Consider the data given below:
and $r = 0\cdot 66$.
Find the regression coefficients.
| $x$ | $y$ | |
|---|---|---|
| Mean | 10 | 20 |
| Standard deviation | 2 | 3 |
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Linear Regression - ISC Class 12 Mathematics Questions with Answers, Page 2
46 past-paper questions on Linear Regression from ISC Class 12 Mathematics papers (2026-2017), newest first, in full. Questions 21-40 are on this page, 20 to a page. Tap "Show answer" under a question to see its answer.
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A study was conducted to investigate the relationship between the number of hours a student studies per week (X) and their scores on a standardized test (Y). The following statistical data was collected from a sample of 50 students:
The correlation coefficient between X and Y is 0.65.
| X | Y | |
|---|---|---|
| Mean | 15 | 75 |
| Standard Deviation (SD) | 4 | 10 |
(a)
Estimate the test score for a student who studies 20 hours per week.
(b)
If the pass mark is 40, then how many hours does a student need to study to pass?
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If the covariance of $x$ and $y$ is $58.08$, the variance of $x$ is $121$ and the standard deviation of $y$ is $8$ then, find the regression coefficient of $x$ and $y$.
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The random variables have regression lines $3x + 2y - 26 = 0$ and $6x + y - 31 = 0$.
Calculate
(a)
Mean value of $x$ and $y$.
(b)
Co-efficient of correlations. [Application]
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Nikhil is investigating the growth patterns of a certain species of slug and measures their thickness, $t$, and length, $l$. The results are shown below:
Using scatter diagram, explain why a line of best fit should not be used for this data?
| Thickness $t$ (mm) | Length $l$ (cm) |
|---|---|
| 9 | 5.9 |
| 8 | 4.1 |
| 3 | 2.1 |
| 6 | 1.8 |
| 4 | 3.0 |
| 10 | 7.8 |
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The line of regression of marks in Statistics ($X$) and marks in Accountancy ($Y$) for a class of 50 students is $3y - 5x + 180 = 0$. The average score in Accountancy is 44 and the variance of marks in Statistics is $\left(\frac{9}{16}\right)^{\text{th}}$ of variance of marks in Accountancy.
(a)
Find the average score in Statistics.
(b)
Find the coefficient of correlation between marks in Statistics and marks in Accountancy.
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XYZ company plans to advertise some vacancies. The Manager is asked to suggest the monthly salary for these vacancies based on the years of experience. To do so, the Manager studies the years of service and the monthly salary drawn by the existing employees in the company.
Following is the data that the Manager refers to:
| Years of service ($X$) | 11 | 7 | 9 | 5 | 8 | 6 | 10 |
|---|---|---|---|---|---|---|---|
| Monthly salary (in ₹ 1000) ($Y$) | 10 | 8 | 6 | 5 | 9 | 7 | 11 |
(a)
Find the regression equation of monthly salary on the years of service.
(b)
If a person with 13 years of experience applies for a job in this company, what monthly salary will be suggested by the Manager?
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The line of regression of marks in Maths ($X$) and marks in English ($Y$) for a class of $50$ students is $3Y - 5X + 180 = 0$. The average score in English is $44$ and variance of marks in Maths is $\frac{9}{16}^{\text{th}}$ of the variance of marks in English. Find the average score in Maths. Also, find out the coefficient of correlation between marks in Maths and English.
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The following table shows the Mean, the Standard Deviation and the coefficient of correlation of two variables $x$ and $y$.
Calculate:
| Series | $x$ | $y$ |
|---|---|---|
| Mean | 8 | 6 |
| Standard deviation | 12 | 4 |
| Coefficient of correlation | 0.6 |
(a)
the regression coefficients $b_{xy}$ and $b_{yx}$
(b)
the probable value of $y$ when $x = 20$
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Out of the two regression lines $x + 2y - 5 = 0$ and $2x + 3y = 8$, find the line of regression of $y$ on $x$.
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If the two regression coefficients are $0.8$ and $0.2$, then the value of coefficient of correlation $r$ will be:
- (a)$\pm 0.4$
- (b)$\pm 0.16$
- (c)$0.4$
- (d)$0.16$
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An analyst analysed 102 trips of a travel company. He studied the relation between travel expenses ($y$) and the duration ($x$) of these trips. He found that the relation between $x$ and $y$ was linear. Given the following data, find the regression equation of $y$ on $x$.
$\sum x = 510, \sum y = 7140, \sum x^2 = 4150, \sum y^2 = 740200, \sum xy = 54900$
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For 5 observations of pairs $(x, y)$ of variables X and Y, the following results are obtained:
$\sum x = 15$, $\sum y = 25$, $\sum x^2 = 55$, $\sum y^2 = 135$, $\sum xy = 83$.
Calculate the value of $b_{xy}$ and $b_{yx}$.
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Choose the correct option for the following questions.
(i)
If the regression line of $x$ on $y$ is $9x + 3y - 46 = 0$ and $y$ on $x$ is $3x + 12y - 7 = 0$, then the correlation coefficient ‘r’ is equal to:
- (a)$-\frac{1}{12}$
- (b)$\frac{1}{12}$
- (c)$-\frac{1}{2\sqrt{3}}$
- (d)$\frac{1}{2\sqrt{3}}$
(ii)
If $\bar{X} = 40$, $\bar{Y} = 6$, $\sigma_x = 10$, $\sigma_y = 1.5$ and $r = 0.9$ for the two sets of data X and Y, then the regression line of X on Y will be:
- (a)$x - 6y - 4 = 0$
- (b)$x + 6y - 4 = 0$
- (c)$x - 6y + 4 = 0$
- (d)$x + 6y + 4 = 0$
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Find the equation of the regression line of $y$ on $x$, if the observations $(x, y)$ are as follows:
$(1, 4), (2, 8), (3, 2), (4, 12), (5, 10), (6, 14), (7, 16), (8, 6), (9, 18)$
Also, find the estimated value of $y$ when $x = 14$.
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Find the regression coefficients $b_{yx}$, $b_{xy}$ and correlation coefficient ‘$r$’ for the following data:
$(2, 8), \quad (6, 8), \quad (4, 5), \quad (7, 6), \quad (5, 2)$
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The correlation coefficient between $x$ and $y$ is $0.6$. If the variance of $x$ is $225$, the variance of $y$ is $400$, mean of $x$ is $10$ and mean of $y$ is $20$, find:
(i)[2.0]
the equations of two regression lines.
(ii)[2.0]
the expected value of $y$ when $x = 2$.
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The following results were obtained with respect to two variables $x$ and $y$:
$\sum x = 15$, $\sum y = 25$, $\sum xy = 83$, $\sum x^2 = 55$, $\sum y^2 = 135$ and $n = 5$
(i)[2.0]
Find the regression coefficient $b_{xy}$.
(ii)[2.0]
Find the regression equation of $x$ on $y$.
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Find the equation of the regression line of $y$ on $x$, if the observations $(x, y)$ are as follows:
$(1, 4), (2, 8), (3, 2), (4, 12), (5, 10), (6, 14), (7, 16), (8, 6), (9, 18)$
Also, find the estimated value of $y$ when $x = 14$.
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Given that the observations are $(9,-4), (10, -3), (11,-1), (13,1), (14,3), (15,5), (16,8)$, find the two lines of regression. Estimate the value of $y$ when $x = 13.5$.
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