'*************************bestfitline() subroutine*******************
'
'   purpose: takes the points in the history array and computes
'            the best fit line (the line that lies closest to all the points
'
'   input: history array
'
'   output: draws the best fit line in the picturebox control
'           displays beginning and end coordinates of the best fit line
'           displays the slope and y-intercept of the best fit line
'
'********************************************************************
Sub bestfitline()
    Dim shiftx As Integer 'how much to shift x and y to make screen
    Dim shifty As Integer 'work better with cartesian coordinates
    shiftx = 80 'make origin start at middle of screen
    shifty = 120 'and also shift it to the bottom of the screen
    
    Dim vertline As Integer 'where to draw the line if the slope is undefined
    vertline = history(0, 1)

    Dim sumx As Double 'sumx is summation of x
    Dim sumy As Double 'sumy is summation of y
    Dim sumxy As Double 'sumxy is summation of x*y
    Dim sumxsq As Double 'sumxsq is summation of x*x
    Dim i As Integer 'i is a counter
    Dim a As Double 'a and b derive from line formula-->y=a+bx
    Dim b As Double
    Dim temp1 As Double
    Dim temp2 As Double
    'best fit line goes from (x1,y1) to (x2,y2)
    Dim x1 As Double
    Dim y1 As Double
    Dim x2 As Double
    Dim y2 As Double
    sumx = 0
    sumy = 0
    sumxy = 0
    sumxsq = 0
    For i = 0 To bfln - 1
        sumx = sumx + (history(i, 1) - shiftx)
        sumy = sumy + (shifty - history(i, 0))
        sumxy = sumxy + ((history(i, 1) - shiftx) * (shifty - history(i, 0)))
        sumxsq = sumxsq + ((history(i, 1) - shiftx) * (history(i, 1) - shiftx))
    Next i
    temp1 = (sumxsq * sumy) - (sumx * sumxy)
    temp2 = (bfln * sumxsq) - (sumx ^ 2)
    If Not (temp2 = 0) Then
        a = temp1 / temp2
    End If
    temp1 = (bfln * sumxy) - (sumx * sumy)
    If Not (temp2 = 0) Then
        b = temp1 / temp2
    End If
    'y=a+bx
    'x=(y-a)/b
    
    y1 = history(0, 0)
    y2 = history(bfln - 1, 0)
    If b = 0 Then 'vertical line problem-->vertical slope means division by zero
        x1 = vertline
        x2 = vertline
    Else
        'translate back into screen coordinates from shifted cartesian coordinates
        x1 = (((shifty - y1) - a) / b) + shiftx
        x2 = (((shifty - y2) - a) / b) + shiftx
    End If
    lx1.Caption = x1
    lx2.Caption = x2
    ly1.Caption = y1
    ly2.Caption = y2
    lb.Caption = a
    If b = 0 Then
        lm.Caption = "infinity"
    Else
        lm.Caption = b
    End If
    Picture4.ScaleMode = vbPixels
    Picture4.DrawWidth = 5
    Picture4.Line (x1, y1)-(x2, y2), RGB(255, 0, 0)
End Sub