Question

(10 points) Because elderly people may have difficulty standing to have their height measured, a study looked at the relationship between overall height and height to the knee. Here are data (in centimeters) for five elderly men:

Knee Height x 56 44 41 44 55
Height y 190 150 145 165 174

What is the equation of the least-squares regression line for predicting height from knee height?

Answer 1

Answer:

$y = 50.243 + 2.387x$    

Step-by-step explanation:

We are given the following in the question:

Knee Height(x):  56     44      41     44     55

        Height(y):  190   150   145   165   174

The least square regression equation is given by:

$y = b_0 + b_1x$

where

$b_0 = \dfrac{\sum y- b_1\sum x}{n}\\\\b_1 = \dfrac{n\sum xy-\sum x\sum y}{n\sum x^2 - (\sum x)^2}$

$\sum x = 240\\\sum y = 824\\\sum (xy) = 40015\\\sum x^2 = 11714$

Putting values, we get,

$b_1 = \dfrac{5(40015)-240(824)}{5(11714)-(240)^2} = 2.387\\\\b_0 = \dfrac{824-2.387(240)}{5} = 50.224$

Thus, the regression equation is:

$y = 50.243 + 2.387x$