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 45 cm?

Explanation:

Step1: Find the slope of the line

Use two - point formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(30,127)$ and $(x_2,y_2)=(40,151)$. Then $m=\frac{151 - 127}{40 - 30}=\frac{24}{10}=2.4$.

Step2: Find the y - intercept of the line

Use the point - slope form $y - y_1=m(x - x_1)$ with the point $(30,127)$ and $m = 2.4$. So $y-127=2.4(x - 30)$. Expand to get $y-127=2.4x-72$. Then $y=2.4x + 55$.

Step3: Predict the height

Substitute $x = 45$ into the equation $y=2.4x + 55$. So $y=2.4\times45+55=108 + 55=163$.

Answer:

163