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Object[Analysis, Fit]

Curve fitting analysis of connected {x,y} datapoints.

Organizational Information

    Name

    Name of this Object.
    Format: Single
    Class: String
    Programmatic Pattern: _String
    Pattern Description: A string.

    ID

    ID of this Object.
    Format: Single
    Class: String
    Programmatic Pattern: _String
    Pattern Description: The ID of this object.

    Object

    Object of this Object.
    Format: Single
    Class: Expression
    Programmatic Pattern: Object[Analysis, Fit, _String]
    Pattern Description: The object reference of this object.

    Type

    Type of this Object.
    Format: Single
    Class: Expression
    Programmatic Pattern: Object[Analysis, Fit]
    Pattern Description: Object[Analysis, Fit]

    Notebook

    Notebook this object belongs to.
    Format: Single
    Class: Link
    Programmatic Pattern: _Link
    Pattern Description: An object of that matches ObjectP[Object[LaboratoryNotebook]].
    Relation: Object[LaboratoryNotebook][Objects]

    Author

    The person who ran the analysis.
    Format: Single
    Class: Link
    Programmatic Pattern: _Link
    Relation: Object[User]

General

Analysis & Reports

    BestFitFunction

    Fit function that calculates the expected Y as a function of X, stored as a pure function.
    Format: Single
    Class: Expression
    Programmatic Pattern: _Function | _QuantityFunction

    BestFitExpression

    The symbolic expression with the best fit parameters replaced by their fitted values.
    Format: Single
    Class: Expression
    Programmatic Pattern: Except[_String]

    BestFitParameters

    The unknown parameters from the SymbolicExpression along with their fitted values and standard deviations.
    Format: Multiple

    [[1]] Parameter Name

      Header: Parameter Name
      Class: Expression
      Programmatic Pattern: _Symbol

    [[2]] Fitted Value

      Header: Fitted Value
      Class: Real
      Programmatic Pattern: NumericP

    [[3]] Standard Deviation

      Header: Standard Deviation
      Class: Real
      Programmatic Pattern: NumericP?NonNegative

    BestFitParametersDistribution

    The multivariate distribution describing the best fit parameters.
    Format: Single
    Class: Compressed
    Programmatic Pattern: _MultinormalDistribution | _DataDistribution

    MarginalBestFitDistribution

    The marginal distribution describing the best fit parameters.
    Format: Multiple

    [[1]] Parameter Name

      Header: Parameter Name
      Class: Expression
      Programmatic Pattern: _Symbol

    [[2]] Fitted Distribution

      Header: Fitted Distribution
      Class: Expression
      Programmatic Pattern: DistributionP[]

    BestFitVariables

    A list of the variables present in the BestFitExpression of the fit function.
    Format: Multiple
    Class: Expression
    Programmatic Pattern: _Symbol

    PredictedResponse

    Predicted y-values when best fit function is applied to data x-values.
    Format: Single
    Class: Compressed
    Programmatic Pattern: {_?NumericQ...} | _?QuantityVectorQ

    BestFitResiduals

    Difference between fit-calculated y-values and the actual y-values from the data points.
    Format: Single
    Class: Compressed
    Programmatic Pattern: {_?NumericQ...}

    Derivative

    Derivative of the fitted function.
    Format: Computable
    Programmatic Pattern: _Function
    Expression: SafeEvaluate[{Field[BestFitFunction]}, Computables`Private`derivativeComputable[Field[BestFitFunction]]]

    CovarianceMatrix

    Describes the sensitivity of the model to changes in the values of the fitted parameters, and is used in the calculation of model unertainty.
    Format: Single
    Class: Expression
    Programmatic Pattern: SquareNumericMatrixP

    HatDiagonal

    Describes the influence each response value has on each fitted value, and is used in outlier detection. Also known as the influence matrix or the projection matrix.
    Format: Single
    Class: Compressed
    Programmatic Pattern: {_?NumericQ...}

    ParallelLineAnalyses

    Parallel Line Analyses performed based on this fit analysis.
    Format: Multiple
    Class: Link
    Programmatic Pattern: _Link
    Relation: Object[Analysis][Reference]

Statistical Information

    ANOVATable

    The statistic table generfated by performing an ANOVA analysis.
    Format: Single
    Class: Expression
    Programmatic Pattern: _Pane

    ANOVAOfModel

    The ANOVA results when source of variation is from the regression model.
    Format: Multiple

    [[1]] DF

      Header: DF
      Class: Real
      Programmatic Pattern: NumericP

    [[2]] Sum of Squares

      Header: Sum of Squares
      Class: Real
      Programmatic Pattern: NumericP

    [[3]] Mean Squares

      Header: Mean Squares
      Class: Real
      Programmatic Pattern: NumericP

    [[4]] F-Statistic

      Header: F-Statistic
      Class: Real
      Programmatic Pattern: NumericP

    [[5]] F-Critical (95%)

