In order to study relationship between the repairing time of accident damaged cars and the cost of repair, the following information is collected: | Repairing time of a car (man hours) | 32 | 40 | 25 | 34 | 29 | 35 | 43 | |---|---|---|---|---|---|---|---| | Repairing cost (thousand ₹) | 25 | 35 | 18 | 29 | 22 | 28 | 46 | Obtain the regression line of $Y$ (repairing cost) on $X$ (repairing time). If the time taken to repair a car is 50 man hours, find an estimate of the repairing cost.

> > [!TLDR] > $\sum x=238,\sum y=203,\sum xy=7232,\sum x^2=8320$; $b_{yx}=\frac{7(7232)-238\cdot203}{7(8320)-238^2}=\frac{2310}{1596}=1.447$; $y=1.447x-20.21$; $x=50\Rightarrow y\approx52.16$. > > Let $x=$ repairing time (man hours), $y=$ repairing cost (thousand ₹), $n=7$. > > | $x$ | $y$ | $xy$ | $x^2$ | > |---|---|---|---| > | 32 | 25 | 800 | 1024 | > | 40 | 35 | 1400 | 1600 | > | 25 | 18 | 450 | 625 | > | 34 | 29 | 986 | 1156 | > | 29 | 22 | 638 | 841 | > | 35 | 28 | 980 | 1225 | > | 43 | 46 | 1978 | 1849 | > | $\sum x=238$ | $\sum y=203$ | $\sum xy=7232$ | $\sum x^2=8320$ | > > Means: $\bar x=\dfrac{238}{7}=34,\ \bar y=\dfrac{203}{7}=29$. > > Regression coefficient of $Y$ on $X$: > $$b_{yx}=\frac{n\sum xy-\sum x\sum y}{n\sum x^2-(\sum x)^2}=\frac{7(7232)-238(203)}{7(8320)-(238)^2}=\frac{50624-48314}{58240-56644}=\frac{2310}{1596}\approx1.447.$$ > …

In order to study relationship between the repairing time of accident damaged cars and the cost of repair, the

Question 28 of 42

In order to study relationship between the repairing time of accident damaged cars and the cost of repair, the following information is collected:

Repairing time of a car (man hours)	32	40	25	34	29	35	43
Repairing cost (thousand ₹)	25	35	18	29	22	28	46

Obtain the regression line of $Y$ (repairing cost) on $X$ (repairing time). If the time taken to repair a car is 50 man hours, find an estimate of the repairing cost.

Gujarat GsebGujarat Board (GSEB) HSC Commerce Board 2023Subjective· 5mImportance★★★★★

67% · 28/42 Questions

🔒 Locked · start free trial →

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Start your 14-day free trial to unlock the full solution →

$\sum x=238,\sum y=203,\sum xy=7232,\sum x^2=8320$ ; $b_{yx}=\frac{7(7232)-238\cdot203}{7(8320)-238^2}=\frac{2310}{1596}=1.447$ ; $y=1.447x-20.21$ ; $x=50\Rightarrow y\approx52.16$ .

Let $x=$ repairing time (man hours), $y=$ repairing cost (thousand ₹), $n=7$ .

$x$	$y$	$xy$	$x^2$
32	25	800	1024
40	35	1400	1600
25	18	450	625
34	29	986	1156
29	22	638	841
35	28	980	1225
43	46	1978	1849
$\sum x=238$	$\sum y=203$	$\sum xy=7232$	$\sum x^2=8320$

Means: $\bar x=\dfrac{238}{7}=34,\ \bar y=\dfrac{203}{7}=29$ .

Regression coefficient of $Y$ on $X$ :

$b_{yx}=\frac{n\sum xy-\sum x\sum y}{n\sum x^2-(\sum x)^2}=\frac{7(7232)-238(203)}{7(8320)-(238)^2}=\frac{50624-48314}{58240-56644}=\frac{2310}{1596}\approx1.447.$

…

Start your 14-day free trial to unlock the full solution →

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

CBSE 2026Set MARCH1 markMCQ
$Q. The best fitted line of regression can be obtained by which method?$
(a) Least Square Method
(b) Karl Pearson's Method
(c) Maximum Square Method
(d) Bowley's Method
›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 …

Start your 14-day free trial to see the full solution →
CBSE 2026Set MARCH1 markMCQ
$\hat{y} = 30 - 1.5x$
(a) $28.5$
(b) $20$
(c) $15$
(d) $45$
›Reveal solutionSolution

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

…

Start your 14-day free trial to see the full solution →
CBSE 2025Set MARCH1 markMCQ
$Q. The regression line always passes through which point?$
(a) $(\bar{x}, \bar{y})$
(b) $(0, \bar{y})$
(c) $(\bar{x}, 0)$
(d) $(0, 0)$
›Reveal solutionSolution

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:

$\hat{y} - \bar{y} = b_{yx}(x - \bar{x})$

…

Start your 14-day free trial to see the full solution →
CBSE 2022Set MARCH1 markMCQ
$Q. The regression line always passes through which point?$
(a) $(\bar{x}, \bar{y})$
(b) $(0, \bar{y})$
(c) $(\bar{x}, 0)$
(d) $(0, 0)$
›Reveal solutionSolution

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.

…

Start your 14-day free trial to see the full solution →
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 …

Start your 14-day free trial to see the full solution →
CBSE 2020Set MARCH1 markMCQ
$e$
(a) $y-\hat{y}$
(b) $\hat{x}-\hat{y}$
(c) $x-\hat{x}$
(d) $\hat{y}-y$
›Reveal solutionSolution

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

For the regression line of $Y$ on $X$ , we estimate $Y$ as $\hat{y} = a + bx$ . For a given observation the error (residual) of estimation is defined as the actual observed value of $Y$ minus the value estimated by the line:

$e = y - \hat{y}$

…

Start your 14-day free trial to see the full solution →
CBSE 2020Set MARCH1 mark
$a$
›Reveal solutionSolution
$a$ = intercept ( $\hat{y}$ at $x = 0$ ); $b$ = regression coefficient $b_{yx}$ = slope = change in $\hat{y}$ per unit change in $x$ .

In the regression line of $Y$ on $X$ ,

$\hat{y} = a + bx,$

$a$ is the intercept constant: the value the line predicts for $\hat{y}$ when $x = 0$ . It fixes the position of the line on the $Y$ -axis.

$b$ is the regression coefficient of $Y$ on $X$ , denoted $b_{yx}$ : it is the slope of the line, i.e. the amount by which the estimated $\hat{y}$ changes for a one-unit increase in $x$ . …
Start your 14-day free trial to see the full solution →

←Previous questionQ16 — The information of investment (in lakh ₹) and its market price (In lak…→Next questionQ18 — The regression line always passes through which point? (a) (barx, bary…

🎓Unlock everything free for 14 days

Unlock everything free for 14 days