estimate of y for a given x Find and interpreting the rank regression coefficient. –Determining if the rank regression coefficient is significant Creating a prediction interval

3. Problem: Girls Bowling 1.Draw and interpret a scatter chart. 2.Find the regression coefficient for the correlation between the number of strikes and the average bowling score. 1.Describe the meaning of the correlation 2.Is this what you expected? If not, why not?. 3.Determine of the correlation is significant. 3.Write the regression equation 4.What is the point estimate of the average of a bowler who rolled 4 strikes? 5.What is the prediction interval of the average of a bowler who rolled 4 strikes? Strikes351112 Average829964627879

4. Problem: Boys Bowling 1.Draw and interpret a scatter chart 2.Find the regression coefficient for the correlation between the number of strikes and the average score. 1.Describe the meaning of the correlation 2.Is this what you expected? If not, why not?. 3.Determine if the correlation is significant. 3.Write the regression equation 4.Estimate of the average of a bowler who rolled 2 strikes 1.Explain why you choose the particular value. Strikes36557045 Average114103 10910587110121

5. GPA and Math SAT 1.Draw and interpret a scatter chart 2.Find the regression coefficient for the correlation between GPA and Math SAT. 1.Describe the meaning of the correlation. 2.Is this what you expected? If not, why not. 3.Determine of the correlation is significant. 3.Write the regression equation 4.Estimate of the point estimate SAT score for a student with a 3.7 GPA 5.Find the prediction interval for the Math SAT score for a GPA of 3.7 GPASAT 3.253500 3.384520 3.011560 3.082600 3.619620 4.634650 5.178680 4.473700 5.059750 4.532750 5.142750

6. Football Points and Wins 1.Draw and interpret a scatter chart 2.Find the regression coefficient for the correlation between GPA and Math SAT. 1.Describe the meaning of the correlation. 2.Is this what you expected? If not, why not. 3.Determine of the correlation is significant. 3.Write the regression equation 4.Find the point estimate for a 0 point difference. 5.Find the prediction interval for a point difference of 60 points Point differenceWins 8212 -277 4110 -1474 -446 10811 -78 2210 13112 -258

7. Rank Correlation: Favorite Color The frequency table to the left lists favorite colors from our poll at the beginning of the year. Find the rank correlation between the two genders and determine if it is significant GirlsBoys Black35 Blue2448 Green2526 Orange41 Purple204 Red422 White11 Gold11 Yellow136

8. Temperature vs Ice The following table lists the mean winter temperature and the number of days of ice on Lake Superior. Find the rank correlation and determine if it is significant. Mean tempdays of ice 22.9487 24.80105 23.98118 20.30136 24.1696 24.94114 22.40125 20.84118 21.73115 24.4997 20.41141 24.41111 23.95123 26.7183 23.11118 23.33116 21.47123 23.97112 24.7599 23.61102 23.88132

9. Girls’ Bowling

10. Problem Girls Bowling 1.r = 0.905; positive/strong. As the girls’ strikes increase, their averages increase. 2.Critical value for a 95% degree of confidence is 0.811. As r is beyond the critical value we reject the hypothesis that r is insignificant. 3. 4.The correlation is significant, use the function

11. Boys’ Bowling

12. Problem Boys Bowling 1.r = 0.488; positive/weak. As the boy’s strikes increase, so does the average, but not consistently 2.Critical value for a 95% degree of confidence is 0.707. As r is within the critical value we accept the hypothesis that r is insignificant. 3. 4.Since the correlation is not significant, we use the mean value for the estimate: 106.5

13. GPA and SAT

14. Problem GPA and SAT 1.r = 0.859; positive perfect. As GPA increases, so does SAT score 2.Critical value is 0.602. As r is beyond the critical value we reject the hypothesis that correlation is insignificant. 3. 4.The correlation is significant, use the function

15. Points and Wins

16. Points and wins 1.r = 0.965; Positive strong. As the points difference increases, so do the points. 2.Critical value is 0.632. As r is beyond the critical value, we reject the claim that the correlation is insignificant 3. 4.The correlation is significant, so we can use the equation.

17. Rank Correlation Favorite color rank correlation: –r = 0.761 –Critical value is 0.600. As r is beyond the critical value, the correlation is significant Temperature and ice –r = -0.661 –Critical value is 0.371. As r is beyond the critical value, the correlation is significant