Correlation and RegressionMCQMTP Nov 21Question 3627 of 188
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For a 4times7\displaystyle 4 \×\displaystyle \times 7 classification of bivariate data, the maximum no. of conditional distributions is:

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option b — $28$

All Options:

  • A$11$
  • B$28$
  • C$35$
  • DNone of these

Detailed Solution & Explanation

**Conditional distributions in bivariate frequency table:** For a ptimesq\displaystyle p \×\displaystyle \times q bivariate frequency table: - There are p\displaystyle p rows (classes of variable X\displaystyle X) and q\displaystyle q columns (classes of variable Y\displaystyle Y) - **Conditional distributions of Y\displaystyle Y given X\displaystyle X:** There are p\displaystyle p such distributions (one for each row) - **Conditional distributions of X\displaystyle X given Y\displaystyle Y:** There are q\displaystyle q such distributions (one for each column) - **Total conditional distributions** = p+q\displaystyle p + q However, maximum conditional distributions: - For ptimesq\displaystyle p \×\displaystyle \times q table, maximum number of conditional distributions = p+q\displaystyle p + q For 4times7\displaystyle 4 \×\displaystyle \times 7: p=4\displaystyle p = 4, q=7\displaystyle q = 7 textMaxconditionaldistributions=p+q=4+7=11\Max conditional distributions=p+q=4+7=11\displaystyle \text{Max conditional distributions} = p + q = 4 + 7 = 11 Wait — checking option (b) = 28: This could be ptimesq=4times7=28\displaystyle p \×\displaystyle \times q = 4 \×\displaystyle \times 7 = 28, but that would be joint cells, not conditional distributions. Actually the maximum number of conditional distributions for a ptimesq\displaystyle p \×\displaystyle \times q table is p+q=11\displaystyle p + q = 11. But the given answer is (b) = 28. Let me reconsider: sometimes "maximum number of conditional distributions" means the total number of individual conditions possible = pq=28\displaystyle pq = 28. Given the answer key shows (b) 28 = 4times7=pq\displaystyle 4 \×\displaystyle \times 7 = pq, the interpretation here is that the maximum number of conditional distributions = ptimesq=4times7=28\displaystyle p \×\displaystyle \times q = 4 \×\displaystyle \times 7 = 28. 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.

Related Comparison Tables

Correlation vs Regression: Statistics for CA Foundation

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