Obtain the regression line of the demand on the price using the following information collected for the demand and the price of a commodity. Estimate the demand of the commodity if price is $\text{\rupee}\,40$: | Price ($\text{\rupee}$) | 38 | 36 | 37 | 37 | 36 | 38 | 39 | 36 | 38 | | Demand (hundred units) | 12 | 18 | 15 | 12 | 17 | 13 | 13 | 15 | 12 |

> > [!TLDR] > $d_x=x-37,\ d_y=y-15$: $\Sigma d_x=2,\Sigma d_y=-8,\Sigma d_x^2=10,\Sigma d_xd_y=-17$; $b_{yx}=\dfrac{9(-17)-(2)(-8)}{9(10)-2^2}=-1.593$; $\bar x=37.22,\bar y=14.11$; $\hat y=73.41-1.593x$; at $x=40,\ \hat y\approx9.69$. > > Let $d_x=x-37,\ d_y=y-15$, $n=9$ (demand $Y$ on price $X$). > > | $x$ | $y$ | $d_x$ | $d_y$ | $d_x^2$ | $d_xd_y$ | > |---|---|---|---|---|---| > | 38 | 12 | 1 | $-3$ | 1 | $-3$ | > | 36 | 18 | $-1$ | 3 | 1 | $-3$ | > | 37 | 15 | 0 | 0 | 0 | 0 | > | 37 | 12 | 0 | $-3$ | 0 | 0 | > | 36 | 17 | $-1$ | 2 | 1 | $-2$ | > | 38 | 13 | 1 | $-2$ | 1 | $-2$ | > | 39 | 13 | 2 | $-2$ | 4 | $-4$ | > | 36 | 15 | $-1$ | 0 | 1 | 0 | > | 38 | 12 | 1 | $-3$ | 1 | $-3$ | > | **Sum** | | **2** | **$-8$** | **10** | **$-17$** | > > Means: $\bar x=37+\dfrac{2}{9}=37.222,\quad \bar y=15+\dfrac{-8}{9}=14.111.$ > > Regression coefficient of $Y$ on $X$: …

Obtain the regression line of the demand on the price using the following information collected for the demand

Question 42 of 42

\text{\text{₹}}\,40

Gujarat GsebGujarat Board (GSEB) HSC Commerce Board 2026Subjective· 5mImportance★★★★★

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$d_x=x-37,\ d_y=y-15$ : $\Sigma d_x=2,\Sigma d_y=-8,\Sigma d_x^2=10,\Sigma d_xd_y=-17$ ; $b_{yx}=\dfrac{9(-17)-(2)(-8)}{9(10)-2^2}=-1.593$ ; $\bar x=37.22,\bar y=14.11$ ; $\hat y=73.41-1.593x$ ; at $x=40,\ \hat y\approx9.69$ .

Let $d_x=x-37,\ d_y=y-15$ , $n=9$ (demand $Y$ on price $X$ ).

$x$	$y$	$d_x$	$d_y$	$d_x^2$	$d_xd_y$
38	12	1	$-3$	1	$-3$
36	18	$-1$	3	1	$-3$
37	15	0	0	0	0
37	12	0	$-3$	0	0
36	17	$-1$	2	1	$-2$
38	13	1	$-2$	1	$-2$
39	13	2	$-2$	4	$-4$
36	15	$-1$	0	1	0
38	12	1	$-3$	1	$-3$
Sum		2	$-8$	10	$-17$

Means: $\bar x=37+\dfrac{2}{9}=37.222,\quad \bar y=15+\dfrac{-8}{9}=14.111.$

Regression coefficient of $Y$ on $X$ : …

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

CBSE 2026Set MARCH1 markMCQ
$Q. The best fitted line of regression can be obtained by which method?$
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›Reveal solutionSolution

The best-fitted regression line is found by the method of least squares.

The regression line is chosen so that the sum of the squares of the deviations of the observed $y$ from the estimated $\hat y$ is minimum, i.e. $\Sigma(y-\hat y)^2$ is least. This is the **least squa …

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CBSE 2026Set MARCH1 markMCQ
$\hat{y} = 30 - 1.5x$
(a) $28.5$
(b) $20$
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(d) $45$
›Reveal solutionSolution

The regression line passes through $(\bar x,\bar y)$ ; putting $\bar x=10$ gives $\bar y=15$ .

…

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CBSE 2025Set MARCH1 markMCQ
$Q. The regression line always passes through which point?$
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A regression line always passes through the point of means $(\bar{x}, \bar{y})$ — option (a).

In the GSEB Class-12 Statistics Linear Regression chapter, the regression line of $Y$ on $X$ is written as:

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…

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CBSE 2022Set MARCH1 markMCQ
$Q. The regression line always passes through which point?$
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Each regression line is constructed to pass through the point of averages $(\bar{x}, \bar{y})$ , which is also where the two regression lines intersect.

…

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CBSE 2022Set MARCH1 mark
$Q. Give the name of a method to obtain the best fitted regression line.$
›Reveal solutionSolution

The best-fitted regression line is obtained by the Method of Least Squares.

Explanation. The method of least squares chooses the line for which the sum of the squares of the deviations (errors) of the observed values from the estimated values is minimum. This criterion yields …

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CBSE 2020Set MARCH1 markMCQ
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Error of estimation $e = y - \hat{y}$ (observed minus estimated) — option (a).

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$a$
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$a$ = intercept ( $\hat{y}$ at $x = 0$ ); $b$ = regression coefficient $b_{yx}$ = slope = change in $\hat{y}$ per unit change in $x$ .

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