What Is OLS? How to Read and Evaluate Linear Regression

What Is OLS

OLS stands for Ordinary Least Squares. In quantitative research, OLS is used to estimate the relationship between one dependent variable and one or more independent variables in a linear regression model. The method is commonly used when you want to estimate the direction and size of relationships after entering several predictors in the same model.

You can represent the basic model as follows:

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. OLS finds the coefficients that minimize the sum of squared residuals between the observed values and the predicted values. Each coefficient is estimated while the other variables in the equation remain part of the model.

More specifically, the model produces a predicted value of Y for each respondent. The distance between the actual Y and the predicted Y is called the residual. OLS selects the set of coefficients that makes the sum of the squared residuals as small as possible. Squaring the residuals prevents positive and negative residuals from canceling each other out during estimation. This gives you a single criterion for comparing possible sets of coefficients.

When you run Linear Regression in SPSS, the software uses OLS to estimate the coefficients in the model. OLS is therefore not the name of a separate results table in SPSS. You read it through tables such as Model Summary, ANOVA, and Coefficients, each of which answers a different part of the regression question.

If your topic includes several latent variables measured by multiple items, OLS is usually run after you have processed the scales. You can also read what a scale is to distinguish scales, items, and composite variables before creating the variables that enter the regression. At this stage, you should already know how each composite score was calculated and which items were retained.

Why OLS Matters in Quantitative Research

OLS helps you answer this question: when an independent variable changes, in what direction and by how much does the dependent variable change, while the other independent variables remain in the model. This is the difference between simply examining correlations and estimating a multiple regression model. A correlation describes a pairwise association, whereas a multiple regression coefficient is interpreted in the presence of the other predictors.

For example, suppose you are studying online purchase intention. The independent variables might be perceived usefulness, trust, and information quality. The dependent variable is purchase intention. OLS allows you to see which variables have positive or negative coefficients, whether those coefficients are statistically significant, and how much of the variation in purchase intention the model explains. You can then compare the estimated pattern with the hypotheses stated in your thesis.

In practice, you usually need to read four groups of information:

• R Square shows the proportion of variation in the dependent variable explained by the independent variables in the research sample.
• ANOVA and the Sig. value show whether the overall model is statistically significant.
• B in the Coefficients table is the unstandardized regression coefficient, which is used to write the regression equation in the original units.
• Beta is the standardized regression coefficient, which is commonly used to compare the relative strength of the independent variables.

You also need to distinguish OLS from analyses involving moderators or mediators. When testing a moderator, you usually add an interaction variable to the model. When testing a mediator, you assess the indirect effect as well. These two situations are explained in more detail in moderating and mediator. The output may still contain regression equations, but the hypotheses and interpretation are different from those of a basic direct-effect model.

OLS is appropriate when the dependent variable is modeled as continuous and the relationships between the variables can be reasonably represented by straight lines. If the dependent variable is binary, such as whether a person buys or does not buy, logistic regression may be more appropriate. If the dependent variable is ordinal, a count, or a special type of proportion, you need to consider a model suited to that data structure rather than forcing it into linear regression. The type of dependent variable should therefore be decided before you interpret the SPSS output.

If you use Likert survey data, many theses calculate the mean score for each scale and then enter the composite scores into OLS. You need to describe this process clearly in the methods chapter, including how the score was calculated, how many items remained, and why each item was retained or removed. A clean regression table does not compensate for an unclear variable-construction process. The reader should be able to trace every variable in the regression back to the questionnaire and the data-processing decisions.

What OLS Value Is Acceptable

There is no single number called an acceptable OLS result. You need to evaluate the model as a whole, each coefficient, and the regression assumptions. A model with a high R Square still needs explanation if it has serious multicollinearity or unsuitable residuals. Looking at one attractive number can hide a problem elsewhere in the output.

The thresholds below are commonly used reference points in theses. Each row includes its source so that you do not separate a number from the methods literature.

