GATE 2024 ST – Question 35

Regression Analysis · Linear Models and Estimation · 1 mark · Numerical answer

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 least-squares slope to two decimals.

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Correct answer: 1.70 to 1.73

Explanation

The no-intercept slope is Σx_iy_i/Σx_i². Numerator=10+6+12+6+24=58; denominator=4+1+9+4+16=34. Estimate=58/34=29/17≈**1.71**.

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