Assignment 1: Introduction to Regression

Due: Thursday, Jan. 24

Correlation

Investigators take a sample of DINKS (dual-income families, where husband and wife both work – and no kids). The investigators have data on the husband’s income and the wife’s income. By definition,

Family income = husband’s income + wife’s income.

The average family income was around $50,000, and 10% of the couples had family income in the range $45,000-$55,000. Fill in the blanks, using the options below, and explain briefly. (a) The correlation between wife’s income and family income is _____. (b) Among couples whose family income is in the range $45,000-$55,000, the correlation between wife’s income and family income is _____.

-1 nearly –1 somewhat negative 0

somewhat positive nearly 1 1

2. Two meteorologists compute the correlation between daily maximum temperatures for Washington D.C. and Boston. One does it for June 1993; the other does it for all of 1993. Who gets the bigger correlation? Briefly explain.

3. An investigator collected data on heights and weights of college students:

	Average	SD
Men’s height	70 in	3 in
Men’s weight	144 lb	21 lb
Women’s height	64 in	3 in
Women’s weight	120 lb	21 lb

The correlation between height and weight for men was 0.60; for the women, it was about the same. If you combine the men and women, what can you say about the correlation between height and weight? Would it about 0.60, somewhat lower than 0.60, or somewhat higher than 0.60? Briefly explain.

Fifteen students in an elementary statistics course at U.C. Berkeley were asked to count dots randomly scattered inside a given square; there were 85 dots in the figure. The counts are shown below. (a) Do you believe the students worked independently? Why? (b) True or false, and briefly explain: Those students who counted high the first time also tended to be high the second time.

Two counts

per student

1st	2^nd
91	85
81	83
86	85
83	84
85	85
85	84
85	89
84	83
91	82
91	82
91	82
85	85
85	85
87	85
90	85

Regression

In one study, the correlation between the educational level of husbands and wives in a certain town was about 0.50; both averaged 12 years of schooling completed, with an SD of 3 years. (a) Predict the educational level of a woman whose husband has completed 18 years of schooling. (b) Predict the educational level of a man whose wife has completed 15 years of schooling. (c) Apparently, well-educated men marry women who are less well educated than themselves. However, the women marry men with even less education. How is this possible? Briefly explain your findings.

For men age 25-34 in large health survey (HANES), the average education level (years of schooling completed) was 13 years, with an SD of about 3 years; their average systolic blood pressure was 124mm, with an SD of 14mm. The correlation between education and blood pressure was –0.1. One man in the sample had 18 years of education, and his blood pressure was 123mm. True or false, and briefly explain: Compared to other men at his educational level, his blood pressure was a bit on the high side.

Note: These problems are taken from Freedman, Pisani, and Purves, Statistics, third edition.