# Hierarchical Multiple Regression SPSS

In this tutorial, we will learn how to perform hierarchical multiple regression analysis SPSS, which is a variant of the basic multiple regression analysis that allows specifying a fixed order of entry for variables (regressors) to control for the effects of covariates or to test the effects of certain predictors independent of the influence of other.

### Step By Step Procedure of Hierarchical Multiple Regression SPSS

The basic command for hierarchical multiple regression analysis SPSS is “regression -> linear”:

In the main dialog box of linear regression (as given below), input the dependent variable. For example “income” variable from the sample file of customer_dbase.sav available in the SPSS installation directory.

Next, enter a set of predictor variables into an independent(s) pan. These variables that you want SPSS to put into the regression model first (that you want to control for when testing the variables). For example, in this analysis, we want to find out whether the “Number of people in the house” predicts the “Household income in thousands”.

We are also concerned that other variables like age, education, gender, union member, or retirement might be associated with both the “number of people in the house” and “household income in thousands”. To make sure that these variables (age, education, gender, union member, and retired) do not explain away the entire association between the “number of people in the house” and “Household income in thousands”, let’s put them into the model first.

This ensures that they will get credit for any shared variability that they may have with the predictor that we are interested in, “Number of people in the house”. any observed effect of “Number of people in the house” can then be said to be “independent of the effects of these variables that already have been controlled for. See the figure below

In the next step put the variable that we are interested in, which is the “number of people in the house”. To include it in the model click the “NEXT” button. You will see all of the predictors (that were entered previously) disappear. Note that they are still in the model, just not on the current screen (block). You will also see Block 2 of 2 above the “independent(s)” pan.

Now click the “OK” button to run the analysis.

Note you can also hit the “NEXT” button again if you are interested in entering a third or fourth (and so on) block of variables.

Often researchers enter variables as related sets. For example demographic variables in the first step, all potentially confounding variables in the second step, and then the variables that you are most interested in in the third step. However, it is not necessary to follow. One can also enter each variable as a separate step if that seems more logical based on the design of your experiment.

### Output Hierarchical Multiple Regression Analysis

Using just the default “Enter” method, with all the variables in Block 1 (demographics) entered together, followed by “number of people in the house” as a predictor in Block 2, we get the following output:

The first table of output windows confirms that variables are entered in each step.

The summary table shows the percentage of explained variation in the dependent variable that can be accounted for by all the predictors together. The change in $R^2$ (R-squared) is a way to evaluate how much predictive power was added to the model by the addition of another variable in STEP 2. In our example, predictive power does not improve with the addition of another predictor in STEP 2.

The overall significance of the model can be checked from this ANOVA table. In this case, both models are statistically significant.

The coefficient table is used to check the individual significance of predictors. For model 2, the Number of people in the household is statistically non-significant, therefore excluded from the model.

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