How to Run Linear Regression in SPSS and Interpret the Results

When to use linear regression

Use linear regression when you want to test whether one or more independent variables explain variation in a dependent variable. For example, your study may test the effects of service quality, price and convenience on satisfaction. Satisfaction is the dependent variable, while the other three factors are the independent variables.

In essence, linear regression estimates an equation of the form Y = β0 + β1X1 + β2X2 + ... + ε. Y is the dependent variable, X represents the independent variables, β represents the regression coefficients and ε is the error term. When you run linear regression using OLS, SPSS estimates the coefficients so that the difference between observed and predicted values is minimized.

Use this analysis when your hypothesis has the form “X affects Y” or “X predicts Y”, the dependent variable is quantitative, and the observations are independent of one another. If the dependent variable has only two outcomes, such as yes or no or purchase or no purchase, consider logistic regression instead of linear regression.

If you are unsure about the equation, variables or the meaning of each coefficient, see linear regression model and linear regression equation. These concepts are closely related, but they do not replace the testing section of the SPSS output.

Prepare the data before running the analysis

Before opening the Linear Regression dialog box, check your .sav or .csv file. Errors at this stage often make the results difficult to interpret, even when SPSS still produces the tables.

First, identify the correct level of the data. Each row should represent one respondent or one unit of observation. Each column should represent one variable. Variables used in the regression should be coded numerically. If a construct is measured with several items, you will usually calculate a representative score by averaging the items after the scale has been assessed. For example, HL1, HL2 and HL3 can be combined into the HL variable through Transform > Compute Variable.

Check Missing Values and special codes such as 99, 999 or -1. If these codes are still treated as valid values, the mean and regression coefficients will be distorted. Go to Variable View to check the data type, variable label, coded values and the way SPSS handles missing data. You should also check rows with too much missing information, respondents who selected the same answer throughout the questionnaire, and cases outside the target population.

If the questionnaire contains reverse-worded items, reverse-code them before calculating the scale score. For a Likert scale from 1 to 5, the usual formula is new score equals 6 minus old score. Record which variables were reversed, which formula you used and when you performed the transformation. Do not edit the original column directly before creating a copy of the data.

Linear regression can use one independent variable or several independent variables. Simple regression has one X. Multiple regression has two or more X variables. With multiple regression, pay particular attention to multicollinearity, because highly similar independent variables can make the coefficients change substantially and make it difficult to draw a separate conclusion for each hypothesis.

Finally, define the theoretical model and expected direction of effects in advance. Looking at the p-value first and then writing the hypothesis increases the risk of interpreting the result backwards. Build the model and hypotheses before running the analysis.

Steps for running linear regression in SPSS

Step 1: Open the Linear Regression dialog box

In SPSS, select Analyze > Regression > Linear. The Linear Regression dialog box opens. Move the dependent variable to Dependent and the independent variables to Independent(s).

If your model has only one group of independent variables, keep Method: Enter. This method enters all variables into the model at the same time and is appropriate when the variables have been identified from the theoretical basis. Stepwise, Forward and Backward methods can produce models that depend heavily on the sample data, so do not use them simply to obtain an attractive results table.

Step 2: Select Statistics and check multicollinearity

Click Statistics. Select Estimates, Model fit, Confidence intervals, Descriptives and Collinearity diagnostics. If you want to assess the additional contribution of a group of variables, you can select R squared change, but the model must have been designed by blocks in advance.

Click Continue to return to the main dialog box. The Collinearity diagnostics option allows SPSS to display VIF and Tolerance in the Coefficients table. You need both pieces of information when running multiple regression.

Step 3: Save predicted values and residuals if needed

Click Save if you need to save Predicted Values or Residuals for assumption checking. For a basic procedure, you can select Unstandardized under Predicted Values and Standardized under Residuals. SPSS creates additional variables in Data View.

Do not save every available type of value if you do not yet know how you will use it. Extra columns can make the file difficult to track. If you save residuals, record which model they belong to, especially when you run several versions of the regression.

Step 4: Check the residual plots

Click Plots. Move *ZPRED to the X box and *ZRESID to the Y box, then select Normal probability plot. The Scatterplot helps you see whether the residuals are distributed relatively randomly around the 0 line. The Normal P-P Plot helps you assess whether the residual distribution deviates clearly from the expected line.

