Question

unit 2 - exploring two variable data
hw 2 - scatterplots and correlation

1. a student wonders if tall women tend to date taller men. she measures herself, her dormitory roommate, and the women in the adjoining rooms; then she measures the next man each woman dates. here are the data (heights in inches):

women 66 64 66 65 70 65
men 72 68 70 68 71 65
a) is there a clear explanatory variable and response variable in this setting? if so, tell which is which. if not, explain why not.
b) make a well - labeled scatterplot of these data.
c) based on the scatterplot, describe the pattern, if any, in the relationship between the heights of women and the heights of the men they date.
d) suppose another 70 - inch - tall female who dated a 73 - in - tall male were added to the data set. how would this influence r?

Explanation:

Step1: Identify variables

The student is trying to see if women's height affects men's height in dating. So the height of women is the explanatory variable (x - variable) and the height of men is the response variable (y - variable).

Step2: Create scatter - plot

To create a scatter - plot, we plot the points (women's height, men's height) on a coordinate plane. For example, the first point is (66,72), the second is (64,68) etc. Label the x - axis as "Height of Women (inches)" and the y - axis as "Height of Men (inches)".

Step3: Analyze scatter - plot pattern

Looking at the scatter - plot, we may observe a positive linear pattern. As the height of women increases, the height of men they date seems to increase as well, though not perfectly linearly.

Step4: Analyze influence on correlation coefficient

The correlation coefficient \(r\) measures the strength and direction of a linear relationship. Adding a point (70,73) which follows the general positive - linear trend seen in the existing data will likely increase the value of \(r\) (make the positive correlation stronger) since it fits the existing pattern.

Answer:

a) The explanatory variable is the height of women and the response variable is the height of men.
b) Plot points (66,72), (64,68), (66,70), (65,68), (70,71), (65,65) on a coordinate plane with x - axis labeled "Height of Women (inches)" and y - axis labeled "Height of Men (inches)".
c) There appears to be a positive linear pattern. As the height of women increases, the height of men they date tends to increase.
d) It will likely increase the value of \(r\) (strengthen the positive correlation).