Correlation and RegressionMCQMTP May 20Question 3625 of 188
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When r=1\displaystyle r = 1, all the points in a scatter diagram would lie

Options

AOn a straight line directed from lower left to upper right
BOn a straight line directed from upper left to lower right
COn a straight line
DBoth (a) and (b)
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Correct Answer

Option aOn a straight line directed from lower left to upper right

All Options:

  • AOn a straight line directed from lower left to upper right
  • BOn a straight line directed from upper left to lower right
  • COn a straight line
  • DBoth (a) and (b)

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Detailed Solution & Explanation

**Perfect Positive Correlation (r=1\displaystyle r = 1):** When r=1\displaystyle r = 1, there is **perfect positive linear correlation** between X\displaystyle X and Y\displaystyle Y. This means: - Every unit increase in X\displaystyle X is accompanied by a proportional increase in Y\displaystyle Y - All data points lie **exactly** on a straight line - Since both variables increase together, the line goes from **lower left to upper right** **Interpretation of r\displaystyle r values:** - r=+1\displaystyle r = +1: Perfect positive correlation — line from lower-left to upper-right - r=1\displaystyle r = -1: Perfect negative correlation — line from upper-left to lower-right - 0<r<1\displaystyle 0 < r < 1: Imperfect positive correlation — points cluster around upward trend - 1<r<0\displaystyle -1 < r < 0: Imperfect negative correlation — points cluster around downward trend 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.

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