Question

Name: Ch. 3 WH 50 blood pressure for people 20 years old is 120, while for those who is 60 years old the average is 140. Using this information, find the equation of the regnession linem 00-20 742 5,. (4 points)The least squares regression equation for the data in the following table is g 3+2 4 4 7 10 10 (a) (〈point Calculate the valu, ofỳfor each data(oin﹂ A )-br / つい/,

Answer 1

Let y= average systolic blood pressure

x=age

Let the estimated regression equation be

$\hat{y}=a+bx$

the average blood pressure is $\hat{y}=120$, when the age is x=20.

substituting these values we get

$120=a+b\times 20$

the average blood pressure is $\hat{y}=140$, when the age is x=60.

substituting these values we get

$140=a+b\times 60$

Subtracting the first from the second we get

$\begin{align*} &(140-120)=(a+b\times 60)-(a+b\times 20)\\ \implies &20=b\times (60-20)\\ \implies &b=\frac{20}{40}=0.50 \end{align*}$

using the value b=0.50 we get

$\begin{align*} &140=a+b\times 60\\ \implies &140=a+0.5\times 60\\ \implies &a=140-0.5\times 60\\ \implies &a=110 \end{align*}$

ans: the estimated equation of regression line is

$\hat{y}=110+0.5x$