Question

3. Compute the equation of the regression line for a dataset that has the statistics given below. Round the values of a and b to two decimal places. ¯ x = 4, s x = 4, ¯ y = 284, s y = 108, r = 0.63 The regression line is ˆ y = x +

Answer 1

Given that

$\bar{x}=4,S_x=4,\text{ }\bar{\text{y}}=284,S_y=108,\text{ r=0.63}$

The formula for the linear regression line is,

$y=a+bx$

Where

$b=r\frac{S_y}{S_x}$

Therefore,

$\begin{gathered} b=0.63\times\frac{108}{4}=0.63\times27=17.01 \\ \therefore b=17.01 \end{gathered}$

Also,

$a=\bar{y}-b\bar{x}$

Solving for a

$\begin{gathered} a=284-(17.01\times4)=284-68.04=215.96 \\ \therefore a=215.96 \end{gathered}$

Now, Substituting the values of a = 215.96 AND b = 17.01 into the general equation

$\hat{y}=17.01x+215.96$

Hence,

$\hat{y}=17.01x+215.96$