Name: Scatter Diagram
Uploaded: 2019-07-19
Duration: 7 min 10 s
Description: This video explains the third quality control tool, scatter diagrams, in great detail with the help of practical examples, which will be very easy to underst...

Question

Find the regression coefficients $b_{y x}, b_{x y}$ and correlation coefficient $' r'$ for the following data:

$(2, 8), (6, 8), (4, 5), (7, 6), (5, 2)$

Accepted Answer

Here, $Σ x_{i} = 2 + 6 + 4 + 7 + 5 = 24$

and $\sum x_{i}^{2} = 4 + 36 + 16 + 49 + 25 = 130$

and $Σ y_{i} = 8 + 8 + 5 + 6 + 2 = 29$

and $\sum y_{i}^{2} = 64 + 64 + 25 + 36 + 4 = 193$

and $\sum x_{i} y_{i} = 16 + 48 + 20 + 42 + 10 = 136$

Now, $\bar{x} = \frac{24}{5} = 4.8$ and $\bar{y} = \frac{29}{5} = 5.8$

So, $b_{y x} = \frac{\sum x_{i} y_{i} - \frac{\sum x_{i} \sum y_{i}}{n}}{\sum x_{i}^{2} - \frac{{(\sum x_{i})}^{2}}{n}}$

$\Rightarrow b_{y x} = \frac{136 - \frac{24 \times 29}{5}}{130 - \frac{24 \times 24}{5}}$

$\Rightarrow b_{y x} = \frac{136 - 139.2}{130 - 115.2}$

$\Rightarrow b_{y x} = \frac{- 3.2}{14.8} = - 0.216$

and $b_{x y} = \frac{\sum x_{i} y_{i} - \frac{\sum x_{i} \sum y_{i}}{n}}{\sum y_{i}^{2} - \frac{{(\sum y_{i})}^{2}}{n}}$

$\Rightarrow b_{x y} = \frac{136 - \frac{24 \times 29}{5}}{193 - \frac{29 \times 29}{5}}$

$\Rightarrow b_{x y} = \frac{136 - 139.2}{193 - 168.2}$

$\Rightarrow b_{x y} = \frac{- 3.2}{24.8} = - 0.129$

Now, $r (x, y) = \sqrt{b_{y x} \cdot b_{x y}}$

$= \pm \sqrt{(- 0.216) (- 0.129)}$

$= \pm \sqrt{0.027864}$

$= \pm 0.1669$

$x$	$1$	$2$	$3$	$4$	$5$
$y$	$7$	$6$	$5$	$4$	$3$

Find the regression coefficients $b_{y x}, b_{x y}$ and correlation coefficient $' r'$ for the following data:

$(2, 8), (6, 8), (4, 5), (7, 6), (5, 2)$

Important Questions on Linear Regression

Learn and Prepare for any exam you want !

Find the regression coefficients byx, bxy and correlation coefficient 'r' for the following data: (2,8), (6,8), (4,5), (7,6), (5,2)

Important Questions on Linear Regression

Learn and Prepare for any exam you want !

Find the regression coefficients $b_{y x}, b_{x y}$ and correlation coefficient $' r'$ for the following data:

$(2, 8), (6, 8), (4, 5), (7, 6), (5, 2)$