GATE 2026 MN – Question 48
For data x=(2,3,4,5),y=(8,9,7,16), the least-squares line is y=2.2x+2.3 and residual sum of squares25.8. Find coefficient of determination r² to two decimals.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0.45 to 0.50
Explanation
The response mean is10. Total squared deviation is(8−10)²+(9−10)²+(7−10)²+(16−10)²=50. Therefore r²=1−SSE/SST=1−25.8/50=0.484, or0.48. The given regression has an intercept, so this standard decomposition applies.