Modeling Height in terms of Femur Length:
Forensic scientists can estimate the height of a person based on
the length of different bones of that person. The table
of values below compares the length of a man’s femur (the
thigh bone) to the height of that man.
$$
\begin{array}{c|c}
\mbox {Length of Femur } \,\, x \,\, \mbox{ (cm)} & \mbox{Height }\,\, y \,\, \mbox{ (cm)} \\ \hline
43.0 & 164\\
43.5 & 166\\
44.0 & 166\\
44.5 & 168\\
45.0 & 170\\
45.5 & 169\\
46.0 & 172\\
46.5 & 173\\
47.0 & 175\\
47.5 & 175\\
\end{array}
$$
a. Draw a scatter diagram for these data points and
determine the line of best fit. (Round the coefficients
to the nearest thousandth.)
b. Interpret the meaning of the slope of the line of best fit.
c. Use the line of best fit from part a to estimate the
height of a man whose femur length is 44.7 cm.
d. Use the line of best fit from part a to estimate the
height of a man whose femur length is 48.5 cm.
Important Note: you will need use a graphing calculator for this POW. You will enter the data into
your calculator and it will give you the coefficients of your linear function.
The details for for how this is done can be found in section 8.6 of our textbook.