      Header: F-Critical (95%)
      Class: Real
      Programmatic Pattern: NumericP

    [[6]] P-Value

      Header: P-Value
      Class: Real
      Programmatic Pattern: NumericP

    ANOVAOfError

    The ANOVA results when source of variation is from the residual error.
    Format: Multiple

    [[1]] DF

      Header: DF
      Class: Real
      Programmatic Pattern: NumericP

    [[2]] Sum of Squares

      Header: Sum of Squares
      Class: Real
      Programmatic Pattern: NumericP

    [[3]] Mean Squares

      Header: Mean Squares
      Class: Real
      Programmatic Pattern: NumericP

    ANOVAOfTotal

    The ANOVA results when source of variation is from the original data.
    Format: Multiple

    [[1]] DF

      Header: DF
      Class: Real
      Programmatic Pattern: NumericP

    [[2]] Sum of Squares

      Header: Sum of Squares
      Class: Real
      Programmatic Pattern: NumericP

    FStatistic

    F Statistic is calculated by performing a F hypothesis test, following the equation MSR/MSE where MSR is the regression mean square, MSE is the mean square error.
    Format: Single
    Class: Real
    Programmatic Pattern: NumericP

    FCritical

    By default, it is the 95% critical value for the F-ratio distribution determined by the degrees of freedom in this object.
    Format: Single
    Class: Real
    Programmatic Pattern: NumericP

    FTestPValue

    The cumulative probability beyond FStatistic for the F-ratio distribution.
    Format: Single
    Class: Real
    Programmatic Pattern: NumericP

    RSquared

    R^2 value, also known as coefficient of determination, is a measure of how well the generated model fits its data.
    Format: Single
    Class: Real
    Programmatic Pattern: NumericP

    AdjustedRSquared

    An adjustment to the R^2 value that penalizes additional complexity in the model.
    Format: Single
    Class: Real
    Programmatic Pattern: NumericP

    AIC

    Akaike information criterion, a measure of the fit model's quality compared with other models.
    Format: Single
    Class: Real
    Programmatic Pattern: _?NumericQ

    AICc

    Corrected Akaike information criterion, a measure of the fit model's quality compared with other models, corrected for small sample sizes.
    Format: Single
    Class: Real
    Programmatic Pattern: _?NumericQ

    BIC

    Bayesian information criterion, a measure of a fit model's quality relative to other fit models, which penalizes model complexity more strongly than AIC.
    Format: Single
    Class: Real
    Programmatic Pattern: _?NumericQ

    EstimatedVariance

    Estimate of the error variance, calculated by dividing the sum squared error by the degrees of freedom (difference between the number of data points and number of model parameters).
    Format: Single
    Class: Real
    Programmatic Pattern: GreaterEqualP[0]

    SumSquaredError

    Sum of squared errors between fit-predicted and actual y-values.
    Format: Single
    Class: Real
    Programmatic Pattern: GreaterEqualP[0]

    StandardDeviation

    StandardDeviation of the fit error, which is equal to the squre root of the EstimatedVariance.
    Format: Single
    Class: Real
    Programmatic Pattern: GreaterEqualP[0]

    MeanPredictionError

    A function that computes mean prediction error from a given x-value. Mean prediction error is the expected error bewteen a predicted y-value and the average of repeated observations of that value.
    Format: Single
    Class: Expression
    Programmatic Pattern: _Function | _QuantityFunction

    MeanPredictionDistribution

    A function that computes mean prediction distribution from a given x-value.
    Format: Single
    Class: Expression
    Programmatic Pattern: _Function | _QuantityFunction

    SinglePredictionError

    A function that computes single prediction error from a given x-value. Single prediction error is the expected error between a predicted y-value and a single obersvation of that value.
    Format: Single
    Class: Expression
    Programmatic Pattern: _Function | _QuantityFunction

    SinglePredictionDistribution

    A function that computes single prediction distribution from a given x-value.
    Format: Single
    Class: Expression
    Programmatic Pattern: _Function | _QuantityFunction

    MeanPredictionInterval

    A function that computes a 95% confidence interval for a mean predicted value from a given x-value.
    Format: Single
    Class: Expression
    Programmatic Pattern: _Function | _QuantityFunction

    SinglePredictionInterval

    A function that computes a 95% confidence interval for a single predicted value from a given x-value.
    Format: Single
    Class: Expression
    Programmatic Pattern: _Function | _QuantityFunction

Standard Curve

Last modified on Mon 26 Sep 2022 15:43:43
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