Question

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

Hint:

For a line forced through the origin, the least-squares slope is \(m=\sum xy/\sum x^2\).

Answer 1

Correct Answer: 2.5

Step 1: Least squares for a line through the origin.
Minimizing \(S(m)=\sum(y_i-mx_i)^2\) gives \(m = \dfrac{\sum x_iy_i}{\sum x_i^2}\).

Step 2: Tabulate.
\(x_iy_i\): 2, 12, 21, 40; sum = 75. \(x_i^2\): 1, 4, 9, 16; sum = 30.

Step 3: Compute m.
\[ m = 75/30 = 2.5 \]

\[ \boxed{m = 2.5} \]