In a trend line equation y=a+b(x-x) , ‘a’ is equal to:

The correct answer is Option (2) → mean of y

By the method of least squares, the first normal equation is obtained by adding the equation over all n observations:

    \(\sum y = na + b\sum(x - \bar{x})\)

The deviations from the mean always add up to zero, \(\sum(x - \bar{x}) = 0\), so

    \( \displaystyle \sum y = na, \quad a = \frac{\sum y}{n} = \bar{y} \)

So a is the mean of y: the trend line passes through \((\bar{x}, \bar{y})\). The slope of the line is b, not a.