Chapter 4.6, Problem 17HP

To determine

To generate a linear regression equation and a median-fit equation.Make a prediction using both of the equation..

Answer to Problem 17HP

Equation of regression line is $y=0.12x+0.33.$

Equation of median-fit line is $y=0.14x-1.04.$

Using regression line $y=0.12(72)+0.33\approx 9in.$

Using median-fit line $y=0.14(72)-1.04\approx 9in.$

Explanation of Solution

Given information:For 10 different people ,measure their height and the length of their.

heads from chin to top.Use these data generate a linear regression equation and a median-fit equation.

Formula used:

The equation for the regression line is given below.

  $\begin{array}{c}y=ax+b.\\ \text{Where},a=\frac{n{\displaystyle \sum xy-({\displaystyle \sum x)({\displaystyle \sum y)}}}}{n{\displaystyle \sum x^2-({\displaystyle \sum x{)}^2}}}.\\ b=\frac{{\displaystyle \sum y-a{\displaystyle \sum x}}}{n}.\\ \text{Where, }\text{n=number}\text{of}\text{observations}.\end{array}$

Calculation:

For 10 different people their Height(inches) and Head Height(inches) is given in below table.

Height(in.)	Head Height(in.)
60	7.5
63.5	7.8
63	8
64	8
65	8.2
68	8.5
72	9
71.5	9
70	8.5

Using a graphing calculator ,the regression line is:

  $y=0.12x+0.33.$

Using a graphing calculator ,the median-fit line is:

  $y=0.14x-1.04.$

Predict a person’s head length if his height 72 inches.

Using regression line $y=0.12(72)+0.33\approx 9in.$

Using median-fit line $y=0.14(72)-1.04\approx 9in.$