| CALC : Math : Regression 011 : Linear Regression : X Transformations : Calculator
Description : Calculate the best line fit to a series of data points: x transformation.
Discussion : Calculates the linear regression sum of squares fit to the data points by transforming x
- z vs x
- z vs x2
- z vs x3
- z vs √x
- z vs x1/3
- z vs 1 / x
- z vs 1 / x2
- z vs 1 / x3
- z vs 1 / √x
- z vs 1 / x1/3
Use the X vs XY plot to compare line types.
Input Variables :
- R = Linear Regression Type
- X = Input Value
- xnums = Line Data Points
- znums = Line Data Points
Output Variables :
- ESS = Error Sum Of Squares
- F = F Ratio
- LR = Regression Formula
- RSS = Regression Sum Of Squares
- TSS = Total Sum Of Squares
- Z = Output Value
- n = Number Of Data Points
- r = Correlation Coefficient
- rr = Coefficient Of Determination
Calculation :
list( n , MX , MZ , SX , SZ , SXX , SZZ , SXZ ) = Regression( xnums , znums , R )
A = ( n SXZ - SX SZ ) / ( n SXX - SX 2 )
B = MZ - A MX
ESS = SZZ - B SZ - A SXZ
RSS = B SZ + A SXZ - SZ 2 / n
TSS = ESS + RSS
rr = RSS / TSS
r = √( rr )
F = ( n - 2 ) RSS / ESS
If R = 1 : Linear
Z = A X + B
Otherwise If R = 2 : Squared
Z = A X 2 + B
Otherwise If R = 3 : Cubed
Z = A X 3 + B
Otherwise If R = 4 : Square Root
Z = A √( X ) + B
Otherwise If R = 5 : Cubed Root
Z = A X 1 / 3 + B
Otherwise If R = 6 : Inverse Linear
Z = A / X + B
Otherwise If R = 7 : Inverse Squared
Z = A / X 2 + B
Otherwise If R = 8 : Inverse Cubed
Z = A / X 3 + B
Otherwise If R = 9 : Inverse Square Root
Z = A / √( X ) + B
Otherwise If R = 10 : Inverse Cubed Root
Z = A / X 1 / 3 + B
End of If Block
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