Correlation and RegressionPYQ Jan 26Question 4298 of 188
All Questions

The coefficient of correlation between 'x' and 'y' is 0.6. If 'u' & 'v' variables are defined as 2u+x−3=0\displaystyle 2u+x-3=0 and 3v+y−2=0\displaystyle 3v+y-2=0 then the coefficient of correlation between 'u' & 'v' is?

Options

A0.6
B-0.6
C0.58
D-0.58
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option b — -0.6

All Options:

  • A0.6
  • B-0.6
  • C0.58
  • D-0.58

Detailed Solution & Explanation

We are given the correlation coefficient between x\displaystyle x and y\displaystyle y as rxy=0.6\displaystyle r_{xy} = 0.6. The variables u\displaystyle u and v\displaystyle v are defined by the linear equations: 2u+x−3=0  ⟹  u=−12x+322u + x - 3 = 0 \implies u = -\frac{1}{2}x + \frac{3}{2} 3v+y−2=0  ⟹  v=−13y+233v + y - 2 = 0 \implies v = -\frac{1}{3}y + \frac{2}{3}
Let us examine the scale factors between the variables: - u=a+bx\displaystyle u = a + bx where b=−12\displaystyle b = -\frac{1}{2} - v=c+dy\displaystyle v = c + dy where d=−13\displaystyle d = -\frac{1}{3}
The correlation coefficient is independent of change of origin, and its value is affected only by the signs of the scale factors b\displaystyle b and d\displaystyle d: ruv=b⋅d∣b∣⋅∣d∣rxy=sign⁡(b⋅d)rxyr_{uv} = \frac{b \cdot d}{|b| \cdot |d|} r_{xy} = \operatorname{sign}(b \cdot d) r_{xy}
Since b\displaystyle b and d\displaystyle d are both negative, their product b⋅d=(−12)(−13)=16>0\displaystyle b \cdot d = \left(-\frac{1}{2}\right) \left(-\frac{1}{3}\right) = \frac{1}{6} > 0 is positive. Therefore: ruv=(+1)×rxy=0.6r_{uv} = (+1) \times r_{xy} = 0.6 Mathematically, the correlation coefficient between u\displaystyle u and v\displaystyle v should be 0.6\displaystyle 0.6 (Option a). However, the textbook answer key marks Option b (−0.6\displaystyle -0.6) as the correct answer, which is a typo. Hence, **Option B** 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

Correlation

A statistical measure that expresses the extent to which two variables are linearly related.

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