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Calling Sequence
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LogarithmicFit(X, Y, v, options)
LogarithmicFit(XY, v, options)
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Parameters
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X
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Vector; values of independent variable
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Y
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Vector; values of dependent variable
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XY
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Matrix; values of independent and dependent variables
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v
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name; (optional) independent variable name
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options
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(optional) equation(s) of the form option=value where option is one of output, summarize or weights; specify options for the LogarithmicFit command
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Description
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The LogarithmicFit command fits a logarithmic function of the form to data by performing a least-squares fit. Given k data points, where each point is a pair of numerical values for (, ), the LogarithmicFit command finds a and b such that the sum of the k residuals squared is minimized. The ith residual is the value at the ith data point.
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In the first calling sequence, the first parameter X is a Vector containing the k values of the independent variable x, and the second parameter Y is a Vector containing the k values of the dependent variable y. The entries of X must evaluate to positive numbers. In the second calling sequence, the first parameter XY is a Matrix with two columns, where the first column corresponds to X and the second column to Y. For X, Y, and XY, one can also use lists or Arrays; for details, see the Input Forms help page.
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If the optional parameter v is provided, then the LogarithmicFit command returns the logarithmic function in variable v with the computed values of a and b. Otherwise, a Vector containing values of a and b is returned.
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The LogarithmicFit command calls the Statistics[LinearFit] command to fit the given data to the model. Additional options accepted by the LinearFit command, such as weights=W where W is a Vector of weights, may be provided to LogarithmicFit. More information about the underlying linear regression solver is available on the LinearFit help page.
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Options
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The options argument can contain one or more of the options shown below. These options are described in more detail on the Statistics/Regression/Options help page.
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output = name or string -- Specify the form of the solution. The output option can take as a value the name solutionmodule, or one of the following names (or a list of these names): AtkinsonTstatistic, confidenceintervals, CookDstatistic, degreesoffreedom, externallystandardizedresiduals, internallystandardizedresiduals, leastsquaresfunction, leverages, parametervalues, parametervector, residuals, residualmeansquare, residualstandarddeviation, residualsumofsquares, rsquared, rsquaredadjusted, standarderrors, tprobability, tvalue, variancecovariancematrix. For more information, see the Statistics/Regression/Solution help page.
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summarize = identical( true, false, embed ) -- Display a summary of the regression model
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svdtolerance = realcons(nonnegative) -- Set the tolerance that determines whether a singular-value decomposition is performed.
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weights = Vector -- Provide weights for the data points.
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Examples
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Fit a logarithmic function to the provided data.
Use the summarize option to return a summary of the regression:
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Model:
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Coefficients
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Estimate
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Standard Error
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t-value
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P(>|t|)
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Parameter 1
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Parameter 2
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R-squared:
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Adjusted R-squared:
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Residuals
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Residual Sum of Squares
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Residual Mean Square
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Residual Standard Error
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Degrees of Freedom
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Five Point Summary
Minimum
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First Quartile
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Median
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Third Quartile
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Maximum
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Use the weights option to assign a weight to each data point. Because the v parameter is not provided, a Vector containing the computed model parameters is returned.
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Compatibility
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The XY parameter was introduced in Maple 15.
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The Statistics[LogarithmicFit] command was updated in Maple 2016.
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The summarize option was introduced in Maple 2016.
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