The p-value < 0.05 reference point needs to be understood together with your research hypotheses and the significance level selected in the methods chapter. Do not look at one variable with a small p-value and conclude that the entire model is good. Sig. in the ANOVA table answers the question about the overall model, while Sig. in the Coefficients table answers the question about each coefficient. These are related results, but they are not interchangeable.

For R Square, there is no common acceptable level for every topic. Human behavior is influenced by many factors, so R² needs to be considered alongside the research context, the number of variables, and the theoretical foundation. You should report adjusted R² as well because this index takes the number of independent variables in the model into account. Explain what the value means for your sample instead of presenting it as a universal quality score.

Sample size also needs to be checked before you run the analysis. With m independent variables, the reference formula n from 50 + 8m from (Tabachnick and Fidell, 2013) is only a methodological reference point. You also need to consider the number of items, the proportion of invalid questionnaires, and additional analyses such as a mediator or moderator. The usable sample after data cleaning is the number that matters for the analysis you actually report.

How to Read OLS Output

Open SPSS and select Analyze > Regression > Linear. Move the dependent variable into Dependent and the independent variables into Independent(s). In Statistics, select Estimates, Model fit, Collinearity diagnostics, and Durbin-Watson. If you want to check residuals, also use the chart options in Plots. Check the selected options before clicking OK so that the output contains the diagnostics you intend to report.

In Plots, you can place *ZPRED on the X-axis and *ZRESID on the Y-axis to examine standardized residuals against standardized predicted values. You can also select a normal probability plot to see whether the residuals deviate substantially from the expected pattern. These charts do not make a model acceptable simply because it looks good visually, but they help you identify signs that require further checking. Interpret the plots together with the numerical diagnostics and the logic of your model.

The table below is illustrative output, not the result of a real study. The column names are kept in the form SPSS commonly displays so that you can compare them with the file currently open.

Model Summary

R Square = 0.468 means that the three independent variables in the example explain about 46.8% of the variation in the dependent variable in the sample. Adjusted R Square = 0.452 is the figure to prioritize when the model contains several variables. Durbin-Watson = 1.842 falls within the reference range from 1 to 3. These figures describe the illustrative model only, so do not copy them into your thesis as if they came from your file.

ANOVA

In this example, Sig. = .000 has been rounded by SPSS. When writing the result, report p < 0.001, not p equal to 0. The overall model is statistically significant at the 5% level. This ANOVA result does not tell you which variable is significant, so you need to continue with the Coefficients table. The degrees of freedom and F statistic should also be copied from the output when you write the model test.

Coefficients

In the example, all three variables have positive B coefficients and Sig. values below 0.05. If the variables are measured in the same direction, you can interpret this as a positive relationship with the dependent variable. The Beta = 0.341 for perceived usefulness is larger than the other two Beta values, so it has the stronger relative effect in the illustrative model. This comparison is relative to the predictors included here and is not a percentage contribution to the dependent variable.

The unstandardized regression equation in the example is: Y = 0.842 + 0.318X1 + 0.241X2 + 0.176X3. When interpreting B = 0.318, keep the original measurement units. When perceived usefulness increases by one unit, the predicted value of Y increases by an average of 0.318 units, while the other variables remain constant. This is an interpretation of the model, not a promise of a causal relationship beyond the data. The constant is interpreted when all predictors equal zero, if that value has a meaningful interpretation for your measurement scale.

You need to read VIF to check multicollinearity. All illustrative VIF values are below 5. This result is not enough to prove that every assumption is perfect, but it does not show a VIF value above the reference point being used. Report the actual VIF values for your own predictors rather than reporting only that the criterion was met.

How to write this in your thesis: “The regression results show that the model is statistically significant, F([df1], [df2]) = [F value], p [< or =] [p-value]. The model explains [Adjusted R²]% of the variation in [dependent variable]. [Variable name] has a [positive/negative] effect on [dependent variable], with β = [Beta], p = [p-value].” Replace everything in square brackets with the actual values from your file. If a result is not statistically significant, write that result directly rather than changing the wording to make the hypothesis appear supported.

