GATE 2020 ST – Question 60

Regression Analysis · Linear Models and Estimation · 2 marks · Numerical answer

Fit an intercept-and-slope OLS regression to x=(−2,−1,0,1,2),y=(3,5,8,9,10). Predict y at x=5.

Show answer and explanation

Correct answer: 16 to 16

Explanation

x̄=0 andȳ=35/5=7, so intercept=7. The cross-product sum is−6−5+0+9+20=18 and Σx²=10, giving slope1.8. Prediction at5 is7+1.8(5)=16.

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…
GATE 2025 ST Q35 – A normal linear regression has n=25 observations, an intercept and four predictors, with…
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?
GATE 2024 ST Q28 – In y i=β₀+β₁x i+ε i, the errors are uncorrelated with common mean zero and variance σ²>0.…
GATE 2024 ST Q29 – In simple linear regression with intercept,n≥3,uncorrelated mean-zero errors of variance…
GATE 2024 ST Q35 – In the no-intercept model y i=β₁x i+ε i with uncorrelated zero-mean errors of common…