stat

STAT 350 (Spring 2017) Homework 11 (20 points + 1 point BONUS) 1

Practice Problems: 12.5 (p. 588), 12.9 (p.588) (4 pts.) 1. For each of the following graphs, identify the form, direction (if possible) and relative

strength. In addition, state if you think that there is an association between X and Y. No explanation is required.

a) b)

c) d)

STAT 350 (Spring 2017) Homework 11 (20 points + 1 point BONUS) 2

(14 pts.) 2. Deep-water (>300m) wave forecasts are important for large cargo ships. One method of prediction suggests that the wind speed (x, in knots) is linearly related to the wave height (y, in feet). A random sample of buoys was obtained, and the wind speed and wave height was measured at each. The summary data is shown below.

n = 20, SXX = 91.75, SYY = 15.952, SXY= 36.4, x̄ = 9.25, ȳ = 1.68 The scatter plot of the data is shown below:

(2 pts.) a) Find the estimated regression line for the regression of Wave Height as a function of

Wind Speed. (1 pt.) b) Does the y-intercept have any physical meaning? (1 pt.) c) How much change in wave height is expected when the wind speed increases by one

knot? Please explain your answer. (1 pt.) d) What is the expected value of wave height when the wind speed is 8.6 knots (10

mph)? (6 pts.) e) Complete the following ANOVA table.

Source of variation Degrees of Freedom Sum of squares Mean square

Regression

Error

Total

(1 pt.) f) What is the estimated variance? (1 pt.) g) What is the proportion of the wave height that is explained by wind speed? (1 pt.) h) From the information in the previous parts of this question, do you believe that there is

an association between wave height and wind speed? Please explain your answer. No additional calculations are required.

STAT 350 (Spring 2017) Homework 11 (20 points + 1 point BONUS) 3

(2 pts.) 3. Some physicians use the cholesterol ratio (CR = total cholesterol/HDL cholesterol) as a measure of a patient’s risk of heart disease. In addition, the triglyceride concentration (TG) is associated with coronary artery disease in many patients. In a study of the relationship between these two variables, a random sample of adults was obtained, and the triglyceride level denoted as x1 in mg/dL and cholesterol ratio (y) was obtained for each person. The scatterplot and regression line of ln(triglyceride level - 129) denoted as x2 vs. cholesterol ratio is below.

The ANOVA summary table is

Source of Variation Sum of Squares Degrees of freedom Mean Square

Regression 103.16 1 103.16

Error 3.20 23 0.14

Total 106.36 24

(1 pt.) a) What is the coefficient of determination? (1 pt.) b) Do you think that an increase in the triglyceride level causes an increase in the

cholesterol level? Please explain your answer. (1 pt.) BONUS: Why do you think that they had to take the logarithm of the triglyceride level? Additional Problems: Note, the book gives the sums so that you can use the computing method

to calculate the estimated value of the parameters, not SXY and SXX. 12.19, 12.21, 12.23