What to Do When OLS Does Not Meet the Criteria

Work from the data toward the model instead of deleting variables simply to make the results table look better. Before each new run, save the output or syntax and record exactly what you changed. This history helps you answer when your supervisor asks why a variable disappeared from the final model. OLS rarely produces a perfect table on the first run, and a documented revision process is easier to defend than unexplained trial and error.

Check the Data and Variable Coding

Review missing values, scale coding, and reverse-coded items. A reverse-coded item that has not been recoded can change the sign of a correlation and a regression coefficient. Check frequency tables, min, max, and mean before running the model again. Values outside the expected Likert range are often a sign that you need to inspect the original data. Confirm that the numerical codes in SPSS match the coding described in your questionnaire.

If you have unusual observations, check outliers. You need to determine whether an observation is a data-entry error, an invalid response, or a real but different case. Deleting a data row simply because it makes the p-value worse is difficult to defend to your supervisor. If you remove an observation, record the criterion, the number of rows removed, and the results before and after the procedure. The reason for exclusion should be connected to data quality or a stated diagnostic rule.

Check Multicollinearity

If VIF is high, examine the correlation matrix between the independent variables and review their conceptual content. Two scales that almost measure the same concept can create multicollinearity. You may consider removing the variable with the weaker theoretical basis, combining concepts only when the theoretical model allows it, or collecting new data if the issue comes from the questionnaire design.

Do not delete an independent variable simply because its coefficient is not statistically significant. A control variable or a variable with a theoretical role may still need to remain in the model. The final decision must be based on the research model, measurement quality, and the analysis plan you stated earlier. A change made after seeing the p-value should be recorded and explained.

Review the Assumptions and Model Form

Check linearity, residuals, and constant variance using appropriate plots. If the relationship between X and Y is curved, a simple linear model may not describe the data well. In that situation, reconsider the research model rather than transforming the data arbitrarily. The transformation or alternative model must have a statistical and theoretical reason.

If the p-value of a coefficient is greater than 0.05, report that the relationship is not statistically significant and compare the result with the hypothesis. Do not change the significance level after seeing the result. Removing a variable should be based on theory, measurement quality, and the criteria stated in advance. A nonsignificant result is still a result that belongs in the reporting record.

Distinguishing OLS from SEM and Easily Confused Indices

OLS and SEM can both be used to study relationships between variables, but their scope is different. OLS usually places observed or composite variables directly into a regression equation. SEM can evaluate the measurement model, latent variables, and structural model at the same time. This difference affects which tables and indices belong in the results chapter.

In CB-SEM, indices such as CFI, TLI, RMSEA, and SRMR are used to assess model fit according to (Hu and Bentler, 1999). These indices should not be placed in an article about OLS or assigned to SmartPLS results. With PLS-SEM, you usually read outer loading, CR, AVE, HTMT, VIF, R², f², and Q². Choose the reporting criteria according to the method you actually used.

OLS is appropriate when the objective is to estimate one or several equations with a continuous dependent variable. SEM is more suitable when the research question requires the simultaneous assessment of latent variables, observed variables, and multiple structural relationships. SEM is not automatically better than OLS. A more complex model also requires you to explain more layers of results during the defense. The method should follow the research question rather than the number of indices produced by the software.

OLS also differs from mediation and moderation testing. A Mediator answers how one variable transmits an effect. A Moderator answers whether a relationship changes according to the level of another variable. You can read moderator to distinguish a moderator from a mediator before creating an equation with an interaction variable. The distinction affects both the equation you estimate and the way you report the hypothesis.

Another practical difference is that OLS is easy to implement in SPSS and works well with observed regression models. SEM requires you to specify the measurement model, structural model, and procedures for assessing convergent validity and discriminant validity. You should therefore not choose SEM simply because you want more indices. You can also refer to the articles under Statistics to place regression within a broader quantitative analysis process.

