Thursday, 29 October 2015

REGRESSION ANALYSIS USING SPSS

In this post, I am going to tell you how to run single as well as multiple regression analysis using SPSS. Let’s illustrate this with an example. Imagine that you are conducting a survey and collecting data on the following matters of respondents.
1.      Gender
2.      Age
3.      Income in Dollars ($$)
4.      Brand Loyalty (Perceived)
5.      Service Quality (Experienced/Perceived)

First of all, you need to input the above mentioned variables in to SPSS. For details on how to enter/ input the variables in the SPSS please see my previous posts. Once, the variables and values are entered, now you are ready to enter the data. And once the data is entered in SPSS Data View window, now you are ready to run descriptive statistics, correlation test (Discussed in this post) or regression analysis (Discuss in this post)





In this example, the variable of Brand Loyalty is entered via likert scale with 1 refers to very  low brand loyalty, 2 refers to low, 3 refers to neutral, 4 refers to high, and 5 refers to very high brand loyalty. The variable of service quality is also based on likert scale with 1 refers to very poor service quality, 2 refers to poor, 3 refers to neutral, 4 refers to good, and 5 refers to very good service quality.  Since, regression analysis is mostly run when data is continuous (Based on likert scale); therefore, the data qualify for running normal correlation analysis.

The command for running regression analysis is as under.
Analyze---Regression----Linear



Now a dialogue box will open in front of you. In this box, on left hand side, you can see all of the variables. Select the dependent variable and transfer it in to Dependent box. Similarly, select the independent variable and transfer it in to independent variable box. 



In our example, we transfer, brand loyalty to the dependent box, and service quality in to the independent box. Then, just press OK.


The result will appear in new output window with four tables and some details.


 Here is how you will interpret these results. The first table with the heading ‘Variables Entered/Removed’ is only for information. It will show that the name of the variables entered in the regression analysis. Normally, we ignore this table.  In the second table with the heading ‘Model Summary’, the value of R, R Square, and Adjusted R Square are important for us. The value of R shows the correlation or association between the variables. In this case, the value of R is .431 which shows that both brand loyalty and service quality is 43.1% positively associated. Similarly, the value of R Square is .186 which means that the independent variable (service quality) is explaining 18.6% variation or change in the dependent variable (brand loyalty). The value of adjusted R square is an improved form of R Square as it adjusts for degree of freedom and interpretation is also similar to R Square. Thus, Adjusted R Square is considered a better indicator of model fitness over simple R Square.
Then in third table with the heading ‘ANOVA’, few values are important for us. The value of F shows that how fit the overall model is. In this example, the value of F is 4.10 which show that overall, the model is fit and can be considered satisfactory. Next to F value, there is Sig value which in this example is 0.058 which shows that the F statistics is significant (Its significant since P value is less than 0.10).
In the last or fourth table with the heading of ‘Coefficients’, there are various information. Mostly, we are interested in the value of B or beta for both constant and independent variable. Normally, we do not give much importance to the constant; however, its interpretation is that if everything else goes zero, still there will be some change in the dependent variable. Thus,  in this example, the beta value of 2.16 for the constant shows that if service quality is zero, still, there will be 2.16 units brand loyalty. The beta value of .407 written in the row of service quality shows that if there is one unit increase in the service quality, the brand loyalty will go up by .407 units. Similarly, other important information is t value which can be used to see if the effect of independent variable on the dependent variable is significant or insignificant. In this example, the value of 2.026 of t value shows that the results are significant (It’s significant since its bigger than 2). We can also check the significance by looking at the Sig value located next to t-value. The value of Sig is 0.058 which is less than 0.10 therefore, we can conclude  that the effect of service quality on brand loyalty are significant and if any hypothesis are constructed, then those hypothesis must be accepted based on the significant t or sig value.
So summing up all the things, normally we report the following things with this order in our report or thesis or article.
1.      Constant’s beta value, t value, and sig value
2.      Independent variable’s beta value, t value, and sig value
3.      R Value
4.      R Square value
5.      Adjusted R Square value
6.      F value with its sig value
    
Multiple Regression Analysis:
In multiple regression analysis, everything is similar to the simple regression analysis as discussed above with the exception that in multiple regression analysis there are more than single independent variable. So simply, when inputting the variables in the regression box, you add multiple variables and run the test.

SPSS Practice File is as under

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