Correlation and RegressionMCQMTP Nov 20Question 3737 of 188
All Questions

The two lines of regression become identical when

Options

Ar=1\displaystyle r = 1
Br=−1\displaystyle r = -1
Cr=0\displaystyle r = 0
DBoth (a) & (b)
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option d — Both (a) & (b)

All Options:

  • Ar=1\displaystyle r = 1
  • Br=−1\displaystyle r = -1
  • Cr=0\displaystyle r = 0
  • DBoth (a) & (b)

Ad

Detailed Solution & Explanation

**Concepts of Regression Lines and Correlation:** The angle theta\displaystyle \\theta between the two lines of regression (y\displaystyle y on x\displaystyle x and x\displaystyle x on y\displaystyle y) is given by: tantheta=frac1−r2∣r∣left(fracsigmaxsigmaysigmax2+sigmay2right)\\tan \\theta = \\frac{1 - r^2}{|r|} \\left( \\frac{\\sigma_x \\sigma_y}{\\sigma_x^2 + \\sigma_y^2} \\right) **Step 1: Condition for Coinciding (Identical) Regression Lines** The two regression lines coincide (become identical) when they are parallel, meaning the angle between them is theta=0circ\displaystyle \\theta = 0^{\\circ}. tantheta=0implies1−r2=0impliesr2=1impliesr=pm1\\tan \\theta = 0 \\implies 1 - r^2 = 0 \\implies r^2 = 1 \\implies r = \\pm 1 - When r=1\displaystyle r = 1, there is a perfect positive linear correlation between the variables, and the two regression lines coincide. - When r=−1\displaystyle r = -1, there is a perfect negative linear correlation between the variables, and the two regression lines also coincide. Therefore, the regression lines coincide when either r=1\displaystyle r = 1 or r=−1\displaystyle r = -1. This corresponds to "Both (a) & (b)". Hence, **Option D** 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

More Questions from Correlation and Regression

The correlation co-efficient between X and Y is 0.8. If we add a number 10 in the X variable and subtracted 20 from Y variable, then the new correlation co-efficient will be -

When both the regression co-efficients are bxy=0.7\displaystyle b_{xy} = 0.7 and byx=0.8\displaystyle b_{yx} = 0.8, respectively, then correlation co-efficient between x and y is

For 9 college students group, the sum of squares of differences in ranks for History and Hindi marks was found to be 62, then what is the value of rank correlation co-efficient?

If r=0.7\displaystyle r = 0.7 then co-efficient of non-determination is

Given x=2y+4\displaystyle x = 2y + 4 and y=kx+6\displaystyle y = kx + 6 are the two lines of regression x on y and y on x respectively. If the value of correlation co-efficient (r) is 0.5, then the value of k is

For a group of students, the sum of squares of differences in ranks for Maths and Physics marks are found to be 60, which is 120 times the value of rank correlation coefficient. How many students are there in the group?

Ready to Master Correlation and Regression?

Practice all 188 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free