Step-by-Step Guide to Regression Analysis Using Stata

Regression analysis is one of the most widely used statistical techniques for examining relationships between variables. It enables a researcher to determine how one or more independent variables are associated with a dependent variable while controlling for other factors.

Stata provides powerful tools for conducting simple linear regression, multiple regression, logistic regression, panel-data regression, time-series regression, and many other econometric models.

This guide provides a practical step-by-step procedure for conducting regression analysis using Stata, from preparing the dataset to interpreting and reporting the final results.

1. Define the Research Problem

Before opening Stata, clearly identify:

• The dependent variable
• The independent variables
• The research objectives
• The research questions
• The hypotheses
• The expected relationships between variables

For example, a study may examine:

Title: Effect of Access to Credit on the Performance of Small Businesses

The variables could be:

• Dependent variable: Business performance
• Independent variable 1: Access to credit
• Independent variable 2: Business experience
• Independent variable 3: Education level
• Independent variable 4: Business size

The conceptual regression model could be expressed as:

Business Performance = β₀ + β₁Credit Access + β₂Experience + β₃Education + β₄Business Size + ε

The regression analysis is then used to estimate the coefficients and determine the statistical relationships between the variables.

2. Prepare the Dataset

Before importing data into Stata, ensure that the dataset is properly organized.

Each:

• Row should represent one observation/respondent.
• Column should represent one variable.

For example:

Variable names should preferably be short, meaningful, and without spaces.

Examples:

performance
credit
experience
education
business_size

3. Import Data into Stata

Stata can import data from Excel and CSV files.

Import Excel data

import excel "C:\data\researchdata.xlsx", firstrow clear

The firstrow option tells Stata that the first row contains variable names.

Import CSV data

import delimited "C:\data\researchdata.csv", clear

After importing the data, save it as a Stata dataset:

save "researchdata.dta", replace

4. Examine the Dataset

Start by examining the structure of the dataset.

describe

This provides information about:

• Number of observations
• Number of variables
• Variable names
• Variable types
• Storage formats

You can also use:

codebook

to obtain more detailed information about variables.

To view the actual observations:

browse

or:

list in 1/20

The latter displays the first 20 observations.

5. Check for Missing Values

Missing observations can affect regression results.

Use:

misstable summarize

You can also examine a particular variable:

summarize performance, detail

If observations have missing values in variables included in a regression model, Stata generally excludes those observations from that estimation.

Researchers should therefore determine whether missing observations are random, systematic, or potentially related to the study variables.

6. Check Variable Coding

Categorical variables should be coded appropriately.

For example:

Gender

1 = Male
2 = Female

Education

1 = Primary
2 = Secondary
3 = Diploma
4 = Degree
5 = Postgraduate

You can attach value labels in Stata:

label define genderlbl 1 "Male" 2 "Female"
label values gender genderlbl

For categorical predictors in regression, Stata’s factor-variable notation can be used, such as:

regress performance credit experience i.education

This tells Stata to treat education as a categorical variable rather than as a continuous numerical scale. Stata officially supports factor-variable notation for regression models.

7. Conduct Descriptive Statistics

Before regression analysis, examine the characteristics of the variables.

Use:

summarize performance credit experience education business_size

For more detailed descriptive statistics:

summarize performance credit experience education business_size, detail

Important statistics include:

• Mean
• Standard deviation
• Minimum
• Maximum
• Number of observations

For categorical variables, use:

tabulate gender

or:

tabulate education

8. Examine Relationships Between Variables

Correlation analysis can provide an initial understanding of relationships among continuous variables.

Use:

pwcorr performance credit experience business_size, sig

The sig option displays significance levels.

A correlation matrix can help identify:

• Direction of relationships
• Strength of relationships
• Potential multicollinearity among independent variables

However, correlation does not by itself establish causation.

9. Create Scatterplots

For a continuous dependent variable and continuous predictor, a scatterplot can help assess whether a linear relationship is plausible.

For example:

scatter performance experience

You can add a fitted regression line:

twoway (scatter performance experience) ///
       (lfit performance experience)

Stata’s official regression guidance recommends examining the relationship graphically before fitting a simple linear regression model.

10. Conduct Simple Linear Regression

Simple linear regression examines the relationship between one dependent variable and one independent variable.

For example:

regress performance experience

The basic structure is:

regress dependent_variable independent_variable

For example:

regress income education

This estimates the association between education and income.

The main coefficient tells you how the predicted dependent variable changes with a one-unit increase in the independent variable, holding the model structure constant. Stata reports the coefficient, standard error, t statistic, p-value, confidence interval, R-squared, and overall model statistics.

11. Conduct Multiple Linear Regression

Multiple regression examines the relationship between one dependent variable and several independent variables.

For example:

regress performance credit experience education business_size

The model can be represented as:

Y = β₀ + β₁X₁ + β₂X₂ + β₃X₃ + β₄X₄ + ε

Where:

• Y = dependent variable
• X₁, X₂, X₃, X₄ = independent variables
• β₀ = constant
• β₁–β₄ = regression coefficients
• ε = error term

The advantage of multiple regression is that the association of each predictor can be examined while accounting for the other predictors included in the model.

12. Understand the Regression Output

A typical Stata regression output contains several important sections.

Number of observations

Number of obs = 200

This indicates the number of observations used in estimating the model.

R-squared

R-squared indicates the proportion of variation in the dependent variable explained by the predictors in the model.

For example:

R-squared = 0.624

This means that the variables included in the model account for approximately 62.4% of the observed variation in the dependent variable, under the model specification.

