### Multiple Regression Analysis in SPSS

# Multiple Regression Analysis in SPSS

Multiple regression analysis is an extension of simple linear regression. It is used when the value of a variable needs to be predicted based on the value of two or more other variables.

Assumptions

Dependent variable should be continuous

Two or more independent variables, which can be either continuous or categorical, are required

A linear relationship should exist between two variables

Independence of observations is required

Data should show homoscedasticity

Data should follow normality

There should be no significant outliers

Here, Anxiety score is considered as dependent variable and Systolic blood pressure and

Body mass index are considered as two independent variables.

The procedure for multiple regression analysis is the same as linear regression, but two independent variables are added instead of one.

In SPSS, multiple regression is found in Analyze > Regression > Linear

Then, linear regression dialog box would open.

Then, dependent variable (Anxiety score) has to be added in Dependent box and independent variables (Systolic blood pressure and Body mass index) are to be added in Block 1 of 1 box.

In Statistics Dialog box, add Estimates, Model fit and Descriptive in regression coefficients group.

Click on ‘Continue’ and ‘Ok’.

# Output of Multiple Regression Analysis

The descriptive statistics are obtained for the independent and dependent variables.

Th model summary table would be obtained.

R denotes the multiple correlation coefficients. This is the Pearson correlation between the actual scores and those predicted by the regression model. R square (also called as coefficient of determination) is the squared multiple correlation. It is the proportion of variance in the dependent variable accounted for by the entire regression model. The R square value of 0.957 indicates that Body mass index and Systolic blood pressure accounted for 95.7% of the total variation in the anxiety score. Adjusted R square value of 0.956 indicates that 95.6% of the variance was explained by the model.

Then, ANOVA table would be obtained.

The F value in the ANOVA table examines whether the overall regression model is a good fit for the data. The table shows that the independent variables significantly predicted the dependent variable, F (2,43)=484.184, p<0.0005.

Then, the Coefficients table would be obtained.

Unstandardized coefficients (B) indicate the extent to which the dependent variable varies with an independent variable when all other independent variables are held constant. The B value for Systolic blood pressure is 0.484, which indicates that when Systolic blood pressure increases by one unit, the anxiety score increases by 0.484 units. Similarly, the B value for Body mass index is 0.488, which indicates that when Body mass index increases by one unit, the anxiety score increases by 0.488 units.

The p values for the two independent variables (Systolic blood pressure and Body mass index) are less than 0.05. Thus, it can be concluded that Systolic blood pressure (t=6.598) and Body mass index (t=3.221) significantly impact the anxiety score.

The following regression equation can be formed from the analysis to predict the impact of Systolic blood pressure and Body mass index on the anxiety score.

Anxiety score = – 63.254 + 0.484 (Systolic blood pressure) + 0.488 (Body mass index)

Data: Multiple_Regression_Data.sav