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Regress[data, funs, vars]
finds a least-squares fit to a list of data as a linear combination of the functions funs of variables vars.
  • The data can have the form {{x1, y1, ..., f1}, {x2, y2, ..., f2}, ...}, where the number of coordinates x, y, ... is equal to the number of variables in the list vars.
  • The data can also be of the form {f1, f2, ...}, with a single coordinate assumed to take values 1, 2, ....
  • The argument funs can be any list of functions that depend only on the variables vars.
  • Regress returns a list of rules for results and diagnostics specified by the option RegressionReport.
  • Regress always finds the linear combination of the functions in the list funs that minimize the sum of the squares of deviations from the values fi.
  • Exact numbers given as input to Regress are converted to approximate numbers with machine precision.
  • The following options can be given:
RegressionReportSummaryReportresults to be included in output
IncludeConstantTruewhether to automatically include a constant as one of the functions
BasisNamesAutomaticnames of basis elements for table headings
WeightsAutomaticweights for each data point
MethodAutomaticmethod used to compute singular values
ToleranceAutomatictolerance to use in computing singular values
ConfidenceLevel0.95confidence level used for confidence intervals
  • Possible settings for Weights are Automatic, a list of numbers with the same length as the data, or a pure function.
  • With the default setting Weights->Automatic, each data point is given a weight of 1.
Linear regression for a straight line:
Click for copyable input
Linear regression for a constant plus a sinusoid:
Click for copyable input