Question

the scatter plot and line of best fit below show the length of 14 peoples femur (the long leg bone in the thigh) and their height in centimeters. based on the line of best fit, what would be the predicted height for someone with a femur length of 66 cm?

Explanation:

Step1: Find the equation of the line of best - fit

The line of best - fit passes through two points \((30,135)\) and \((48,177)\). First, find the slope \(m\) using the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
\[m=\frac{177 - 135}{48 - 30}=\frac{42}{18}=\frac{7}{3}\]
Then, use the point - slope form \(y - y_1=m(x - x_1)\) with the point \((30,135)\). The equation of the line is \(y-135=\frac{7}{3}(x - 30)\), which simplifies to \(y=\frac{7}{3}x+65\).

Step2: Predict the height

We want to find the height \(y\) when the femur length \(x = 66\). Substitute \(x = 66\) into the equation \(y=\frac{7}{3}x+65\).
\[y=\frac{7}{3}\times66+65\]
\[y = 7\times22+65\]
\[y=154 + 65\]
\[y = 219\]

Answer:

219