GATE 2024 ST – Question 65

Regression Analysis · Regression Inference and Quadratic Forms · 2 marks · Numerical answer

In a regression with 25 observations,intercept and two predictors, the overall test uses F₀=11R²/(1−R²),rejecting if F₀>F_(α;2,22). Given F_(.025;2,22)=4.38,F_(.05;2,22)=3.44, find the smallest R² leading to rejection at α=.05, rounded to two decimals.

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Correct answer: 0.22 to 0.26

Explanation

Solve 11R²/(1−R²)>3.44 to obtain R²>3.44/(11+3.44)=3.44/14.44≈.23823. The cutoff rounded to two decimals is **.24**. Strictly the unrounded rejection set has this value as an infimum rather than an attained smallest value; .24 itself exceeds it.

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