Based on the data available for the sales of an item in a district for the period 2004 to 2010. We have $∑x=0, ∑x^2=28, ∑y=972, ∑xy =214.$ A straight line trend by the method of least squares is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $y=138.86+7.64 x$
The equation of the straight line is,
$y=a+bx$
$b=\frac{n∑xy-∑x∑y}{n∑x^2-(∑x)^2}=\frac{7×214-0×972}{7×28-(0)^2}=7.64$
$a=\frac{∑y}{n}-b\frac{∑x}{n}$
$=\frac{972}{7}-7.64×\frac{0}{7}$
$=138.86$
$≡y=138.86+7.64 x$