1. WARM – UP
Can you accurately predict your TEST grade based on your QUIZ grade?
STUDENT
QUIZ
TEST 1 2 3 4 5 6 7 8 88 84
100 92 70 80 81 95
102 94 90 85 99 97
Describe the association between Quiz Grades and Test Grades.
Write the equation of the line of regression.
Use this model to predict a Test Grade from a Quiz grade of 50.
Is this a good model?

2. STUDENT
QUIZ
TEST 1 2 3 4 5 6 7 8 88 84
100 92 70 80 81 95
102 94 90 85 99 97
Describe the association between Quiz Grades and Test Grades
Write the equation of the line of regression.
Use this model to predict a Test Grade from a Quiz grade of 50.
Is this a good model?
TEST Grade
Residuals
QUIZ Grade
QUIZ Grade
TEST = (QUIZ) =
= (50)

3. WARM – UP
# Hours of Study
Test Grade .5 3
1.5 2 1 72 98 82 89 76 73
Does a significant relationship exist between number of hours studying and test grades?
H0: β1 = 0
Ha: β1 ≠ 0
β=True Slope of the linear relationship.
Lin Reg t-Test
Since the p-value is less than 0.05, we REJECT H0. There is sufficient evidence to conclude that # hours of study and Test grades are related.

4. Is there a relationship between the amount of lead verses the amount of Zinc present in fish? State Hypothesis and Conclusion.
Dependent Variable is: Zinc
R-squared = 85.7%
s = with 8 – 2 = 6 degrees of freedom
Variable Coefficient SE(Coeff) T-ratio P-Value
Intercept
Lead
Because the p-val < 0.05 Reject Ho. There is evidence to conclude that a relationship exists b/t lead and zinc content in fish.

5. Regression Inference C.I.
To estimate the rate of change/slope, we use a Confidence Interval. The formula for a confidence interval for 1 is:

6. WARM – UP
STUDENT
QUIZ
TEST 1 2 3 4 5 6 7 8 88 84
100 92 70 80 81 95
102 94 90 85 99 97
Find the 95 % Conf. Interval for the Rate of Improvement from the Quiz to the Test .
Dependent Variable is: Test
R-squared = 35.3%
s = with 8 – 2 = 6 degrees of freedom
Variable Coefficient SE(Coeff) T-ratio P-Value
Intercept
Quiz
We can be 95% confident that for every additional point increase in quiz grade your test grade is predicted to be to points higher.

7. Powerboat Registrations In Thousands
EXAMPLE: Manatees living off the coast of Florida are often killed by powerboats. Here are data from 1984 – 1990
Powerboat Registrations In Thousands
Manatees
Killed
459 24
585 33
614
645 39
675 43
711 52
719 51
Dependent Variable is: Manatees
R-squared = 98.2%
s = with 7 – 2 = 5 degrees of freedom
Variable Coefficient SE(Coeff) T-ratio P-Value
Intercept
Boats <0.0001
Find the 95% confidence interval for the rate at which the Manatee deaths change with regards to powerboat registration.
We can be 95% confident that for every additional 1000 powerboat registered, between and more Manatees are killed.

9. Estimate the Rate of change for the relationship between lead and zinc using a 99% Confidence Interval
Metal Concentrations in 1999 Spokane River Fish Samples (concentrations in parts per million (ppm) Source: WA State Dept. of Ecology report)
Lead Zinc                
Dependent Variable is: Zinc
R-squared = 85.7%
s = with 8 – 2 = 6 degrees of freedom
Variable Coefficient SE(Coeff) T-ratio P-Value
Intercept
Lead
We can be 99% confident that the true slope of the relationship between lead and zinc is between .

10. Show that the p-value is 0
Show that the p-value is by using the t formula and calculating the p-value.
Lead Zinc                
Dependent Variable is: Zinc
R-squared = 85.7%
s = with 8 – 2 = 6 degrees of freedom
Variable Coefficient SE(Coeff) T-ratio P-Value
Intercept
Lead
SE(b1)

11. HW Page 661: 11, 12, 16-18

12. Is there a relationship between the amount of lead verses the amount of Zinc present in fish? State Hypothesis and Conclusion .
Metal Concentrations in 1999 Spokane River Fish Samples (concentrations in parts per million (ppm) Source: WA State Dept. of Ecology report)
Lead Zinc                
Dependent Variable is: Zinc
R-squared = 85.7%
s = with 8 – 2 = 6 degrees of freedom
Variable Coefficient SE(Coeff) T-ratio P-Value
Intercept
Lead
P-value
Because the p-val < 0.05 there is significant evidence to conclude that a relationship exists b/t lead and zinc content in fish.

13. Performing a Linear Regression t-Test from the Calculator
Is there a relationship in the amount of lead verses the amount of Zinc present in fish?
Lead Zinc                
STAT  Test  LinRegTTest
Because the p-val < 0.05 there is significant evidence to conclude that a relationship exists b/t lead and zinc content in fish.

14. Is there a relationship between the amount of lead verses the amount of Zinc present in fish? State Hypothesis and Conclusion .
Metal Concentrations in 1999 Spokane River Fish Samples (concentrations in parts per million (ppm) Source: WA State Dept. of Ecology report)
Lead Zinc                
Seb =
P-value =
Because the p-val < 0.05 there is significant evidence to conclude that a relationship exists b/t lead and zinc content in fish.