Question

prediction from line of best fit
score: 5/7 penalty: 0.25 off
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 66 cm?
answer attempt 1 out of 2

Explanation:

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

We have the points $(60,198)$ and $(63,205)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting the points, we get $m=\frac{205 - 198}{63 - 60}=\frac{7}{3}$.

Step3: Use the point - slope form $y - y_1=m(x - x_1)$

Using the point $(60,198)$ and $m = \frac{7}{3}$, the equation of the line is $y-198=\frac{7}{3}(x - 60)$.

Step4: Simplify the equation

$y-198=\frac{7}{3}x-140$, then $y=\frac{7}{3}x + 58$.

Step5: Predict the height for $x = 66$

Substitute $x = 66$ into the equation: $y=\frac{7}{3}\times66+58$.
$y = 154+58$.
$y = 212$.

Answer:

212