Outliers are no problem

Algebra Level 5

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 \( y = mx+b,\) then \( m =\dfrac pq\), where \(p\) and \(q\) are coprime prime positive integers, and \( b\) is an integer, find \(p+q+b.\)

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