Click Continue, then select OK to run the analysis. If you want to rerun it after removing a variable, save the previous output and record why the model was changed. EFA or regression rarely produces exactly the structure you expect on the first run. Each variable removal needs a methodological reason, not simply the fact that the variable made the p-value look worse.

Step 5: Save and name the output

In the Output Viewer window, select File > Save As to save the .spv file. Name it according to the model, such as Hoi_quy_mo_hinh_1.spv. You should also save the syntax by clicking Paste instead of OK in the dialog box, then run the syntax with the Run button.

Syntax allows you to reproduce the analysis when new data become available or when you need to explain the procedure to your supervisor. A command may look like REGRESSION /DEPENDENT HL /METHOD=ENTER CL DV GC.. The variable names in the syntax must match Variable View in the file.

Reading the output

SPSS usually returns the main tables Variables Entered/Removed, Model Summary, ANOVA, Coefficients and several diagnostic tables. Read them in order, starting with overall model fit and then moving to each hypothesis.

The Model Summary table reports R, R Square, Adjusted R Square and Std. Error of the Estimate. R Square indicates the proportion of variation in Y explained by the X variables in the sample. Adjusted R Square adjusts for the number of variables and sample size, so it is often more suitable when comparing models with different numbers of variables.

The ANOVA table tests the overall fit of the model. The F and Sig. columns show whether the model containing the independent variables explains Y better than a model containing only the constant. If Sig. is below the significance level you selected, the overall model is statistically significant.

The Coefficients table is where you test each hypothesis. B is the unstandardized coefficient, which you use to write the regression equation. Beta is the standardized coefficient, which helps you compare the relative effects of variables when they use different scales. The t and Sig. columns are used to test the coefficient. VIF and Tolerance are used to assess multicollinearity.

The table below is illustrative output, not the result of an actual study. Assume that HL is satisfaction, CL is service quality, GC is price and TT is convenience.

Using the B values, the illustrative equation can be written as HL = 0,765 + 0,421CL + 0,176TT + 0,093GC. However, include a variable in your interpretation of the equation only after considering its statistical significance and direction of effect. A coefficient that is not statistically significant should not be described as a confirmed effect.

You can also see a solved linear regression exercise to practise connecting Model Summary, ANOVA and Coefficients into a complete conclusion.

Evaluation criteria

Do not combine every number in the output into one conclusion. Each indicator answers a different question. The table below uses only thresholds with a clear source.

For the p-value, first identify the sign of B or Beta. If Sig. is below 0,05 and the coefficient is positive, the data support a positive effect as hypothesized. If Sig. is below 0,05 but the coefficient is negative, the effect is significant but runs opposite to the expected direction. If Sig. is above 0,05, report insufficient statistical evidence to support the effect rather than writing that the variable has no effect at all.

Consider VIF together with Tolerance, correlations among the variables and the theory. A low VIF does not automatically prove that the model is good. If VIF is high, check for overlapping item content, the way composite scores were calculated and whether two constructs are measuring the same content.

Durbin-Watson is mainly useful when you need to consider residual autocorrelation in an appropriate context. With cross-sectional survey data, you still need to report assumption checks according to the research design. Do not turn one threshold into evidence of the model's overall quality.

How to write this in your thesis

The results section should follow this order: describe the model, test the overall model, test each hypothesis and state the conclusion. You do not need to copy the entire SPSS output into Chapter 4. Present a standardized table, retain the columns that matter and explain them in the text immediately below the table.

You can adapt this paragraph directly: “The linear regression results show that the model containing [number of independent variables] variables explaining [dependent variable name] is statistically significant, F([df1], [df2]) = [F value], p = [p-value]. The Adjusted R Square is [value], meaning that the model explains approximately [x]% of the variation in [Y] in the study sample. Among the independent variables, [X1] has a [positive/negative] effect on [Y], with β = [Beta], p = [p-value]. Therefore, hypothesis [H1] is [accepted/supported].”

If a hypothesis is not supported, you can write: “The coefficient of [X2] is [positive/negative] but is not statistically significant at the 5% level, β = [Beta], p = [p-value]. Therefore, the study does not have sufficient evidence to support hypothesis [H2] in the survey sample.” This wording separates the sign of the coefficient from the testing conclusion and prevents you from calling a nonsignificant result an effect.

