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(S_y)/(S_x)`

Therefore,

`\begin{gathered} b=0.63*(108)/(4)=0.63*27=17.01 \\ \therefore b=17.01 \end{gathered}`

Also,

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

Solving for a

`\begin{gathered} a=284-(17.01*4)=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`