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 correlation2. Is this what you expected? If not, why not?.3. Determine of the correlation is significant.

3. Write the regression equation4. 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 3 5 1 1 1 2

Average

82 99 64 62 78 79

Problem: Boys Bowling

1. Draw and interpret a scatter chart2. Find the regression coefficient for the correlation

between the number of strikes and the average score.1. Describe the meaning of the correlation2. Is this what you expected? If not, why not?.3. Determine if the correlation is significant.

3. Write the regression equation4. Estimate of the average of a bowler who rolled 2

strikes1. Explain why you choose the particular value.

Strikes 3 6 5 5 7 0 4 5

Average 114 103 103 109 105 87 110 121

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

GPA SAT

3.253 500

3.384 520

3.011 560

3.082 600

3.619 620

4.634 650

5.178 680

4.473 700

5.059 750

4.532 750

5.142 750

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

Pointdifference Wins

82 12

-27 7

41 10

-147 4

-44 6

108 11

-7 8

22 10

131 12

-25 8

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

Girls Boys

Black 3 5

Blue 24 48

Green 25 26

Orange 4 1

Purple 20 4

Red 4 22

White 1 1

Gold 1 1

Yellow 13 6

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 temp days of ice22.94 8724.80 10523.98 11820.30 13624.16 9624.94 11422.40 12520.84 11821.73 11524.49 9720.41 14124.41 11123.95 12326.71 8323.11 11823.33 11621.47 12323.97 11224.75 9923.61 10223.88 132

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 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

ˆ 60.844 7.610( )y x

ˆ 60.844 7.610(4)

91.284

y

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 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

96.549 2.275( )y x

GPA and SAT

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

ˆ 91.134 267.78y x

ˆ 91.134(3.7) 267.78

605

y

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 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.

ˆ 0.0312 8.3822y x

ˆ 0.0312(0) 8.3822

8.4

y

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