2024_Winter_PH 7B HW2.docx-2

PH 7B Public Health Statistics II Homework 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: Regression fallacy assumes that something has reverted to normal as a result of corrective measures done during its inconsistent state. It was assumed that no one exceeded the speed limit because of the radar detectors. 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: 0.25×2.5/4.0 0.25×1.6 0.25×1.6 0.4 65−0.4×63 65−25.2 39.8 39.8+0.4×68 39.8+27.2 The predicted height of a daughter when the height of her mother is 68 inches is 67 inches 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 b=0.6×10/10 b=0.6 a=110−0.6×110 a=110−66 a=44 Y=44+0.6×122 Y=44+73.2 Y=117.2 Because of this the average IQ for a husband whose wife had an avg. IQ of 122 is 117.2 which is below 120. 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. Model 1 Error: -20, -20, -10,10,-39 √((− 20) 2 + (20) 2 + (− 10) 2 + (10) 2 + (− 39) 2 )/5 ( )/5 √ (− 20) 2 + 20 2 + 100 + 100 + 39 2 (2x400+1721)/5 √ 12605/5 √ 22.45