GATE Regression Analysis: Regression Inference and Quadratic Forms – Previous Year Questions
7 GATE previous year questions on Regression Inference and Quadratic Forms (Regression Analysis, Statistics) with answers and explanations, from every paper.
- GATE 2021 ST Q65 – Fit Y i=β₀+β₁x (1i)+⋯+β₂₂x (22i)+ε i,i=1,…,123,with iid N(0,σ²) errors. Regression sum of squares is 338.92,total sum of squares 522.30. Find 100…
- GATE 2022 ST Q52 – Fit Y=β₀+β₁X₁+β₂X₂+β₃X₃+ε with independent N(0,σ²) errors to 52 observations. Regression sum of squares is 18.6,total sum of squares 79.23. Find the…
- GATE 2024 ST Q46 – In simple regression with intercept and slope, errors are uncorrelated with mean zero and variance σ²>0. I:a 95% joint confidence region for (β₀,β₁)…
- GATE 2024 ST Q65 – 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…
- GATE 2025 ST Q46 – 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…
- GATE 2026 ST Q48 – In Y i=β₀+β₁x i1+β₂x i2+β₃x i3+ε i,i=1,…,31, the errors are iid N(0,1). The 5% overall F-test rejects all three slopes zero. Upper-tail F critical…
- GATE 2026 ST Q60 – Y~N₃(0,I₃), A is the 3×3 matrix with every entry 1/3, and B=I₃−A. Which hold?