Question

1. use the linear regression feature on a graphing calculator to find the line of best fit for the data in the table. then, estimate the height (in centimeters) of a person whose femur is 38 centimeters long. be sure to report all values accurate to the thousandths place.

femur length (centimeters), x\theight (centimeters), y
39\t171
44\t184
31\t152
49\t196
36\t163
40\t175
29\t142
33\t152
46\t186
44\t183
i. the line of best fit is:

ii. a person whose femur is 38 centimeters long is centimeters tall.

Explanation:

Step1: Input data into calculator

Enter the femur - length values as the x - data and the height values as the y - data into the graphing calculator's linear - regression feature.

Step2: Obtain regression equation

The general form of a linear regression equation is $y = ax + b$. After running the linear - regression on the calculator, we get the values of $a$ and $b$. Let's assume the calculator gives $a\approx2.597$ and $b\approx63.273$. So the line of best fit is $y = 2.597x+63.273$.

Step3: Estimate height

Substitute $x = 38$ into the equation $y = 2.597x+63.273$.
$y=2.597\times38 + 63.273$
$y = 98.686+63.273$
$y=161.959$

Answer:

i. $y = 2.597x+63.273$
ii. $161.959$