Question

One of the normal equations for fitting a straight line \(y=a+bx\) is

• A. \(\sum y=a\sum x+b\sum x^2\)
• B. \(\sum y=na+b\sum x\)
• C. \(\sum xy=na+b\sum x^2\)
• D. \(\sum x=\sum y+b\sum x\)

Hint:

Normal equations for the regression line \[ \boxed{ y=a+bx } \] are \[ \boxed{ \begin{aligned} \sum y &= na+b\sum x,\\[2mm] \sum xy &= a\sum x+b\sum x^2. \end{aligned} } \]

Answer 1

The Correct Option is B

For fitting the straight line \[ y=a+bx \] by the method of least squares, the two normal equations are \[ \sum y=na+b\sum x \] and \[ \sum xy=a\sum x+b\sum x^2. \] Among the given options, one of the normal equations is \[ \boxed{\sum y=na+b\sum x.} \] Hence, \[ \boxed{(B)} \] is the correct answer.