Question

(T) Anthropologists use a linear model that relates human femur (thighbone) length to height. The model allows an anthropologist to determine the height of an individual when only a partial skeleton (including the femur) is found. Here we find the model by analyzing the data on femur length and height for the eight males given in the table.

(a) Make a scatter plot of the data.

(b) Find and graph the regression line that models the data.

(c) An anthropologist finds a human femur of length 53cm. How tall was the person?

Short answer

a. The scatter plot of the data is obtained

b. The regression equation for \(y\) is \(y = 1.88074x + 82.64974\).

c. When the femur of length is \(53{\mathop{\rm cm}\nolimits} \), the tall of the person was \(182.3{\mathop{\rm cm}\nolimits} \).

Step-by-step solution

Make a scatter plot of the data

a)

Consider the femur length as the\(x - \)coordinates and height as the\(y - \)coordinates.

The procedure to sketch the scatter plot of the given table of data by using the graphing calculator is as follows:

To make the scatter plot of the given data visuallyby using the graphing calculator as shown below:

1. Open the graphing calculator. Select the “STAT PLOT” and enter the point\(\left( {x,y} \right)\)of given data in the tab.
2. Enter the “GRAPH” button in the graphing calculator.

Visualization of scatter plot of the given data is shown below:

Determine and graph the regression line that models the data

b)

The procedure to use the computing device to obtain the regression line for \(y\) and graph of the regression line is as shown below:

1. Open the computing calculator. Enter all the values of \(x\) in the \(x\) values tab and \(y\) values in the \(y\) values tab.
2. Select the “Calculate the regression equation” button in the computing calculator

Obtain the regression equation is shown below:

The regression equation for\(y\)is\(y = 1.88074x + 82.64974\).

Visualization of the graph of the regression line is shown below

Determine the tall of the person

c)

Substitute\(x = 53\)in the regression equation as shown below:

\(\begin{aligned}y &= 1.88074\left( {53} \right) + 82.64974\\ &= 99.67922 + 82.64974\\ &= 182.328\end{aligned}\)

Thus, when the femur of length is \(53{\mathop{\rm cm}\nolimits} \), the tall of the person was \(182.3{\mathop{\rm cm}\nolimits} \).