GATE 2021 ST – Question 65

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

Fit Y_i=β₀+β₁x_(1i)+⋯+β₂₂x_(22i)+ε_i,i=1,…,123,with iid N(0,σ²) errors. Regression sum of squares is 338.92,total sum of squares 522.30. Find 100 times the adjusted R²,to two decimals.

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Correct answer: 57.00 to 57.40

Explanation

There are 22 predictors plus an intercept,so residual df=123−23=100 and total df=122. SSE=522.30−338.92=183.38. Adjusted R²=1−(183.38/100)/(522.30/122)≈.5716569. Thus **100R²_adj=57.17**.

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