Chapter 4.6, Problem 21HP

To determine

To find: A linear regression equation and a median fit equation.

Answer to Problem 21HP

The required head length using regression line is $9\text{in}$ and median fit line is $9\text{in}$ .

Explanation of Solution

Given information:

The length of the head is from chin to top

Record the height and length of individual in a tabulated manner.

Identify the regression line of the data using a graphing calculator.

  $y=0.12x+0.33$

Identify the median-fit line of the data using a graphing calculator.

  $y=0.14x-1.04$

Now, consider the height of the individual to be $72\text{in}$ .

Substitute $72$ for $x$ in the equation of regression line $y=0.12x+0.33$

  $\begin{array}{c}y=0.12\times 72+0.33\\ =9\text{in}\end{array}$

Substitute $72$ for $x$ in the equation of median fit line $y=0.14x-1.04$

  $\begin{array}{c}y=0.14\times 72-1.04\\ =9\text{in}\end{array}$

Hence, the required head length using regression line is $9\text{in}$ and median fit line is $9\text{in}$ .