GATE 2026 CH – Question 63
The data given in the table are fitted to the equation $y = mx$ using the method of least squares. The value of $m$ is ______ (rounded off to one decimal place).
| $x$ | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| $y$ | 2 | 6 | 7 | 10 |
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Show answer and explanation
Correct answer: 2.49 to 2.51
Explanation
For a line through the origin, minimising $\sum(y - mx)^2$ gives $m = \frac{\sum xy}{\sum x^2}$. Here $\sum xy = 2 + 12 + 21 + 40 = 75$ and $\sum x^2 = 1 + 4 + 9 + 16 = 30$, so $m = \frac{75}{30} = 2.5$.