The values of 'a' and 'b' if the equation of straight line trend by least square method is given by \(y = a + bx\) such that \(\sum x = 0, \sum y = 84, \sum xy = 108, \sum x^2 = 70\) for 6 observations are:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(a = 14;\ b = 1.54\)
The normal equations of the least squares line \(y = a + bx\) are
\(\sum y = na + b\sum x\)
\(\sum xy = a\sum x + b\sum x^2\)
With \(\sum x = 0\) and \(n = 6\) they separate:
\( \displaystyle a = \frac{\sum y}{n} = \frac{84}{6} = 14 \)
\( \displaystyle b = \frac{\sum xy}{\sum x^2} = \frac{108}{70} \approx 1.54 \)
CBSE Applied Mathematics (Class XII):
Computation of Straight-line Trend by Using Method of Least Squares