Common Errors

The first error is calling R Square the percentage effect of each variable. R² is the explanatory level of the entire model, not the percentage effect of one variable. To compare relative effects, look at Standardized Beta, while also considering the scales and the model context. Beta does not mean that a predictor explains exactly that percentage of the dependent variable.

The second error is writing Sig. = 0.000. SPSS displays three decimal places, and this value should be understood as p less than 0.001. The third error is concluding that there is a causal relationship from regression using cross-sectional survey data alone. Use wording that fits the research design, such as “is associated with” or “has an effect according to the hypothesized model,” when the design and theory allow it.

Another error is ignoring control variables, failing to report sample size, or running several models while keeping only the model with the best-looking results. Save the syntax, the results from each round, and the reason for removing or retaining variables. If you use a tool other than SPSS, such as R, JASP, or AMOS, state the software and procedure clearly. Paying for an SPSS service may save time in the short term, but it increases the risk that you cannot explain the output table during your defense. You also lose the analysis trail if the service does not give you the syntax, settings, and data-processing record.

A further error is mixing PLS-SEM and CB-SEM criteria into OLS. For example, outer loading, AVE, and HTMT belong to measurement model assessment in SEM. They are not criteria for deciding whether an OLS regression table is acceptable. Make a list of the indices you need to report before running the analysis so that you do not place irrelevant numbers in Chapter 4.

Frequently asked questions

What is OLS in linear regression?

OLS is the Ordinary Least Squares method used to estimate coefficients in a linear regression model. It selects the coefficients that minimize the sum of squared residuals between actual and predicted values. The coefficients are then interpreted through the SPSS output tables and the assumptions checked for the model.

Is OLS a test in SPSS?

OLS is the estimation method behind linear regression, not the name of a separate test in the SPSS menu. When you select Analyze > Regression > Linear, SPSS produces the Model Summary, ANOVA, and Coefficients tables for evaluating the OLS model. You should read those tables together rather than treating one table as the complete result.

What OLS value is acceptable?

There is no single acceptable OLS threshold. You need to examine the p-value of the model and coefficients, adjusted R², VIF, Durbin-Watson, residuals, and the fit between the model and the theory. A VIF below 5 is cited in (Hair et al., 2019), while Durbin-Watson from 1 to 3 is used as a reference according to (Field, 2013). The final assessment should also explain the sample and the measurement process.

Why is OLS regression not statistically significant?

The true relationship may be weak, the sample size may be insufficient, the scale may have problems, the independent variables may overlap, or the model may omit an important variable. Check the data, scale reliability, correlations, VIF, and assumptions before deciding whether to adjust the model. Keep a record of the checks so that any later model change can be explained.

If the overall model is significant but one individual coefficient is not, the two results do not conflict. ANOVA evaluates the full set of independent variables, while the Coefficients table evaluates each variable while the other variables are included. A significant model therefore does not require every individual predictor to be significant.

How is OLS different from SEM?

OLS usually estimates relationships between observed or composite variables. SEM allows you to assess the measurement model and structural model simultaneously, especially when the topic includes latent variables. The choice between OLS and SEM should be based on the research question, data type, and theoretical model. It should also match the software and reporting procedure described in your methods chapter.

Can OLS be used to test a mediator or moderator?

You can use OLS regression equations to test some mediator or moderator models in SPSS, but the interpretation and number of required equations differ from a simple regression. For an indirect effect, pay attention to the bootstrap confidence interval rather than looking only at the p-value of one equation. A moderation model requires attention to the interaction term and its interpretation at different levels of the moderator.

Reopen the .sav file, identify the dependent and independent variables, then run Analyze > Regression > Linear again with Model fit, Collinearity diagnostics, and Durbin-Watson selected. Record the results according to the output tables. If you need to run the analysis on your own data file, M4 analysis by DoThesis supports SPSS and SmartPLS workflows without replacing real data with sample numbers.