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Linear Regression - ISC Class 12 Mathematics Questions with Answers

46 past-paper questions on Linear Regression from ISC Class 12 Mathematics papers (2026-2017), newest first. Open one to see its answer.

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For two variables $x$ and $y$, if $\sigma_x = 5$, $r = \frac{-1}{2}$, $b_{yx} = \frac{-2}{7}$ then find the value of $\sigma_y$. 2026 · 1 mark · Short answer
Statement 1: Two regression coefficients cannot have the same sign. Statement 2: Both the regression coefficients can be… 2026 · 1 mark · MCQ
A survey of 50 families to study the relationships between expenditure on accommodation in (₹ $x$) and expenditure on food and… 2026 · 4 marks · Short answer
If the regression lines of a bivariate distribution are $4x - 5y + 33 = 0$ and $20x - 9y - 107 = 0$, then Calculate the… 2026 · 4 marks · Case based
Justify which scatter diagram given above represents a regression equation with positive slope. 2026 · 1 mark · Short answer
Consider the following data of a bivariate distribution: - The mean of the variables $x$ and $y$ are 25 and 30 respectively. -… 2026 · 4 marks · Case based
If $\bar{x} = 28$, $\bar{y} = 32$, $b_{yx} = 1.8$ and $b_{xy} = 0.5$, then the regression equation of $y$ on $x$ is: 2026 · 1 mark · MCQ
A school runs two training modules for sports competition. The data for a sample of 6 batches is given below. $X$: Average number… 2026 · 4 marks · Short answer
Consider the following data: $x$ $y$ $x - \bar{x}$ $y - \bar{y}$ $(x - \bar{x})^2$ $(y - \bar{y})^2$ $(x - \bar{x})(y - \bar{y})$… 2025 · 3 marks · Short answer
A survey of 50 families to study the relationships between expenditure on accommodation in (₹ x) and expenditure on food and… 2025 · 4 marks · Short answer
Read the following statements and choose the correct option. (I) The correlation coefficient and the regression coefficients are… 2025 · 1 mark · MCQ
Two lines of regression are given as $4x + 3y + 7 = 0$ and $3x + 4y + 8 = 0$. Identify the line of regression of $x$ on $y$. 2025 · 2 marks · Short answer
The graph below shows the two lines of regressions for a certain set of $x$ and $y$ values. What is the mean of $x$ and mean of… 2025 · 1 mark · MCQ
Which one of the following statements is correct? 2025 · 1 mark · MCQ
Consider the following table: $x$ 3 $a$ $y$ 2 $b$ Complete the table if $\bar{x} = 4, \bar{y} = 2$. If $b_{yx} = \frac{1}{2}$ and… 2025 · 3 marks · Short answer
Out of the two regression lines given below, find the line of regression of $x$ on $y$. $x + 2y - 5 = 0$ and $2x + 3y - 8 = 0$. 2025 · 2 marks · Short answer
Find the regression line of best fit from the following data: $\sum x = 24$, $\sum y = 44$, $\sum xy = 306$, $\sum x^2 = 164$… 2025 · 2 marks · Short answer
A movie cinema is considering significantly reducing the price of their popcorn as they believe their customers spend more on… 2025 · 4 marks · Long answer
Which of the following statement(s) DOES NOT/DO NOT hold true related to regression analysis: Statement I: $|r|$ is the geometric… 2025 · 1 mark · MCQ
In statistical modelling, regression analysis is a set of statistical processes for estimating the relationships between a… 2025 · 1 mark · MCQ
Consider the data given below: $x$ $y$ Mean 10 20 Standard deviation 2 3 and $r = 0\cdot 66$. Find the regression coefficients. 2025 · 2 marks · Short answer
A study was conducted to investigate the relationship between the number of hours a student studies per week (X) and their scores… 2025 · 4 marks · Long answer
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… 2025 · 1 mark · Short answer
The random variables have regression lines $3x + 2y - 26 = 0$ and $6x + y - 31 = 0$. Calculate Mean value of $x$ and $y$… 2025 · 4 marks · Short answer
Nikhil is investigating the growth patterns of a certain species of slug and measures their thickness, $t$, and length, $l$. The… 2025 · 1 mark · Short answer
The line of regression of marks in Statistics ($X$) and marks in Accountancy ($Y$) for a class of 50 students is… 2024 · 4 marks · Short answer
XYZ company plans to advertise some vacancies. The Manager is asked to suggest the monthly salary for these vacancies based on… 2024 · 4 marks · Short answer
The line of regression of marks in Maths ($X$) and marks in English ($Y$) for a class of $50$ students is $3Y - 5X + 180 = 0$… 2023 · 4 marks · Short answer
The following table shows the Mean, the Standard Deviation and the coefficient of correlation of two variables $x$ and $y$… 2023 · 4 marks · Short answer
Out of the two regression lines $x + 2y - 5 = 0$ and $2x + 3y = 8$, find the line of regression of $y$ on $x$. 2023 · 1 mark · Short answer
If the two regression coefficients are $0.8$ and $0.2$, then the value of coefficient of correlation $r$ will be: 2023 · 1 mark · MCQ
An analyst analysed 102 trips of a travel company. He studied the relation between travel expenses ($y$) and the duration ($x$)… 2023 · 4 marks · Short answer
For 5 observations of pairs $(x, y)$ of variables X and Y, the following results are obtained: $\sum x = 15$, $\sum y = 25$… 2022 · 2 marks · Short answer
Choose the correct option for the following questions. If the regression line of $x$ on $y$ is $9x + 3y - 46 = 0$ and $y$ on $x$… 2022 · 2 marks · Short answer
Find the equation of the regression line of $y$ on $x$, if the observations $(x, y)$ are as follows… 2021 · 4 marks · Short answer
Find the regression coefficients $b_{yx}$, $b_{xy}$ and correlation coefficient ‘$r$’ for the following data… 2020 · 4 marks · Numerical
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… 2020 · 4 marks · Short answer
The following results were obtained with respect to two variables $x$ and $y$: $\sum x = 15$, $\sum y = 25$, $\sum xy = 83$… 2019 · 4 marks · Short answer
Find the equation of the regression line of $y$ on $x$, if the observations $(x, y)$ are as follows… 2019 · 4 marks · Short answer
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… 2018 · 4 marks · Short answer
From the given data: Variable $x$ $y$ Mean 6 8 Standard Deviation 4 6 and correlation coefficient: $\frac{2}{3}$. Find… 2018 · 4 marks · Short answer
Find the line of regression of $y$ on $x$ from the following table. $x$ 1 2 3 4 5 $y$ 7 6 5 4 3 Hence, estimate the value of $y$… 2018 · 4 marks · Short answer
Find the regression coefficient $b_{yx}$ and $b_{xy}$ and the two lines of regression for the following data: X 2 6 4 7 5 Y 8 8 5… 2018 · 4 marks · Short answer
By using the data $\bar{x} = 25$, $\bar{y} = 30$, $b_{yx} = 1.6$ and $b_{xy} = 0.4$, find: The regression equation $y$ on $x$… 2017 · 3 marks · Short answer
Calculate the Spearman’s rank correlation coefficient for the following data and interpret the result: $X$ 35 54 80 95 73 73 35… 2017 · 5 marks · Numerical
Find the line of best fit for the following data, treating $x$ as dependent variable (Regression equation $x$ on $y$): $X$ 14 12… 2017 · 5 marks · Short answer

Linear Regression - ISC Class 12 Mathematics Questions with Answers

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