GATE 2022 ST – Question 52

Regression Analysis · Regression Inference and Quadratic Forms · 2 marks · Numerical answer

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 ANOVA F statistic for H₀:β₁=β₂=β₃=0,to three decimals.

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Correct answer: 4.907 to 4.909

Explanation

The numerator has 3 degrees of freedom and the residual has 52−4=48. SSE=79.23−18.6=60.63. Thus F=(18.6/3)/(60.63/48)=297.6/60.63≈**4.908**.

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