What Is Regression? How to Read Regression Results in SPSS

What is regression

Regression is a method for examining the relationship between a dependent variable and one or more independent variables. In a quantitative thesis, you often use regression to answer questions such as whether service quality affects satisfaction, which factors predict purchase intention, or how strongly each factor affects the outcome variable.

For linear regression, the basic model is:

Y = β0 + β1X1 + β2X2 + ... + βkXk + ε

Here, Y is the dependent variable, X1 through Xk are the independent variables, β0 is the constant, β1 through βk are the regression coefficients, and ε is the error term. The sign of a coefficient shows the direction of the effect. A positive coefficient indicates that Y tends to increase as X increases, while a negative coefficient indicates an inverse relationship.

You need to distinguish regression from correlation. Correlation shows the extent to which two variables move together, but it does not give you a prediction model or test the role of several independent variables at the same time. Regression allows you to enter multiple variables into one model, control for the effects of the other variables, and test each research hypothesis.

If you are reviewing the full analysis process, you can also open the Statistics section to compare regression with other tests.

Why regression matters in quantitative research

In a quantitative study, regression usually comes after you have cleaned the data, assessed scale reliability, and created representative variables for the constructs. If your model includes Reliability, Price, Service Quality, and Satisfaction, you can calculate the mean score for each scale and then enter the representative variables into the regression model.

Regression helps you answer four main questions. First, is the overall model statistically significant. Second, how much of the variation in the dependent variable does the model explain. Third, which independent variables have significant effects. Fourth, is each effect positive or negative, and how strong is it relative to the other effects.

In SPSS, the first three tables you need to read are Model Summary, ANOVA, and Coefficients. Model Summary usually contains R, R Square, Adjusted R Square, and Std. Error of the Estimate. ANOVA reports the F test for the overall model. Coefficients reports B, Std. Error, Beta, t, and Sig. for each variable.

Regression can also be used in models with a mediator or moderator. The hypothesis structure and interpretation are different from those used in a simple regression model. If your study includes a mediator, see the guide to mediator. For a moderator, you need to understand the interaction between the independent variable and the moderator instead of looking at one regression coefficient in isolation.

Linear regression is appropriate when the dependent variable is a continuous numerical variable, such as a satisfaction score, purchase intention, or performance. Logistic regression is appropriate when the outcome is a binary group, such as purchased or did not purchase, or passed or did not pass. Choosing the wrong type of regression can lead to questions about your method and conclusions even if the software still produces output.

What counts as an acceptable regression result

There is no single number that determines whether every regression model is acceptable. You need to consider the significance of the model, the significance of each coefficient, the explanatory power, and the assumptions at the same time. The table below lists common reference points in theses, together with their sources so that you do not report thresholds without support.

These thresholds do not replace an assessment of the research design, theory, and data quality. For example, a variable with Sig. below 0.05 but a very small coefficient still needs a cautious interpretation in terms of practical importance. Conversely, a coefficient that is not statistically significant should not be retained only because its sign matches your expectation.

If you run regression after aggregating the items, you also need to check the scale quality first. Cronbach's Alpha of 0.7 or above is commonly considered acceptable (Nunnally, 1978), while a Corrected Item-Total Correlation of 0.3 or above is a commonly used reference point (Nunnally and Bernstein, 1994). You can also see what a scale is before running the model.

How to read regression output

Suppose you run a linear regression with HL as the dependent variable and CLDV, GC, and TC as the three independent variables. The numbers below are illustrative output, not results from a real study.

Read Model Summary first to see how much the model explains. In the example, Adjusted R Square = 0.478 means that the model explains about 47.8% of the variation in HL after adjustment. The remaining variation is related to factors not included in the model and to error, but you should not describe it as a specific cause unless you have tested that cause.

Next, read ANOVA. If Sig. = 0.000, write p < 0.001 in your thesis instead of writing p = 0.000, because a p-value should not, in principle, be reported as exactly 0. This result indicates that the overall model is statistically significant in the illustrative output.

Finally, read the Coefficients table. Standardized Beta is used to compare the relative effects of the independent variables because the variables have been placed on the same standardized scale. Unstandardized B is more appropriate when you want to write the regression equation in the original units. The Sig. column determines whether the effect of that variable has statistical support.

For the example above, the standardized equation can be presented as: HL = 0.421CLDV + 0.187GC + 0.064TC. In your interpretation, conclude only that CLDV and GC have significant positive effects in the example. TC has a positive coefficient, but p = 0.418, so there is not enough evidence to conclude that the hypothesis concerning TC is supported.

What to do when the regression result is not acceptable

If ANOVA Sig. is above 0.05, first check whether you selected the correct dependent and independent variables. Then check the sample size, variable coding, missing data, and data-entry errors. Do not delete a variable simply to make Sig. smaller, because that decision has no methodological basis.

