GATE 2021 ST – Question 35
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 x=(3.29,21.53,48.69),y=(8.62,26.86,54.02). Find α̂+β̂,to two decimals.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 6.31 to 6.35
Explanation
Every observation satisfies y_i=x_i+5.33 exactly. Since the x values are not all equal,the unique least-squares line has β̂=1 and α̂=5.33. Their sum is **6.33**.