In hierarchical multiple regression analysis, the researcher determines the order that variables are entered into the regression equation. The researcher may want to control for some variable or group of variables. The researcher would perform a multiple regression with these variables as the independent variables. From this first regression, the researcher has the variance accounted for this corresponding group of independent variables. The researcher will run another multiple regression analysis including the original independent variables and a new set of independent variables. This allows the researcher to examine the contribution above and beyond the first group of independent variables.
Illustrated Example
Researchers in workaholism were interested in the effects of spouses’ workaholic behavior on marital disaffection. Previous research suggested that locus of control, positive affect, and negative effect are related to marital disaffection. The researchers decide to enter the variables that research suggested were related to marital disaffection first, then enter the subscales of workaholism last.
[data]
Results
To examine the unique contribution of workaholism in the explanation of marital disaffection, a hierarchical multiple regression analysis was performed. Variables that explain marital disaffection were entered in two steps. In step 1, marital disaffection was the dependent variable and (a) locus of control, (b) positive affect, and (c) negative affect were the independent variables. In step 2, the subscales of the WART were entered into the step 1 equation. Before the hierarchical multiple regression analysis was perform, the independent variables were examined for collinearity. Results of the variance inflation factor (all less than 2.0), and collinearity tolerance (all greater than .76) suggest that the estimated βs are well established in the following regression model.
The results of step 1 indicated that the variance accounted for (R^{2} ) with the first three independent variables (LOC, positive and negative affects) equaled .03 (adjusted R^{2} = .02), which was significantly different from zero (F_{(3, 297)}=3.08, p<.05). Negative affect was the only statistically significant independent variable, β = .13, p<.05. In step 2, the five subscales of the WART were entered into the regression equation. The change in variance accounted for (ΔR^{2}) was equal to .17, which was significantly different from zero (F_{(8, 292)}=3.08, p<.05). The unstandardized regression coefficients (B) and intercept, the standardized regression coefficients (β), for the full model are reported in Table 3. Only two of the subscales of workaholism contributed significantly to the explanation of marital disaffection, control and impaired communication.
Table 1
Unstandardized Regression
Coefficients (B) and Intercept, the Standardized Regression Coefficients (β),
tvalues, and pvalues
for Variables as Predictor of Marital Disaffection
Variables 
B 
β 
tvalue 
pvalue 
Intercept 
27.16 

5.20 
<.01 
LOC 
.08 
.03 
.50 
.62 
POSITIVE 
.72 
.04 
.71 
.48 
NEGATIVE 
1.18 
.08 
1.38 
.17 
COMPUL 
1.52 
.09 
1.36 
.18 
CONTROL 
4.15 
.25 
3.39 
<.01 
IMPAIR 
5.28 
.27 
4.10 
<.01 
DELEGATE 
1.28 
.09 
1.70 
.09 
SELFW 
.88 
.06 
.99 
.32 