Question:medium

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).
x1234
y26710

Show Hint

For a line forced through the origin, the least-squares slope is \(m=\sum xy/\sum x^2\).
Updated On: Aug 10, 2026
Show Solution

Correct Answer: 2.5

Solution and Explanation

$m$ is the weighted average of point-wise ratios $y_i/x_i$ weighted by $x_i^2$: ratios are 2, 3, 2.333, 2.5 with weights 1,4,9,16 (sum 30). Weighted sum = 2+12+21+40=75. $m=75/30=2.5$, matching the calculus-based derivation.
\[ \boxed{m = 2.5} \]
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