Least square problem

Question

A student wonders if tall women tend to date taller men than do short women. She measures herself, her dormitory roommate, and the women in the adjoining room; then she measures the next man each woman dates. Here are the date (heights in inches)



Women (x)
66
64
66
65
70
65
Men (y)
72
68
70
68
71
65

What would be the equation in the form of y=___x+____?

Answer 1

The regression line would model the relationship between the height of men vs. the height of women:

 

m = [Σ(x_i-x_avg)(y_i-y_avg)]/Σ(x_i-x_avg)²

 

x_avg = Σx_i / n = (66+64+66+65+70+65) / 6 = 66

y_avg = Σy_i / n = (72+68+70+68+71+65) / 6 = 69

 

So, m = [(66-66)(72-69)+(64-66)(68-69)+(66-66)(70-69)+(70-66)(71-69)+(65-66)(65-69)] / [(66-66)²+(64-66)²+(66-66)²+(65-66)²+(70-66)²+(65-66)²] = 0.6818

 

b = y_avg - m*x_avg = 69 - (0.6818)(66) = 24

 

So y = 0.6818 x + 24

 

This is on level for a statistics course.

 

 

If you are looking for a simpler method, carefully plot the points and then draw a best fit line.  You can then figure out the slope and y-intercept using your skills from algebra.