Then the sign of the Son of Man will appear in heaven, and then all the tribes of the earth will mourn, and they will see the Son of Man coming on the clouds of heaven with power and great glory. And he will send his angels with a great sound of a trumpet, and they will gather together his elect from the four winds, from one end of heaven to the other. Matthew 24:30-31
Pipeng Free Online Software : Regression Calculators
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Pipeng : Linear Regression Calculation Module

Regression Calculators

Description : Calculate the best line fit for data points using linear regression.

Discussion : The accuracy of the fit can be measured by the coefficient of determination r2, and the corresponding correlation coefficent r = √r2.

Enter the data points as pairs separated by a comma, with each line pair on a new line. The data points can be in any order.

Calculator Tools In This Module:

CALC : Math : Regression 001 : Linear Regression : Linear Power Exponential and Log Relationships : Calculator
CALC : Math : Regression 011 : Linear Regression : X Transformations : Calculator


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Module List

CALC : Math : Regression 001 : Linear Regression : Linear Power Exponential and Log Relationships : Calculator

Description : Calculate the best line fit to a series of data points: linear, power, logarithmic or exponential line coefficients.

Discussion : Calculates the linear regression sum of squares fit to the data points using

  • Linear - z vs x
  • Power - log z vs log x
  • Logarithmic - z vs log x
  • Exponential - log z vs x

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 : Power
  C = e B
  Z = C X A
 Otherwise If R = 3 : Logarithmic
  Z = A log( X ) + B
 Otherwise If R = 4 : Exponential
  C = e B
  Z = C e A X
 End of If Block

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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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