Question

the scatter plot and line of best fit below show the length of 12 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 72 cm?

Explanation:

Step1: Find two points on the line of best - fit

Let's take two points on the line of best - fit, say $(45,150)$ and $(55,170)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 45,y_1=150,x_2 = 55,y_2 = 170$. So $m=\frac{170 - 150}{55 - 45}=\frac{20}{10}=2$.

Step3: Use the point - slope form $y - y_1=m(x - x_1)$ to find the equation of the line

Using the point $(45,150)$ and $m = 2$, we have $y-150=2(x - 45)$. Expanding gives $y-150=2x-90$, and then $y = 2x+60$.

Step4: Predict the height for $x = 72$

Substitute $x = 72$ into the equation $y = 2x+60$. So $y=2\times72 + 60=144+60=204$.

Answer:

204