How to interpret the results of the linear regression test in SPSS?
A previous article explained how to interpret the results obtained in the correlation test. Case analysis was demonstrated, which included a dependent variable (crime rate) and independent variables (education, implementation of penalties, confidence in the police, and the promotion of illegal activities). The aim of that case was to check how the independent variables impact the dependent variables. The test found the presence of correlation, with the most significant independent variables being education and promotion of illegal activities. Now, the next step is to perform a regression test.
However, this article does not explain how to perform the regression test, since it is already present here. This article explains how to interpret the results of a linear regression test on SPSS.
What is regression?
Regression is a statistical technique to formulate the model and analyze the relationship between the dependent and independent variables. It aims to check the degree of relationship between two or more variables. This is done with the help of hypothesis testing. Suppose the hypothesis needs to be tested for determining the impact of the availability of education on the crime rate. Then the hypothesis framed for the analysis would be:
- Null hypothesis H_{01}: Availability of education does not impact the crime rate.
- Alternate hypothesis H_{A1}: Availability of education impacts the crime rate.
- Null hypothesis H_{02}: Promotion of illegal activities does not impact the crime rate.
- Alternate hypothesis H_{A1}: Promotion of illegal activities impacts the crime rate.
Then, after running the linear regression test, 4 main tables will emerge in SPSS:
- Variable table
- Model summary
- ANOVA
- Coefficients of regression
Variable table
The first table in SPSS for regression results is shown below. It specifies the variables entered or removed from the model based on the method used for variable selection.
- Enter
- Remove
- Stepwise
- Backward Elimination
- Forward Selection
Variables Entered/ Removed^{a}
Model | Variables Entered | Variables Removed | Method | Model |
---|---|---|---|---|
1 | Availability of Education, Promotion of Illegal Activities^{b} | Enter | 1 |
a. Dependent Variable: Crime Rate b. All requested variables entered.
There is no need to mention or interpret this table anywhere in the analysis. It is generally unimportant since we already know the variables.
Model summary
The second table generated in a linear regression test in SPSS is Model Summary. It provides detail about the characteristics of the model. In the present case, promotion of illegal activities, crime rate and education were the main variables considered. The model summary table looks like below.
Model summary
Model | R | R-square | Adjusted R-square | Std. Error of the Estimate |
---|---|---|---|---|
1 | .713a | .509 | .501 | .60301 |
a. Predictors: (Constant), Availability of Education, Promotion of Illegal Activities
Elements of this table relevant for interpreting the results:
- R-value represents the correlation between the dependent and independent variable. A value greater than 0.4 is taken for further analysis. In this case, the value is .713, which is good.
- R-square shows the total variation for the dependent variable that could be explained by the independent variables. A value greater than 0.5 shows that the model is effective enough to determine the relationship. In this case, the value is .509, which is good.
- Adjusted R-square shows the generalization of the results i.e. the variation of the sample results from the population in multiple regression. It is required to have a difference between R-square and Adjusted R-square minimum. In this case, the value is .501, which is not far off from .509, so it is good.
Therefore, the model summary table is satisfactory to proceed with the next step. However, if the values were unsatisfactory, then there is a need for adjusting the data until the desired results are obtained.
ANOVA table
This is the third table in a regression test in SPSS. It determines whether the model is significant enough to determine the outcome. It looks like below.
ANOVA^{a}
Model | Sum of Squares | df | Mean Square | F | Sig. | |
---|---|---|---|---|---|---|
1 | Regression | 97.860 | 2 | 24.465 | 67.283 | .000^{b} |
Residual | 94.540 | 262 | .364 | |||
Total | 192.400 | 264 |
a. Dependent Variable: Crime Rate Predictors: (Constant), Availability of Education, Promotion of Illegal Activities
Elements of this table relevant for interpreting the results are:
- P-value/ Sig value: Generally, 95% confidence interval or 5% level of the significance level is chosen for the study. Thus the p-value should be less than 0.05. In the above table, it is .000. Therefore, the result is significant.
- F-ratio: It represents an improvement in the prediction of the variable by fitting the model after considering the inaccuracy present in the model. A value is greater than 1 for F-ratio yield efficient model. In the above table, the value is 67.2, which is good.
These results estimate that as the p-value of the ANOVA table is below the tolerable significance level, thus there is a possibility of rejecting the null hypothesis in further analysis.
Coefficient table
Below table shows the strength of the relationship i.e. the significance of the variable in the model and magnitude with which it impacts the dependent variable. This analysis helps in performing the hypothesis testing for a study.
Coefficients^{a}
Unstandardized Coefficients | Standardized Coefficients | |||||
---|---|---|---|---|---|---|
Model | B | Std. Error | Beta | t | Sig. | |
1 | (Constant) | .486 | .148 | 3.278 | .001 | |
Availability of Education | -.178 | .105 | -.198 | 1.705 | .089 | |
Promotion of Illegal Activities | .464 | .084 | .441 | 5.552 | .000 |
Only one value is important in interpretation: Sig. value. The value should be below the tolerable level of significance for the study i.e. below 0.05 for 95% confidence interval in this study. Based on the significant value the null hypothesis is rejected or not rejected.
If Sig. is < 0.05, the null hypothesis is rejected. If Sig. is > 0.05, then the null hypothesis is not rejected. If a null hypothesis is rejected, it means there is an impact. However, if a null hypothesis is not rejected, it means there is no impact.
In this case, the interpretation will be as follows.
Coefficients table
Independent Variable | Sig value | Hypothesis Testing Result at 95% confidence interval | Interpretation |
---|---|---|---|
Availability of Education | 0.089 | Null Hypothesis not rejected (0.089 > 0.05) | No significant change in crime rate due to availability of Education. This is because of the Sig. value is 0.08, which is more than the acceptable limit of 0.05. |
Promotion of Illegal Activities | 0.000 | Null Hypothesis Rejected (0.000 < 0.05) | The significant change in crime rate due to the promotion of illegal activities, because of the Sig. value is 0.000, which is less than the acceptable value of 0.05. With a 1% increase in the promotion of illegal activities, the crime rate will increase by 0.464% (B value). |
Therefore, the analysis suggests that the promotion of illegal activities has a significant positive relationship with the crime rate.
Lastly, the findings must always be supported by secondary studies who have found similar patterns.
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