Ideal height of your mate. Refer to the Chance (Summer 2008) study of the height of the ideal mate, Exercise.
Ideal height of your mate. Anthropologists theorize that humans tend to choose mates who are similar to themselves. This includes choosing mates who are similar in height. To test this theory, a study was conducted on 147 Cornell University students ( Chance , Summer 2008). Each student was asked to select the height of his or her ideal spouse or life partner. The researchers fit the simple linear regression model, E(y) = β0 β1x where y = ideal partner’s height (in inches) and x = student’s height (in inches). The data for the study (simulated from information provided in a scatterplot) are saved in the IDHEIGHT file. The next table lists selected observations from the full data set.
a. The researchers found the estimated slope of the line to be negative. Fit the model to the data in the IDHEIGHT file using statistical software and verify this result.
Gender
Actual Height
Ideal Height
F
59
60
F
60
70
F
60
72
F
61
65
F
61
67
.
.
.
.
.
.
.
.
.
M
73.5
66
M
74
67
M
74
68
M
74
69
M
74
70
Based on Lee, G., Velleman, P., and Wainer, H. “Giving the finger to dating services.” Chance , Vol. 21, No. 3, Summer 2008.
b. The negative slope was interpreted as follows: “The taller the respondent was, the shorter they felt their ideal partner ought to be.” Do you agree?
c. The result, part b, contradicts the theory developed by anthropologists. To gain insight into this phenomenon, use a scatterplot to graph the full data set. Use a different plotting symbol for male and female students. Now focus on just the data for the female students. What trend do you observe? Repeat for male students.
d. Fit the straight-line model to the data for the female students. Interpret the estimated slope of the line.
e. Repeat part d for the male students.
f. Based on the results, parts d and e , comment on whether the study data support the theory developed by anthropologists.
The data in the IDHEIGHT file were used to fit the simple linear regression model, E(y) = β0 β1x where y = ideal partner’s height (in inches) and x = student’s height (in inches).
a. Fit the straight-line model to the data for the male students. Find an estimate for s , the standard deviation of the error term, and interpret its value practically.
b. Repeat part a for the female students.
c. For which group, males or females, is student’s height the more accurate predictor of ideal partner’s height?
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