The process of multiple regression deals with the relationship of multiple types of independent variables (or predictor variables) and dependent variables (or criterion variables.) Basically, in the process of multiple regression, the dependent variables are modeled as a function of several independent variables to correspond to the coefficients of the multiple regression that comes along with the constant term. Since multiple regression consists of large numbers of observations, 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 are the regression coefficients in Multiple regression (i=1,2…..n) which represents the value at which the criterion variable changes when the predictor variable changes simultaneously in Multiple regression.
For example, the test score of a student in an exam will be dependent on various factors, like his focus level while attending the class, his intake of food and sleep before an exam, etc. With the help of multiple regression, one can estimate the appropriate relationship among these factors.
Multiple regression in SPSS is done by selecting “Analyze” from the menu option. Then, from “Analyze,” select “regression” and from “regression,” select “Linear” and then “perform multiple regression.”
There are certain terminologies in multiple regression that help to better understand multiple regression.
The beta value in multiple regression is used in measuring how effectively the predictor variable influences the criterion variable. In multiple regression, it is measured in terms of standard deviation.
R in multiple regression is the measure of association between the observed value and the predicted value of the criterion variable. R Square or R2 in multiple regression is the square of the measure of association which indicates the variability in the criterion variable. Adjusted R2 in multiple regression takes the number of variables in the model and the number of data points in the model under consideration.
Assumptions
There should be proper specification of the model in multiple regression. This means that only relevant variables must be included in the multiple regression model. This means that in multiple regression, the model should be reliable.
Linearity must be assumed in multiple regression. This means that in multiple regression, the model should be linear in nature.
Normality must be assumed in multiple regression. This means that in multiple regression, variables must have a normal distribution.
Homoscedasticity must be assumed in multiple regression. This means that in multiple regression, the variability in errors must be the same across all levels.
