If the regression line of $Y$ on $X$ is $\hat{y} = 11 + 3x$ and $S_x : S_y = 3 : 10$, find the coefficient of determination.

If the regression line of Y on X is haty = 11 + 3x and Sₓ : Sy = 3 : 10, find the coefficient of determination

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From $b_{yx} = 3$ and $S_x : S_y = 3 : 10$ , $r = 3 \times \tfrac{3}{10} = 0.9$ , so $r^2 = 0.81$ .

GSEB Class-12 Statistics, Linear Regression:

The regression line of $Y$ on $X$ is $\hat{y} = 11 + 3x$ , so the regression coefficient is $b_{yx} = 3$ .

Using the relation $b_{yx} = r \cdot \dfrac{S_y}{S_x}$ , we get: …

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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
$Q. What is coefficient of determination in the study of regression for two variables?$
(a) Product of two standard deviations
(b) Square of correlation coefficient
(c) Square of covariance
(d) Product of two variances
›Reveal solutionSolution

The coefficient of determination equals $r^2$ , the square of the correlation coefficient — option (b).

In the GSEB Class-12 Statistics Linear Regression chapter, the coefficient of determination measures the proportion of the total variation in the dependent variable that is explained by the independent variable through the regression relationship.

It is defined as: …

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CBSE 2023Set MARCH1 markMCQ
$Q. What is coefficient of determination in the study of regression for two variables?$
(a) (A) Product of two standard deviations
(b) (B) Square of correlation coefficient
(c) (C) Square of covariance
(d) (D) Product of two variances
›Reveal solutionSolution

The coefficient of determination is $r^2$ , i.e. the square of the correlation coefficient. Option (B).

In regression analysis of two variables, the coefficient of determination $r^2$ gives the proportion of the total variation in the dependent variable that is explained by the independent variable through the regression lin …

Start your 14-day free trial to see the full solution →
CBSE 2022Set MARCH1 markMCQ
$Q. What is coefficient of determination in the study of regression for two variables?$
(a) Product of two standard deviation
(b) Square of correlation coefficient
(c) Square of covariance
(d) Product of two variances
›Reveal solutionSolution

The coefficient of determination is $r^2$ , the square of the correlation coefficient.

Reasoning. The coefficient of determination $r^2$ gives the fraction of the total variation in the dependent variable that is explained by the regression on the independent variable. It is, by definition, the square of Karl Pearso …

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Q.If the regression line of $Y$ on $X$ is $\hat{y} = 11 + 3x$ and $S_x : S_y = 3 : 10$ , find the coefficient of determination.

Concept understanding — Relationship between Regression Coefficients and Correlation

Q.If the regression line of YYY on XXX is y^=11+3x\hat{y} = 11 + 3xy^​=11+3x and Sx:Sy=3:10S_x : S_y = 3 : 10Sx​:Sy​=3:10, find the coefficient of determination.

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Q.If the regression line of $Y$ on $X$ is $\hat{y} = 11 + 3x$ and $S_x : S_y = 3 : 10$ , find the coefficient of determination.

Unlock everything free for 14 days