Regression coefficient Regression coefficient

Regression coefficient

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What is regression coefficient?

Regression coefficient in regression is a measure of the change in the value of the dependent variable with respect to the corresponding change in the independent variable. 

The coefficients are the values that are multiplied with the predictor values. Let’s say you have regression equation 

y = 3X + 5. 

Where,

  • +3 = coefficient,
  • x = predictor,
  • +5 = constant.

The sign of each coefficient shows the direction in which the relationship between a predictor variable and the response variable moves:

  • A positive sign: if the predictor variable increases, the response variable also increases.
  • A negative sign: if the predictor variable increases, the response variable decreases.

The Regression Coefficient, also called as a slope coefficient as it shows the slope of the line (the change in the dependent variable for the unit change in the independent variable.)

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Equation of regression coefficient

The regression coefficient of x on y

It is denoted by bxy and measures the change in x for each unit change in y. it is represented as:

The value of bxy can be found with the below formula provided the deviations are obtained from the means of x and y are given:

When the deviations are taken, the following formula is used:

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The regression coefficient of y on x

It is denoted by byx and measures the change in y for each unit change in x. it is represented as:

The value of byx can be found with the below formula provided the deviations are obtained from the means of y and x are given:

When the deviations are taken, the following formula is used:

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