Q 28 - Precalculus Enhanced with Graphing Utilities

Question

Research performed at NASA, led by Dr. Emily R. Morey-Holton, measured the lengths of the

right humerus and right tibia in 11 rats that were sent to space on Spacelab Life Sciences 2. The data on page 175

were collected.

(a) Draw a scatter diagram of the data treating length of the right humerus as the independent variable.

(b) Based on the scatter diagram, do you think that there is a linear relation between the length of the right humerus

and the length of the right tibia?

(c) Use a graphing utility to find the line of best fit relating length of the right humerus and length of the right

tibia.

(d) Predict the length of the right tibia on a rat whose right humerus is 26.5 millimeters (mm).

Step-by-Step Solution

Answer

(a) The scatter diagram is 

(b) If we look at the obtained scatter diagram, we have the feeling that if we wanted to connect all the obtained points we will get the direction that will best describe their relationship.

(c) $y=1.39x+1.11$

(d) The length of the right tibia is about 38mm.

Step 1. Given Information

Research performed at NASA, led by Dr. Emily R. Morey-Holton, measured the lengths of the

right humerus and right tibia in 11 rats that were sent to space on Spacelab Life Sciences 2. The data on page 175

were collected.

Part (a) of Step 1. Scatter plot

The scatter diagram is 

Part (b) of Step 1. linear relation

If we look at the obtained scatter diagram, we have the feeling that if we wanted to connect all the obtained points we will get the direction that will best describe their relationship.

Part (c) of Step 1. line of best fit

The line of the best fit relating length of the right humerus and length of the right tibia is 

$y=1.39x+1.11$

Part (d) of Step 1. The length of the right tibia on a rat whose right humerus is 26.5 millimeters

The relation between the length of the right tibia and the length of the right humerus is given by, 

$y=1.39x+1.11$

Substitute the value of $x=26.5$, in the equation and evaluate.

$$\begin{gathered} y=1.39·26.5+1.11 \\ y=37.945 \end{gathered}$$

The length of the right tibia is about 38mm.