GATE 2025 ST – Question 46

Regression Analysis · Regression Inference and Quadratic Forms · 2 marks · Multiple choice

For y_i=α+βx_i+ε_i,i=1,…,24, iid N(0,σ²) errors, the centered sums are S_xx=22.82,S_yy=43.62,S_xy=15.48. Find the F₁,₂₂ statistic testing β=0 against β≠0, to two decimals.

2.54
2.98
3.17
6.98

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Correct answer: (D) 6.98

Explanation

Regression sum of squares SSR=S_xy²/S_xx=15.48²/22.82≈10.501. Residual SSE=43.62−SSR≈33.119. F=(SSR/1)/(SSE/22)≈**6.98, D**.

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