Outliers are no problem

Algebra Level 4

Find the best line to fit the data points \( (1,0), (2,0), \ldots, (9,0), (10,40).\) Use the least squares method: the line should be the one that minimizes the sum of the squares of the errors in the \(y\)-coordinates.

If the line is written as \( y = mx+b,\) where \( m =\frac pq\) with \(p\) and \(q\) being coprime prime positive integers and \( b\) is an integer, find \(p+q+b.\)