A. Estimate the Equation of the Regression Line

AP Stats Name______

1. The average age of lifeguards is 24. We sampled 36 lifeguards. We know that s = 2 and

Ho :m = 24 a = 0.05. Test the hypothesis . Find the power of the test if the average age H A :m > 24 is really 25.

2. A study found that age and blood pressure are correlated. The data is shown below.

Age (x) 45 65 34 21 17 19 42 55 37 52 28 23 37 43 Blood Pressure (y) 140 145 90 95 90 92 125 140 110 130 100 90 120 130

a. Estimate the equation of the regression line.

b. Estimate the Blood pressure for a person who is 50.

c. Find the residual amount for a person who is 42.

d. Explain the slope in context of the problem.

e. Find r 2 . Explain it in context of the problem.

f. Find se . Explain it in context of the problem.

g. Find the probability that a person 50 years old has a blood pressure of at least 132. 3. The flow rate in a device used for air quality measurement depends on the pressure drop x 9in inches of water) across the device’s filter. Suppose that for x values between 5 and 20, these two variables are related according to the simple linear regression model with true regression line y= -0. 12 + 0 . 095 x . a. What is the true average flow rate for a pressure drop of 10 in? a drop of 15 in? b. What is the true average change in flow rate associated with a 1 in. increase in pressure drop? Explain. c. What is the average change in flow rate when pressure drop decreases by 5 in?

4. A sample of small cars was selected, and the values of x = horsepower and y = fuel efficiency (mpg) were determined for each car. Fitting the simple linear regression model gave the estimated regression equation ^ y=44. 0 - 0 . 150 x . a. How would you interpret b = -0.150? ^ b. Substituting x = 100 gives y = 29.0. Give two different interpretations of this number. c. What happens if you predict efficiency for a car with a 300 hp engine? Why do you think this has occurred? d. Interpret r2 = 0.680 in the context of this problem.

e. Interpret se= 3.0 in the context of this problem.

5. In the context of simple linear regression, explain the following differences: ^ a. The difference between the line y=a + b x and the line y= a + bx . b. The difference between b and b . c. The difference between a+ b x* and a+ bx* where x* denotes a particular value of the independent variable. d. The difference between s and r .

6. The following data on x = treadmill run time to exhaustion (in minutes) and y = 20-km ski time (in minuts) was taken from the article...

x 7.7 8.4 8.7 9 9.6 9.6 10 10.2 10.4 11 11.7 y 71 71.4 65 68.7 64.4 69.4 63 64.6 66.9 62.6 61.7

a. Draw the scatterplot for these data. Does the scatterplot suggest that the simple linear regression model is appropriate? b. Determine the equation of the estimated regression line, and draw the line on your scatterplot. c. What is your estimate of the average change in ski time associated with a 1-min increase in treadmill time? d. What would you predict ski time to be for an individual whose treadmill time is 10 min? e. Should the model be used as a basis for predicting ski time when treadmill time is 15 min? Explain. f. Calculate and interpret the value of r2 . g. Calculate and interpret the value of se