Expert Answer to "For the following paired data, find the regression..."

gamau6v

Answered question

2021-12-02

For the following paired data, find the regression equation.
(1, 2), (3, 7), (5, 9), (9, 15), (4, 7)

Answer & Explanation

Himin1945

Beginner2021-12-03Added 12 answers

Step 1
The equation is created by making the following table:
$\begin{array}{cc} x & y & x y & x^{2} & y^{2} \\ 1 & 2 & 2 & 1 & 4 \\ 3 & 7 & 21 & 9 & 49 \\ 5 & 9 & 45 & 25 & 81 \\ 9 & 15 & 135 & 81 & 225 \\ 4 & 7 & 28 & 16 & 49 \\ \sum x = 22 & \sum y = 40 & \sum x y = 231 & \sum x^{2} = 132 & \sum y^{2} = 408 \end{array}$
Step 2
Therefore it follows:
$\overset{―}{x} = \frac{22}{5}, \overset{―}{y} = \frac{40}{5} = 8$
$b_{y x} = \frac{n \sum x y - \sum x \sum y}{n \sum x^{2} - {(\sum x)}^{2}}$
$= \frac{5 (231) - 22 \times 40}{5 \times 132 - {(22)}^{2}}$
$= \frac{25}{16}$
Step 3
Regression line y on x is
$y - \overset{―}{y} = b_{y x} (x - \overset{―}{x})$
$y - 8 = \frac{25}{16} (x - \frac{22}{5})$
Hence the regression equation is $y = 1.5625 x + 1.125$ .

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school statistics

Didn't find what you were looking for?