Question

Given the lines of regression as 2x-9y+6= 0 and x-2y+1 =0
Which statement is correct? (1 mark)
OPTIONS
The Value Of correlation coefficient r= 3/2
The Value Of correlation coefficient r= 1/2
The Value Of correlation coefficient r= 974
The Value Of correlation coefficient r= 2/3​

Answer 1

Answer:

Using the given lines of regression $2x-9y+6= 0$ and $x-2y+1 =0$. we can find the value of correlation coefficient (r). from the given options, the correct answer: Option d: The value of correlation coefficient $r= \frac{2}{3}$.

Step-by-step explanation:

From the given question,

                    $2x-9y+6= 0$ --------------(1)

                      $x-2y+1 =0$ --------------(2)

Formula for coefficient of correlation(r) $=\sqrt{b_{yx}*b_{xy} }$

For find the value of $b_{yx}$, we should consider the first equation(1).

From equation (1), the regression line of y on x is,

$2x-9y+6= 0$  →       $-9y=(-2x-6)$

                                   $-9y=-(2x+6)$

cancel the minus(-) in both sides. It can be written as,

                                     $9y=2x+6$

                                       $y=\frac{2}{9} x+\frac{6}{9}$

The value of $b_{yx}$ is the coefficient of $x$.

                               ∴   $b_{yx}=\frac{2}{9}$

Similarly, we should find the value of $b_{xy}$, we should consider the second equation(2).

From equation (2), the regression line of x on y is,

$x-2y+1 =0$   →            $x=2y-1$

The value of $b_{xy}$ is the coefficient of $y$.

                               ∴   $b_{xy}=2$

Now we can find the coefficient of correlation(r).

                                        $r=\sqrt{b_{yx}*b_{xy} }$

                                          $=\sqrt{\frac{2}{9} *2 }$

                                          $=\sqrt{\frac{4}{9} }$

                                       $r=\frac{2}{3}$

Final Answer:

Option d: The value of correlation coefficient $r= \frac{2}{3}$.