Multiple Regression

Multiple regression generally explains the relationship between multiple independent or predictor variables and one dependent or criterion variable.  A dependent variable is modeled as a function of several independent variables with corresponding coefficients, along with the constant term.  Multiple regression requires two or more predictor variables, and this is why it is called multiple regression.

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The multiple regression equation explained above takes the following form:

y = b1x1 + b2x2 + … + bnxn + c.

Here, bi’s (i=1,2…n) are the regression coefficients, which represent the value at which the criterion variable changes when the predictor variable changes.

As an example, let’s say that the test score of a student in an exam will be dependent on various factors like his focus while attending the class, his intake of food before the exam and the amount of sleep he gets before the exam.  Using this test one can estimate the appropriate relationship among these factors.

Multiple regression in SPSS is done by selecting “analyze” from the menu.  Then, from analyze, select “regression,” and from regression select “linear.”


  • There should be proper specification of the model in multiple regression.  This means that only relevant variables must be included in the  model and the model should be reliable.
  • Linearity must be assumed; the model should be linear in nature.
  • Normality must be assumed in multiple regression.  This means that in multiple regression, variables must have normal distribution.
  • Homoscedasticity must be assumed; the variance is constant across all levels of the predicted variable.

There are certain terminologies that help in understanding multiple regression.  These terminologies are as follows:

  • The beta value is used in measuring how effectively the predictor variable influences the criterion variable, it is measured in terms of standard deviation.
  • R, is the measure of association between the observed value and the predicted value of the criterion variable.  R Square, or R2, is the square of the measure of association which indicates the percent of overlap between the predictor variables and the criterion variable.  Adjusted R2 is an estimate of the R2 if you used this model with a new data set.


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