Originally Posted by

**danijelrd** Hy everyone. First, Im sorry if I missed subforum. Please help me about this problem of least squares method. I solved first part of problem when you have to do least square method, but I dont understand how to put triangle in that coordinate system and calculate area of it. my online calculation of l.s.m is here ->

http://i46.tinypic.com/okvssn.jpg
Problem -> With the method of least squares find best line f(x) which goes through six given points from A to F. Calculate area of triangle bounded with that line, and axis X and Y.

Points are : A ( 18.6 , -143.8 ) ; B ( 29.5 , -250.2 ) ; C (32.5 , -278.3 ) ; D ( 41.5 , -365.8 ) ; E ( 54.5 , -490.9 ) ; F ( 62.9 , -575.5 )

I'll assume that the LS line from your jpeg is correct: $\displaystyle y = -9.71801194177x + 37.1606433422$.

From here, take one of two avenues:

**First Method: Calculus**

The area of the triangle is the area under the curve (LS line, in this case) bounded from below by the Y-axis ($\displaystyle X=0$) and from above by the X-axis ($\displaystyle y=0$). The lower X-limit is 0 and the upper X-limit is the solution to $\displaystyle 0 = -9.71801194177x + 37.1606433422$, which is $\displaystyle \tfrac{37.1606433422}{9.71801194117}\approx 3.82389356638635$.

$\displaystyle \int_{x=0}^{x=3.82389} -9.71801x + 37.16064 = (-\tfrac{9.71801}{2}x^2 + 37.16064x)|^{3.82389}_{0} \approx 74.049$

Second Method: Find the triangle's coordinates, compute the area of the relevant rectangle, then take half that number. That is, $\displaystyle \frac{b\cdot h}{2}$.