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Multiple regression

Dr. Simon Moss

Purpose of multiple regression

Multiple regression analysis is used to examine the relationship between one numerical variable, called a criterion, and a set of other variables, called predictors. In addition, multiple regression analysis is used to investigate the correlation between two variables after controlling another covariate.

To illustrate, consider a researcher who wants to know whether or not the number of jars of Chicken Tonite you consume--the dependent variable or criterion--relates to frequency of psychotic behaviours, frequency of crossing roads, and age--the independent variables or predictors.

Multiple regression serves two functions. First, this technique yields an equation that predicts the dependent variable or criterion from the various independent variables or predictors. This function, however, is seldom utilised in psychology. Second, and more importantly, this technique identifies the independent variables that relate to the dependent variable, after controlling the other variables. For instance, this procedure can determine the relationship between Chicken Tonite and crossing roads in individuals who are equivalent on psychotic behaviours, age, and so on.

Procedure

To demonstrate multiple regression, you should first access SPSS and create a data file that resembles the following.

To subject these data to multiple regression:

  1. Select the "Analyse" menu and choose "Regression" and then "Linear".
  2. Designate "Chicken" as the dependent variable.
  3. Designate "Psycho", "Crossing", and "Age" as the independent variables.
  4. Although optional, you can also press "Statistics", tick "Part and Partial correlations", and then press "Continue".
  5. Press OK. An extract of the output is presented below.

Derivation of the equation

Regression assumes the dependent or criterion variable can be predicted from the independent or predictor variables using an equation. The equation is assumed to resemble the following formula:

Dependent variable = B0 + B1 x iv1 + B2 x iv2 + B3 x iv3 ...

The B values denote numbers, such as 3.6. Using some special formula, multiple regression then estimates these B values. These B values are then reported in the column labelled B. Locate this column in the previous outcome. These B values can then be used to specify the equation. Note that 8.09E-02 denotes 8.09 x 10-2, which equals 0.0809& that is, the decimal place is moved two places to the left. In this case, the equation is:

Chicken = 4.933 + 0.630 x Psycho + 0.081 x Crossing--0.151 x Age

This equation can be used to predict the dependent variable from the independent variables. To illustrate, suppose that a person scored 2 for "Psycho", 8 for "Crossing", and 10 for "Age". Now, enter these values into the equation. This process yields a 5.33. That is, we predict this participant will score 5.33 on the dependent variable or criterion "Chicken".

The accuracy of this equation

This equation is regarded as accurate if the residuals are minimal. To illustrate the concept of residuals:



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Last Update: 7/7/2016