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/her ideal spouse or life partner. The researchers fit the simple linear regression model, E1y2 = b0 + b1x, 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 HEIGHT file. The accompanying 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 using statistical software and verify this result.

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.

Transcribed Image Text:

Gender Actual Height Ideal Height F 59 F 60 F 60 F 61 F 61 62266 70 72 65 67 MMMMM 73.5 74 74 74 74 66899 70 67