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

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

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? Strikes Average

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. Strikes Average

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

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

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

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

Girls’ Bowling

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 As r is beyond the critical value we reject the hypothesis that r is insignificant The correlation is significant, use the function

Boys’ Bowling

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 As r is within the critical value we accept the hypothesis that r is insignificant Since the correlation is not significant, we use the mean value for the estimate: 106.5

GPA and SAT

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

Points and Wins

Points and wins 1.r = 0.965; Positive strong. As the points difference increases, so do the points. 2.Critical value is 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.

Rank Correlation Favorite color rank correlation: –r = –Critical value is As r is beyond the critical value, the correlation is significant Temperature and ice –r = –Critical value is As r is beyond the critical value, the correlation is significant