GATE Regression Analysis: Linear Models and Estimation – Previous Year Questions
11 GATE previous year questions on Linear Models and Estimation (Regression Analysis, Statistics) with answers and explanations, from every paper.
- GATE 2021 ST Q18 – In Y i=β₀+β₁x i+ε i,i=1,…,n,n≥3,the errors are iid with mean zero and variance σ². Let β̂₀,β̂₁ be OLS estimators,x̄=Σx i/n,S₁=Σ(x i−x̄)²,S₂=Σy i(x…
- GATE 2021 ST Q35 – For Y i=α+βx i+ε i,i=1,2,3,fixed x i and iid errors of mean zero and finite variance,let α̂,β̂ be OLS estimates. Data are…
- GATE 2022 ST Q54 – Fit Y=β₀+β₁X+ε with independent N(0,σ²) errors to x=(0,1,2,3,4),y=(3,4,5,6,7). Let Ŷ₀ be the least-squares fitted mean at X=6. If Var Ŷ₀=cσ²,find c to…
- GATE 2023 ST Q26 – Consider y k=α₀+α₁ ln k+ε k,k=1,…,n,with iid errors of density e(− x )/2 on ℝ. Which statement is true?
- GATE 2023 ST Q58 – For t=1,…,100,consider y t=α₀+α₁t+α₂t²+ε t,where ε t are iid N(μ,1) and μ is unknown. Which parameters have unbiased estimators?
- GATE 2024 ST Q28 – In y i=β₀+β₁x i+ε i, the errors are uncorrelated with common mean zero and variance σ²>0. Let ȳ be the response mean and β̂₁ the least-squares slope.…
- GATE 2024 ST Q29 – In simple linear regression with intercept,n≥3,uncorrelated mean-zero errors of variance σ², let ŷ i be least-squares fitted values,T₁=Σ(y i−ŷ…
- GATE 2024 ST Q35 – In the no-intercept model y i=β₁x i+ε i with uncorrelated zero-mean errors of common finite variance, data are (2,5),(1,6),(3,4),(2,3),(4,6). Find the…
- GATE 2025 ST Q24 – For data (x i,y i) with Σx i²>0, β̂ minimizes Σ(y i−βx i)². Put v i=y i−x i,u i=2x i, and let γ̂ minimize Σ(v i−γu i)². If β̂=10, find γ̂.
- GATE 2025 ST Q35 – A normal linear regression has n=25 observations, an intercept and four predictors, with unknown error variance. If R²=5/6, find adjusted R² to two…
- GATE 2025 ST Q54 – For Y=Xβ+ε with ε~N n(0,I),X real n×p and λ>0, let β̂=(XᵀX+λI p)⁻¹XᵀY. Which hold?