PH 7B Public Health Statistics IIHomework 2
Question 1 (5pts): A community in Irvine has installed several radar detectors to address the
speeding problems. Ever since that, no one has exceeded the speed limit. This is a
phenomenon of:
A. Regression effect
B. Regression fallacy
C. Simpson’s paradox
D. None of the above
Explain:
Question 2 (5pts): The following results were obtained in a study of about 2,000 families:
average height of mother= 63 inches, SD=2.5 inches. Average height of daughter= 65 inches,
SD=4.0 inches. r= 0.25. What is the predicted height of a daughter when the height of her
mother is 68 inches?
A. 62 inches
B. 64 inches
C. 66 inches
D. 67 inches
Show your work:
Question 3 (5pts). IQ scores are scaled to have an average of about 110, and an SD of about
10, both for men and for women. The correlation between the IQs of husbands and wives is
about 0.6. A large study of families found that the men whose IQ was 130 had wives whose IQ
averaged 122. For the wives whose IQ was 122, the average IQ of their husbands are:
A. Between 130 and 140
B. 130
C. Between 120 and 130
D. Below 120
Explain:
PH 7B Public Health Statistics II
Homework 2
Question 4 (20 pts). Two regression models are fitted to a small data set using different
statistical approaches (eg. simple or multiple linear regression). For each subject, the table
shows the actual value of y and the predicted value from the regression line. (use n=5, keep 2
decimal places)
Model 1
Model 2
Actual value of y
Predicted value of y
Actual value of y
Predicted value
of y
54
74
54
64
35
15
35
55
76
86
76
56
27
17
27
76
18
57
18
48
1) Compute the r.m.s for each model, show your work.
2) Which model do you prefer to predict y? Explain.
PH 7B Public Health Statistics II
Homework 2
Question 5 (15 pts). A study has recruited 100 children in Orange County and collected data
on their height at age 6 years old and age 10 years old (the scatter diagram is football-shaped):
Average height at 6 = 126 cm SD=5cm
Average height at 10 = 146 cm SD=4cm, r=0.60
1) Find the r.m.s error for the regression prediction of height at 10 years old from height at
6 years old. Show your work and interpret your results.
2) Find the r.m.s error for the regression prediction of height at 6 years old from height at
10 years old. Show your work and interpret your results.
3) Which model has better performance?
