Regression

Introduction

Regression analysis helps understand how the dependent variable changes when any of the independent variables is varied, while any other independent variables are held fixed.

Inputs

summarystatsinput

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Regression Name: Specify a name for your regression – if you are intending on undertaking more than one, a unique name relating to the variables being processed is advised

Regression Dataset Input: The dataset containing the variables to be tested.

Regression Dependent Variable: The response (dependent) variable to be used in the regression.

Regression Independent Variable(s): The explanatory (independent) variable(s) to be used in the regression.

Outputs

Output includes regression coefficients and correlation coefficients.

Regression Coefficients:

  • Intercept
  • Estimate(s)
  • Std. Error
  • t value (the estimated value divided by its estimated standard error)
  • Pr(>|t|) (the probability for testing the hypothesis)
  • sigma (standard deviation)
  • r.squared : R2 Co-efficient of determination (the amount of variation in the dependent variable explained by variation in the independent variables)
  • adj.r.squared: Adjusted R2
  • fstatistic : F (the ratio of two measures of variability)
  • fstatistic : DFR (degrees of freedom for regression )
  • fstatistic : DFE (degree of freedom for error)

Correlation Coefficients: a measurement of how two variables are related.

Advanced

The following formula is used in the implementation of linear regression.

\(ŷ = a + b_i x_i\)

where:
\(y\) is dependent variables
\(x\) are the independent variable(s)
\(ŷ\) is the vector of fitted values
\(a\) is the y intercept
\(b\) is the estimate(s) of the slope

The residual vector is \(y-ŷ\).

References

  1. Buechler, S.(2007) Statistical Models in R: Some Examples, Department of Mathematics, University of Notre Dame.
  2. Ferrari, D. and T. Head (2010) Regression in R Part I: Simple Liner Regression, Statistical Consulting Center, UCLA Department of Statistics.
  3. http://en.wikipedia.org/wiki/Residual_sum_of_squares.