If a variable has Sig. above 0.05, whether you retain or remove it should depend on the theoretical model and the research plan. You can report that the variable is not statistically significant, discuss why the research context may differ from your expectation, or recheck the scale if there is a reasonable basis for doing so. Running many versions until one produces attractive results creates a serious risk when the committee asks about your procedure.

If VIF is high, examine the correlations among the independent variables and the content of the items. Two scales may be measuring concepts that are too similar. You also need to check whether reverse-coded items were coded correctly. Removing an item only because VIF is high requires a reason, and you should record the model version before and after the change.

If you identify an outlier, examine the original value, the questionnaire response, and the data-collection context. Do not delete a data row simply because it changes the p-value. You can read more about outliers to check for unusual observations before deciding what to do.

If the residuals seriously violate linearity, homoscedasticity, or distributional assumptions, report the issue and consider an alternative appropriate for the type of variable. You may need to transform the data, use a different estimation method, or discuss the issue with your supervisor. Software cannot turn an invalid research design into a valid model.

Distinguishing regression, correlation, and logistic regression

Correlation usually answers the question of how strongly two variables are related. Linear regression answers how one or more independent variables explain a dependent variable after the other variables have been considered. Therefore, a correlation coefficient and a regression coefficient are not two names for the same statistic.

Linear regression is used for a continuous dependent variable. For example, an average satisfaction score from a Likert scale can be used as a dependent variable in many business studies, provided that the data treatment and assumptions are explained clearly. Logistic regression is used when the dependent variable is a group, usually a binary group. The interpretation of coefficients, odds, and probabilities is different from that of linear regression.

Regression also differs from mediation and moderation analysis. A mediator explains the mechanism of an effect, while a moderator changes the strength or direction of a relationship. If you are testing a moderator, see the guide to moderator and do not interpret an interaction coefficient as an ordinary direct effect.

You can also read about moderating if your model hypothesizes that one variable changes the relationship between X and Y. This part needs to be designed through the hypothesis, the method for creating the interaction variable, and the way the output will be reported. It should not be inferred from one p-value alone.

Common mistakes

The first mistake is looking only at R Square and concluding that the model is good. A high R Square does not automatically show that the model is correct, because you still need to read ANOVA, Coefficients, VIF, and the residual diagnostics.

The second mistake is writing Sig. = 0.000 in the thesis. Report it as p < 0.001. The third mistake is using an unstandardized Beta to compare the relative effects of the variables. When the purpose is relative comparison, state clearly that you are using Standardized Beta.

The fourth mistake is making a causal conclusion from cross-sectional survey data alone. From regression, you can say that an independent variable has an effect or predictive relationship according to the research model, but you should be cautious about claiming an absolute cause.

The fifth mistake is renaming variables in the output without keeping a codebook. Each variable needs a clear name, measurement content, and calculation method. Keep the syntax file, original data file, and every processed version so that you can explain the analysis when your supervisor asks.

Frequently asked questions

What is regression in SPSS?

In SPSS, regression is a procedure for examining the relationship between one dependent variable and independent variables. For linear regression, you usually go to Analyze > Regression > Linear, place the outcome variable in Dependent, and place the explanatory variables in Independent(s).

When should you use linear regression?

Use linear regression when the dependent variable is treated as a continuous numerical variable and the research question focuses on the level, direction, or predictive ability of the independent variables. Before running it, check how the variable was measured and assess the model assumptions.

What counts as an acceptable regression result?

You cannot decide this using one threshold alone. Check whether the model is significant through ANOVA, whether each variable has an appropriate Sig., the value of Adjusted R Square, VIF, Durbin-Watson, and the residual diagnostics. Reference points must be connected to sources, such as VIF below 5 according to (Hair et al., 2019) and Durbin-Watson from 1 to 3 according to (Field, 2013).

Why is my regression not statistically significant?

The model may not fit the data, the sample size may be insufficient, the independent variables may not explain the dependent variable in this context, or the scale and coding may have problems. Check the data and assumptions first, then report the non-significant result honestly instead of automatically deleting variables.

Do you need to run regression after Cronbach's Alpha and EFA?

Usually, when the independent and dependent constructs are measured with multiple items, you need to assess reliability and scale structure before creating representative variables for regression. The exact sequence depends on the research model, but you need to explain it clearly in the methods chapter.

Can regression prove causation?

Regression shows the level of association or predictive ability supported by your model and data. With a cross-sectional survey, avoid overly strong wording such as proving an absolute cause unless the research design and theoretical reasoning support that conclusion.

How to write this in your thesis

Open your SPSS file, check the order of Model Summary, ANOVA, and Coefficients, then record the statistics and assumptions before writing the interpretation. If you need to run regression on your own .sav or .csv file, you can use M4 data analysis before submitting your thesis.