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GATE 2026 Chemical Engineering, Q63 · Mathematics

The correct answer is 2.49 to 2.51.

Question

The data (x,y) = (1,2), (2,6), (3,7), (4,10) are fitted to y = mx using the method of least squares. The value of m is ______ (rounded off to one decimal place).

Official answer: 2.49 to 2.51

Why

GATE 2026 official key: 2.49 to 2.51. Fitting y=mx through the origin by least squares minimizes Σ(y−mx)2,\Sigma (y−mx)², giving m =Σxy/Σx2=(2+12+21+40)/(1+4+9+16)=75/30=2.5.= \Sigma xy/\Sigma x² = (2+12+21+40)/(1+4+9+16) = 75/30 = 2.5.

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.

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