Question

Heights (in centimeters) and weights (in kilograms) of 7 supermodels are given below. Find the regression equation, letting the first variable be the independent (x) variable, and predict the weight of a supermodel who is 173 cm tall.

HeightWeight17454166471765617655174551765416850

Answer 1

The regression equation:
y = a x+ b
a = ( n *∑(x y) - (∑x∑y) )/ ( N *∑x² - (∑x)²)
b = (∑y - a*∑x) / N,
where: N = 7, ∑x = 1210, ∑y=371, ∑ x y=64,168.
Using calculations or Excell tools, we can find the regression equation:
y = 0.758 - 78.08
The weight of supermodel who is 173 cm tall:
y = 0.758 * 173 - 78.08 = 53.054 kg

Answer 2

Data

Height (x) Weight (y)
174 54
166 47
176 56
176 55
174 55
176 54
168 50

Use a graphing program to find the regression. I used Excel. The result was:

y = 0.7583x - 78.083, with r^2 = 0.9242

Now subsitute x = 173 to find the predicted height:

y = 0.7583(173) - 78.083 = 53 kg