Dim x(9), y(9)

'
s = 17108069
m7 = s Mod 7
'


m = m7 + 3
'
x(1) = 0
x(2) = 1
x(3) = 2
x(4) = 3
x(5) = 4
x(6) = 5
x(7) = 6
x(8) = 7
x(9) = 8

'
y(1) = 263
y(2) = 254
y(3) = 243
y(4) = 231
y(5) = 228
y(6) = 201
y(7) = 188
y(8) = 162
y(9) = 142

'
'y(1) = Exp(x(1))
'y(2) = Exp(x(2))
'y(3) = Exp(x(3))
'y(4) = Exp(x(4))
'y(5) = Exp(x(5))
'y(6) = Exp(x(6))
'y(7) = Exp(x(7))
'y(8) = Exp(x(8))
'y(9) = Exp(x(9))


'

' Exponential case:

'
xsum = 0
For j = 1 To m
xsum = xsum + x(j)
Next j

'
x2sum = 0
For j = 1 To m
x2sum = x2sum + (x(j)) ^ 2
Next j

'
xlogysum = 0
For j = 1 To m
xlogysum = xlogysum + x(j) * Log(y(j))
Next j


'
ylogsum = 0
For j = 1 To m
ylogsum = ylogsum + Log(y(j))
Next j
'
a = (ylogsum * x2sum - xsum * xlogysum) / (m * x2sum - xsum ^ 2)
b = (m * xlogysum - xsum * ylogsum) / (m * x2sum - xsum ^ 2)
'
'MsgBox a
ABIG = Exp(a)
'MsgBox ABIG
'MsgBox b

error2 = 0

For j = 1 To m
error2 = error2 + (y(j) - ABIG * Exp(b * x(j))) ^ 2
Next j

'MsgBox error2

p2200 = ABIG * Exp(b * 19)

'MsgBox p2200

' http://mathworld.wolfram.com/LeastSquaresFittingExponential.html

' https://en.wikipedia.org/wiki/List_of_countries_by_future_population_(United_Nations,_low_fertility_variant)


' Linear case:

sx = 0
For j = 1 To m
sx = sx + x(j)
Next j

sy = 0
For j = 1 To m
sy = sy + y(j)
Next j


sxy = 0
For j = 1 To m
sxy = sxy + x(j) * y(j)
Next j

sx2 = 0
For j = 1 To m
sx2 = sx2 + x(j) ^ 2
Next j


g = (m * sxy - sx * sy) / (m * sx2 - sx ^ 2)
i = (sy - g * sx) / m

'MsgBox g
'MsgBox i

error2linear = 0
For j = 1 To m
error2linear = error2linear + (y(j) - g * x(j) - i) ^ 2
Next j

di = Abs(error2linear - error2)


'MsgBox di
'MsgBox error2linear


' Quadratic case:

' https://www.azdhs.gov/documents/preparedness/state-laboratory/lab-licensure-certification/technical-resources/calibration-training/12-quadratic-least-squares-regression-calib.pdf


m = 3

y(1) = 0
y(2) = 1
y(3) = 4


sx = 0
For j = 1 To m
sx = sx + x(j)
Next j

sx2 = 0
For j = 1 To m
sx2 = sx2 + x(j) ^ 2
Next j

xx = sx2 - sx ^ 2 / m

sy = 0
For j = 1 To m
sy = sy + y(j)
Next j

sxy = 0
For j = 1 To m
sxy = sxy + x(j) * y(j)
Next j

xy = sxy - sx * sy / m



sx3 = 0
For j = 1 To m
sx3 = sx3 + x(j) ^ 3
Next j


xx2 = sx3 - sx * x2 / m

sx2y = 0
For j = 1 To m
sx2y = sx2y + x(j) ^ 2 * y(j)
Next j


x2y = sx2y - sx2 * sy / m



sx4 = 0
For j = 1 To m
sx4 = sx4 + x(j) ^ 4
Next j


x2x2 = sx4 - sx2 ^ 2 / m

a = (x2y * xx - xy * xx2) / (xx * x2x2 - xx2 ^ 2)

MsgBox a

b = (xy * x2x2 - x2y * xx2) / (xx * x2x2 - xx2 ^ 2)

MsgBox b


c = sy / m - b * sx / m - a * sx2 / m


MsgBox c