When reporting the equation, use the unstandardized B. When comparing the effects of variables, use standardized Beta and state clearly that this is a comparison within the model, not a percentage change in the dependent variable. To present the methodological basis, you can place regression within the quantitative analysis process described in SPSS references such as (Hoàng Trọng and Chu Nguyễn Mộng Ngọc, 2008) and (Nguyễn Đình Thọ, 2011).

Common mistakes when running linear regression

Entering individual items into the regression instead of representative scores. If the theoretical model contains constructs such as service quality or satisfaction, you usually need to assess the scale first and then calculate a representative variable according to the planned procedure. Entering every item at once can make the model difficult to interpret and increase correlations among the variables.

Choosing Stepwise simply to retain variables with small p-values. This selection method can make the model heavily dependent on the current sample. If theory identifies the group of variables to be tested, Method Enter is usually easier to justify.

Looking only at R Square. A high R Square does not ensure that every hypothesis is significant, and it does not replace checking residuals, VIF and the signs of the coefficients. Read Model Summary, ANOVA and Coefficients together.

Deleting variables until the model looks good. Removing a variable may be necessary when it violates a predefined criterion or creates a clear diagnostic problem. You must record the reason, model version and effect of the change. Do not delete a variable only because the result does not support your expectation.

Confusing linear regression with correlation. Correlation describes the relationship between each pair of variables. Multiple regression examines the coefficient of one variable while the other variables are also included in the model. The two results can therefore differ.

Frequently asked questions

What is linear regression?

Linear regression estimates the relationship between a dependent variable and one or more independent variables using a linear equation. In a quantitative thesis, it is commonly used to test hypotheses in the form X affects Y.

Distinguish simple regression from multiple regression. Simple regression has one X variable, while multiple regression has several X variables and allows you to examine the separate effect of each X while the other variables remain in the model.

Which variable should I put in Dependent when running linear regression in SPSS?

The variable placed in Dependent is the dependent variable, usually the outcome side of the research model. The variables placed in Independent(s) are the factors hypothesized to explain or predict the dependent variable.

If the dependent variable is a construct measured with several items, create a representative score using the method specified in the methods chapter, such as the mean of the items that meet the requirements.

What value is considered acceptable in linear regression?

There is no fixed R Square that applies to every study. Assess the statistical significance of the model through the ANOVA table, the significance of each coefficient through the Coefficients table, VIF, residuals and consistency with the theory.

Common reference checks include VIF below 5 according to (Hair et al., 2019), Durbin-Watson from 1 to 3 according to (Field, 2013), and a sample size of at least 50 + 8m according to (Tabachnick and Fidell, 2013). These are sourced reference criteria, not an automatic certificate that a model is good.

What should I do when the regression Sig. is above 0.05?

If the Sig. value of a coefficient is above 0.05 at the 5% significance level, you do not have sufficient statistical evidence to support the hypothesis about that variable's effect. Check the coding, reverse-coded items, score calculation and sample size before drawing a conclusion.

If the data and procedure are correct, report the unsupported result. Do not change the method, change the hypothesis or remove the variable simply to reduce the p-value. You can discuss that the result did not match expectations in the context of the study sample.

How should I handle a high VIF?

First, check whether the independent variables overlap in content, were scored incorrectly or include both a composite variable and its component items. Review the correlation matrix and theoretical basis before deciding what to do.

Possible options include combining variables that genuinely belong to the same construct, removing a variable with a clear methodological justification or rebuilding the model. Record your choice and explain it to your supervisor. Do not remove a variable based on one run without considering the measurement content.

Do I need to check assumptions before writing the results?

Yes. Check linearity, residuals, multicollinearity and influential cases as appropriate for your research design. The scatterplot of ZPRED and ZRESID, the Normal P-P Plot and the indicators in Coefficients are practical starting points in SPSS.

If you identify a problem, investigate the data and measurement method before looking for a software-based fix. A model with many small p-values still requires careful explanation if it seriously violates its assumptions.

Open your data file, make a list of the dependent and independent variables, then run the model with Method Enter and save both the output and syntax before making changes. If you need to run regression on your own .sav or .csv file and turn the results into tables and a thesis chapter draft, you can use DoThesis M4 data analysis.