GATE AG 2008 • Q21 MCQ • 2 Marks

Section 1: Engineering Mathematics

Probability and Statistics

Subtopic: Correlation and regression analysis

Question Statement:

The correlation analysis between X and Y variables assuming the parabolic relationship revealed a nonlinear correlation coefficient of 0.98. The percentage of the total variation that remains unexplained by assuming a parabolic relationship between X and Y is

Options:

  • (A) 2.0
  • (B) 96.0
  • (C) 3.96
  • (D) 10.0

Official Answer Key:

C

Step-by-Step Solution & Explanation

Coefficient of determination = η² = 0.98² = 0.9604, i.e. 96.04% of variation is explained. Unexplained % = 100 − 96.04 = 3.96%.

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