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Maths Linear Regression

Calculate the best fit line for scatter data points using the least squares linear regression method. The curve does not have to pass through each data point.

For straight line or linear curves (Z = A x + B) the regression is performed directly on the X and Z data values. For power curves (Z = A x^B) the regression is performed on the ln(X) and ln(Z) values. For logarithmic curves (Z = ln(X)) the regression is performed on the ln(X) and Z values. For exponential curves (Z = A e^B) the regression is performed on the X and ln(Z) values. For the user defined transform (Z = A f(X) + B) the regression is performed on f(X) and Z where f(X) is the user defined transform.

The X and Z offsets can be used to change the origin for log values (ln(X - Xo) and ln(Z - Zo)) and user defined transform (f(X - Xo)). The offsets are not used for the X and Z values.

The Z unit value is applied for the log of negative Z values. The Z unit value is not applied for X and Z values, or for user defined transforms (user defined transforms should account for the sign of the data points).

The regression data and regression parameters are displayed in the output view at the bottom of the page. The correlation coefficient r is a measure of how well the curve fits the data points (close to one is better). Extrapolated values should be used carefully.

Enter vector data as X,Z pairs separated by a comma or tab, with each pair on a new line. Or copy and paste the data points from a spreadsheet. Enter array data X and Z values as separate comma or tab separated lists. Store file data to a text file as comma or tab separated pairs (X,Z), with each pair on a new line (or copy and past cells from a spreadsheet). Refer to the example text file in resources.

Use the data plot option on the plot bar to display the data points and the best fit line.

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CALCULATOR : Linear Regression (Vector Data) [FREE]   ±

Calculate the best fit from vector data points using linear, power, logarithmic and exponential curves.

Enter data as comma or tab separated pairs (X,Z), with each pair on a new line (or copy and past cells from a spreadsheet). The regression output is displayed at the bottom of the page. Use the Data Plot option to plot the data points and the best fit curve.

Tool Input

  • zutype : Unit Z Value Type
  • rtype : Regression Type
  • offtype : Regression Offset Type
    • Xou : User Defined X Offset
    • Zou : User Defined Z Offset
  • Xdata : X Data Values
  • Zdata : Z Data Values
  • X : X Input Value

Tool Output

  • Z : Z Output Value
  • Zu : Unit Z Value
  • xo : X Offset
  • zo : Z Offset
CALCULATOR : Linear Regression (Array Data) [FREE]   ±

Calculate the best fit from array data points using linear, power, logarithmic and exponential curves.

Enter data as two separate arrays of comma separated values (X data and Z data). The regression output is displayed at the bottom of the page. Use the Data Plot option to plot the data points and the best fit curve.

Tool Input

  • zutype : Unit Z Value Type
  • rtype : Regression Type
  • offtype : Regression Offset Type
    • Xou : User Defined X Offset
    • Zou : User Defined Z Offset
  • Xdata : X Data Values
  • Zdata : Z Data Values
  • X : X Input Value

Tool Output

  • Z : Z Output Value
  • Zu : Unit Z Value
  • xo : X Offset
  • zo : Z Offset
CALCULATOR : Linear Regression (File Data - Modern Browser Required) [FREE]   ±

Calculate the best fit from text file data points using linear, power, logarithmic and exponential curves (a modern browser is required).

Save the data to a text file as comma or tab separated pairs (X,Z), with each pair on a new line (or copy and past cells from a spreadsheet). The regression output is displayed at the bottom of the page. Use the Data Plot option to plot the data points and the best fit curve. Refer to the example text file in resources.

Tool Input

  • zutype : Unit Z Value Type
  • rtype : Regression Type
  • offtype : Regression Offset Type
    • Xou : User Defined X Offset
    • Zou : User Defined Z Offset
  • Xdata : X Data Values
  • Zdata : Z Data Values
  • X : X Input Value

Tool Output

  • Z : Z Output Value
  • Zu : Unit Z Value
  • xo : X Offset
  • zo : Z Offset
CALCULATOR : Linear Regression With Transformations (Vector Data) [FREE]   ±

Calculate the best fit from vector data points using linear, power, logarithmic and exponential curves, or a user defined transformation.

Enter data as comma separated pairs (X,Z), with each pair on a new line (or copy and past cells from a spreadsheet). Select an X transformation (x, x^2, or x^3 etc...), or use a user defined transformation. User defined transformations can be any valid javascript expression in terms of x and xo (eg 7.3 * exp((x - xo) / 3.1) - 3.752 ). The regression output is displayed at the bottom of the page. Use the Data Plot option to plot the data points and the best fit curve.

Tool Input

  • zutype : Unit Z Value Type
  • rtype : X Regression Type
    • T : User Defined X Transformation
  • offtype : Regression Offset Type
    • Xou : User Defined X Offset
    • Zou : User Defined Z Offset
  • Xdata : X Data Values
  • Zdata : Z Data Values
  • X : X Input Value

Tool Output

  • Z : Z Output Value
  • Zu : Unit Z Value
  • xo : X Offset
  • zo : Z Offset
CALCULATOR : Linear Regression With Transformations (Array Data) [FREE]   ±

Calculate the best fit from array data points using linear, power, logarithmic and exponential curves, or a user defined transformation.

Enter data as two separate arrays of comma separated values (X data and Z data). Select an X transformation (x, x^2, or x^3 etc...), or use a user defined transformation. User defined transformations can be any valid javascript expression in terms of x and xo (eg 7.3 * exp((x - xo) / 3.1) - 3.752 ). The regression output is displayed at the bottom of the page. Use the Data Plot option to plot the data points and the best fit curve.

Tool Input

  • zutype : Unit Z Value Type
  • rtype : X Regression Type
    • T : User Defined X Transformation
  • offtype : Regression Offset Type
    • Xou : User Defined X Offset
    • Zou : User Defined Z Offset
  • Xdata : X Data Values
  • Zdata : Z Data Values
  • X : X Input Value

Tool Output

  • Z : Z Output Value
  • Zu : Unit Z Value
  • xo : X Offset
  • zo : Z Offset
CALCULATOR : Linear Regression With Transformations (File Data - Modern Browser Required) [FREE]   ±

Calculate the best fit from text file data points using linear, power, logarithmic and exponential curves, or a user defined transformation (a modern browser is required).

Save the data to a text file as comma separated pairs (X,Z), with each pair on a new line (or copy and past cells from a spreadsheet). Select an X transformation (x, x^2, or x^3 etc...), or use a user defined transformation. User defined transformations can be any valid javascript expression in terms of x and xo (eg 7.3 * exp((x - xo) / 3.1) - 3.752 ). The regression output is displayed at the bottom of the page. Use the Data Plot option to plot the data points and the best fit curve. Refer to the example text file in resources.

Tool Input

  • zutype : Unit Z Value Type
  • rtype : X Regression Type
    • T : User Defined X Transformation
  • offtype : Regression Offset Type
    • Xou : User Defined X Offset
    • Zou : User Defined Z Offset
  • Xdata : X Data Values
  • Zdata : Z Data Values
  • X : X Input Value

Tool Output

  • Z : Z Output Value
  • Zu : Unit Z Value
  • xo : X Offset
  • zo : Z Offset
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