The regression equation x and y is 3x + 2y = 100 , the value of bxy

Option a: -2/3. Solution: Given Equation: 3x + 2y = 100 We need to find the regression coefficient of x on y , denoted by bxy . Step 1: Express x in terms of y The regression line of x on y is written in the form x = a + bxy y . Rearranging the given equation: 3x = -2y + 100 x = -2/3y + 100/3 Step 2: Identify bxy Comparing this equation with x = a + bxy y , we get the coefficient of y : bxy = -2/3 Note on Typo: The source file lists Option C ( 3/2 ) as correct, which is a typographical error. The mathematically correct value is -2/3 , which corresponds to Option A. Hence, Option A is the correct answer.

The regression equation $x$ and $y$ is $3x + 2y = 100$, the value of $b_{xy}$

The correct answer is Option a: $-\\frac{2}{3}$. **Given Equation:** $$3x + 2y = 100$$ We need to find the regression coefficient of $x$ on $y$, denoted by $b_{xy}$. **Step 1: Express $x$ in terms of $y$** The regression line of $x$ on $y$ is written in the form $x = a + b_{xy} y$. Rearranging the given equation: $$3x = -2y + 100$$ $$x = -\\frac{2}{3}y + \\frac{100}{3}$$ **Step 2: Identify $b_{xy}$** Comparing this equation with $x = a + b_{xy} y$, we get the coefficient of $y$: $$b_{xy} = -\\frac{2}{3}$$ **Note on Typo:** The source file lists Option C ($\frac{3}{2}$) as correct, which is a typographical error. The mathematically correct value is $-\frac{2}{3}$, which corresponds to Option A. Hence, **Option A** is the correct answer.

Correlation and RegressionMCQMTP Apr 21Question 3744 of 188

All Questions

The regression equation $\displaystyle x$ and $\displaystyle y$ is $\displaystyle 3x + 2y = 100$ , the value of $\displaystyle b_{xy}$

Options

\displaystyle -\\frac{2}{3}

\displaystyle \\frac{100}{3}

\displaystyle \\frac{3}{2}

\displaystyle \\frac{2}{3}

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option a — $\displaystyle -\\frac{2}{3}$

All Options:

A $\displaystyle -\\frac{2}{3}$
B $\displaystyle \\frac{100}{3}$
C $\displaystyle \\frac{3}{2}$
D $\displaystyle \\frac{2}{3}$

Detailed Solution & Explanation

**Given Equation:**

3x + 2y = 100

We need to find the regression coefficient of

\displaystyle x

\displaystyle y

, denoted by

\displaystyle b_{xy}

. **Step 1: Express

\displaystyle x

in terms of

\displaystyle y

** The regression line of

\displaystyle x

\displaystyle y

is written in the form

\displaystyle x = a + b_{xy} y

. Rearranging the given equation:

3x = -2y + 100

x = -\\frac{2}{3}y + \\frac{100}{3}

**Step 2: Identify

\displaystyle b_{xy}

** Comparing this equation with

\displaystyle x = a + b_{xy} y

, we get the coefficient of

\displaystyle y

b_{xy} = -\\frac{2}{3}

**Note on Typo:** The source file lists Option C (

\displaystyle \frac{3}{2}

) as correct, which is a typographical error. The mathematically correct value is

\displaystyle -\frac{2}{3}

, which corresponds to Option A. Hence, **Option A** is the correct answer.

About This Chapter: Correlation and Regression

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Correlation Coefficient, Regression Equations

This chapter covers Correlation Coefficient, Regression Equations and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 4-6 Marks weightage. Focus on understanding core concepts rather than memorizing.

Key Concepts to Understand

Regression

A statistical method used for estimating the relationships between a dependent variable and one or more independent variables.

Related Comparison Tables

Correlation vs Regression: Statistics for CA Foundation

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The regression equation x\displaystyle xx and y\displaystyle yy is 3x+2y=100\displaystyle 3x + 2y = 1003x+2y=100, the value of bxy\displaystyle b_{xy}bxy​