Question

The following sample of observations was randomly selected. (Round your answers to 2 decimal places.)

x: 4 5 3 6 10
y: 4 6 5 7 7

Required:
Determine the regression equation

Answer 1

The regression equation is:

`y=3.77+0.36 x`

Explanation:

The general form of a regression equation is:

`y=\alpha +\beta x`

Here,

α = intercept

β = slope

Compute the value of intercept and slope as follows:

`\begin{aligned} \alpha &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = ( 29 \cdot 186 - 28 \cdot 173)/( 5 \cdot 186 - 28^2) =3.767\approx 3.77 \\ \\\beta &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = ( 5 \cdot 173 - 28 \cdot 29 )/( 5 \cdot 186 - \left( 28 \right)^2) =0.363\approx 0.36\end{aligned}`

The regression equation is:

`y=3.77+0.36 x`