If $b_{yx} = 0.8$ then find the value of $b_{vu}$ for the following $u$ and $v$. (i) $u = x - 105$ and $v = y - 90$ (ii) $u = \dfrac{x - 1400}{100}$ and $v = \dfrac{y - 750}{50}$ (iii) $u = 10(x - 4.6)$ and $v = y - 75$.

If byx = 0.8 then find the value of bvu for the fo – Class 12 Statistics

Question 22 of 42

b_{yx} = 0.8

(i)

u = x - 105

and

v = y - 90

(ii)

u = \dfrac{x - 1400}{100}

and

v = \dfrac{y - 750}{50}

(iii)

u = 10(x - 4.6)

and

v = y - 75

Gujarat GsebGujarat Board (GSEB) HSC Commerce Board 2022Subjective· 3mImportance★★★★★

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With $u=\tfrac{x-a}{h}$ , $v=\tfrac{y-b}{k}$ : $b_{vu}=\tfrac{h}{k}b_{yx}$ . Answers: (i) $0.8$ , (ii) $1.6$ , (iii) $0.08$ .

Rule. A regression coefficient is unaffected by a change of origin but is scaled by the ratio of the scale factors. If $u=\dfrac{x-a}{h}$ and $v=\dfrac{y-b}{k}$ , then

$b_{vu}=\frac{h}{k}\,b_{yx}.$

Given $b_{yx}=0.8$ .

(i) $u=x-105\Rightarrow h=1$ ; $v=y-90\Rightarrow k=1$ .

$b_{vu}=\frac{1}{1}\times 0.8=0.8.$

(ii) $u=\dfrac{x-1400}{100}\Rightarrow h=100$ ; $v=\dfrac{y-750}{50}\Rightarrow k=50$ . …

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2025Set MARCH1 markMCQ
$Q. When one regression coefficient is negative, the other would be :$
(a) Positive
(b) Zero
(c) Negative
(d) None of them
›Reveal solutionSolution

Regression coefficients have the same sign as each other (and as $r$ ); one negative $\Rightarrow$ the other negative.

The correlation coefficient relates to the two regression coefficients by

$r=\pm\sqrt{b_{yx}\cdot b_{xy}}.$

Since $r^2=b_{yx}\cdot b_{xy}$ and $r^2\ge 0$ , the product $b_{yx}\cdot b_{xy}$ must be $\ge 0$ . Two numbers whose product is non-negative must have the same sign. Hence both regression coefficients are either positive together or negative together — they cannot differ in sign.

…

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CBSE 2025Set MARCH1 mark
$x$
›Reveal solutionSolution

Doubling both variables scales $S_x$ and $S_y$ equally, so the ratio $\dfrac{S_y}{S_x}$ and the regression coefficient are unchanged.

GSEB Class-12 Statistics, Linear Regression:

The regression coefficient of $Y$ on $X$ is:

$b_{yx} = r \cdot \frac{S_y}{S_x}$

Let the new variables be $x' = 2x$ and $y' = 2y$ . Change of scale does not affect the correlation coefficient $r$ , and the standard deviations scale by the same factor:

$S_{x'} = 2 S_x, \qquad S_{y'} = 2 S_y$

Therefore the new regression coefficient is: …

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CBSE 2024Set MARCH1 markMCQ
$Q. The correlation coefficient :$
(a) $r=b_{xy}\times b_{yx}$
(b) $r=\pm\sqrt{b_{xy}\times b_{yx}}$
(c) $r=\pm\sqrt{\dfrac{1}{b_{xy}\times b_{yx}}}$
(d) $r=\dfrac{1}{b_{xy}\times b_{yx}}$
›Reveal solutionSolution

The correlation coefficient $r$ is the geometric mean of the regression coefficients: $r=\pm\sqrt{b_{xy}\times b_{yx}}$ .

The two regression coefficients are $b_{yx}=r\dfrac{\sigma_y}{\sigma_x}$ and $b_{xy}=r\dfrac{\sigma_x}{\sigma_y}$ . Multiplying them:

$b_{yx}\times b_{xy}=r\frac{\sigma_y}{\sigma_x}\cdot r\frac{\sigma_x}{\sigma_y}=r^2.$

Hence …

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CBSE 2023Set MARCH1 mark
$b > 0$
›Reveal solutionSolution

A regression coefficient $b>0$ indicates a positive/direct relationship — the two variables move in the same direction.

A regression coefficient measures the average change in the dependent variable for a unit change in the independent variable. When $b>0$ , an increase in the independent variable is accompanied by an increase in the dependent variable (and a decrease by a decrease). Thus $b>0$ interprets a positive (direct) relationship be …

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CBSE 2020Set MARCH1 markMCQ
$Q. Which statement is correct ?$
(a) X and Y are two variables, there can be at the most more regression.
(b) Co-efficient of correlation lies between $-1$ and $+1$ .
(c) In scatter diagram, if the plotted points show a downward trend, the correlation will be positive.
(d) Both the regression co-efficients cannot be greater than one.
›Reveal solutionSolution
The correct statement is that the coefficient of correlation always lies between $-1$ and $+1$ ; the other options are incorrect or garbled.

Examine each option:

(a) Garbled/incorrect (there are exactly two lines of regression, not "at the most more").

(b) Correct — Karl Pearson's coefficient of correlation $r$ always satisfies $-1 \le r \le +1$ .

(c) Incorrect — in a scatter diagram a downward trend indicates negative correlation, not positive. …
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Q.If $b_{yx} = 0.8$ then find the value of $b_{vu}$ for the following $u$ and $v$ .

Concept understanding — Regression Coefficients — byx and bxy

Q.If byx=0.8b_{yx} = 0.8byx​=0.8 then find the value of bvub_{vu}bvu​ for the following uuu and vvv.

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Q.If $b_{yx} = 0.8$ then find the value of $b_{vu}$ for the following $u$ and $v$ .

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