Question

4. 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= 11, sx= 1, ¯y= 306, sy= 106, r= -0.62The regression line is ˆy= x+

Answer 1

Given data

`\bar{x}=11,\text{ S}_y=106,\text{ S}_X=1,\bar{\text{ y}}=306,r=-0.62`

Let us solve for a and b

Solving for b

The formula to use is,

`b=r(S_y)/(S_x)`
`\begin{gathered} b=-0.62*(106)/(1)=-0.62*106=-65.72 \\ \therefore b=-65.72 \end{gathered}`

Solving for a

The formula to solve for a is,

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

Therefore,

`\begin{gathered} a=306-(-65.72)*11 \\ a=306-(-722.92)=306+722.92=1028.92 \\ \therefore a=1028.92 \end{gathered}`

The formula for the regression line is,

`\hat{y}=bx+a`

Substituting the values of a and b

`\hat{y}=-65.72+1028.92`

Hence, the regression line is

`\hat{y}=-65.72x+1028.92`