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Regression coefficients

By Jim Frost

Regression coefficients are estimates of the unknown population parameters and describe the relationship between a predictor variable and the response. In linear regression, coefficients are the values that multiply the predictor values. Suppose you have the following regression equation: y = 3X + 5. In this equation, +3 is the coefficient, X is the predictor, and +5 is the constant.

The sign of each coefficient indicates the direction of the relationship between a predictor variable and the response variable.

  • A positive sign indicates that as the predictor variable increases, the response variable also increases.
  • A negative sign indicates that as the predictor variable increases, the response variable decreases.

The coefficient value represents the mean change in the response given a one unit change in the predictor. For example, if a coefficient is +3, the mean response value increases by 3 for every one unit change in the predictor.

Related

Synonyms:
Coefficients
Related Articles:
  • How to Interpret Coefficients and P-values in Regression
  • How To Interpret R-squared in Regression Analysis
  • How High Does R-squared Need to Be?
  • Introduction to Bootstrapping in Statistics with an Example
  • Nominal, Ordinal, Interval, and Ratio Scales
  • Overfitting Regression Models: Problems, Detection, and Avoidance

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