Adjusted R-squared

Adjusted R-squared accounts for the number of predictors included in the model and can be useful when comparing models containing different numbers of explanatory variables.

F-statistic

The F-test evaluates the joint statistical significance of the regression model.

The associated:

Prob > F

provides the p-value for the overall test.

13. Interpret the Regression Coefficients

Suppose Stata produces:

experience     Coefficient = 2.45
               P>|t|       = 0.003

The coefficient of 2.45 means that a one-unit increase in experience is associated with an estimated 2.45-unit increase in the dependent variable, holding the other variables in the model constant.

The p-value can be used when conducting the specified hypothesis test.

For example, if the significance level is 5%:

p < 0.05

provides evidence against the null hypothesis that the coefficient equals zero.

Stata reports the coefficient, standard error, t statistic, p-value, and confidence interval for each predictor.

14. Interpret the Constant

The _cons row represents the estimated intercept.

For example:

_cons = 15.40

This represents the predicted value of the dependent variable when all predictors included in the model equal zero.

Whether this interpretation is substantively meaningful depends on the variables and whether zero is a realistic value for them.

15. Test for Multicollinearity

Multicollinearity occurs when independent variables are highly correlated with one another.

After running the regression:

regress performance credit experience education business_size

run:

estat vif

Stata’s estat vif calculates variance inflation factors for the predictors in a linear regression model.

Researchers often use VIF as a diagnostic indicator. There is no universal cutoff that applies to every research context, so the values should be considered alongside correlations, the research design, and the substantive meaning of the variables.

16. Test for Heteroskedasticity

Heteroskedasticity occurs when the variance of the regression errors is not constant.

After regression, use:

estat hettest

Stata documents estat hettest as a test for heteroskedasticity.

You can also visually inspect the residuals:

rvfplot, yline(0)

A systematic pattern in a residual-versus-fitted plot may indicate that the model requires further investigation. Stata provides residual plots and several influence and specification diagnostics following linear regression.

17. Use Robust Standard Errors When Appropriate

If heteroskedasticity is present or robust inference is otherwise appropriate, one commonly used approach is:

regress performance credit experience education business_size, vce(robust)

Robust standard errors change the estimated standard errors and therefore statistical inference; they do not automatically solve every possible problem with model specification.

Stata provides robust and cluster-robust variance estimators for linear models.

18. Test Model Specification

The Ramsey RESET test can be used as one diagnostic for possible functional-form or omitted-variable problems.

After regression:

estat ovtest

Stata documents estat ovtest as the Ramsey regression specification-error test for omitted variables.

The result should not be interpreted as definitive proof that variables are or are not omitted. Researchers should combine statistical diagnostics with theory, prior literature, and the study design.

19. Check Residuals

Residuals are the differences between observed and predicted values.

You can generate predicted values:

predict yhat

Generate residuals:

predict residuals, residuals

Then examine them:

summarize residuals

You can also plot them:

rvfplot, yline(0)

Stata supports generating predictions, residuals, standardized residuals, studentized residuals, and influence measures after linear regression.

20. Check for Influential Observations

Some observations may have a disproportionate influence on the regression estimates.

For example:

predict cooksd, cooksd

You can then inspect the largest values:

summarize cooksd, detail

Stata provides several influence diagnostics, including Cook’s distance, leverage, DFBETAs, DFITS, COVRATIO, and Welsch distance.

An influential observation should not automatically be deleted. The researcher should investigate whether it represents a data-entry error, an unusual but valid observation, or a feature of the population.

21. Include Categorical Independent Variables

Categorical predictors should normally be represented using factor-variable notation.

For example:

regress performance credit experience i.gender i.education

Here:

• i.gender treats gender as categorical.
• i.education treats education categories as categorical.

Stata automatically creates the appropriate indicator variables and reference category.

22. Examine Interaction Effects

Sometimes the effect of one independent variable depends on another variable.

For example, suppose the relationship between credit access and performance may differ by gender.

You can specify:

regress performance credit##i.gender experience education

The ## notation includes:

• The main effect of credit
• The main effect of gender
• The interaction between credit and gender

After estimation, margins can help interpret the interaction:

margins gender, at(credit=(0 1))

A graphical presentation can be produced using:

marginsplot

23. Consider Nonlinear Relationships

Not every relationship is necessarily linear.

For example, you might hypothesize that experience has a nonlinear relationship with performance.

You can include a squared term:

regress performance experience c.experience#c.experience education

This allows the relationship between experience and performance to have curvature.

The decision to use nonlinear terms should be based on theory, prior evidence, graphical examination, or a clearly justified functional form.

24. Consider Clustered Data

If observations are grouped—for example, respondents are nested within schools, communities, firms, districts, or health facilities—ordinary standard errors may not adequately account for within-group dependence.

For example:

regress performance credit experience education, vce(cluster district)

This estimates standard errors clustered at the district level.

The appropriate clustering level should be determined from the research design and sampling structure.

25. Choose the Correct Regression Model

Not every dependent variable should be analyzed using ordinary linear regression.

Continuous dependent variable

Use:

regress y x1 x2 x3

Binary dependent variable

For example:

1 = employed
0 = unemployed

A logistic regression may be appropriate:

logit employed education experience age

or:

logistic employed education experience age

Ordered categorical outcome

For example:

1 = Low
2 = Moderate
3 = High

An ordinal logistic model may be appropriate:

ologit satisfaction age income education

Count outcome

For count data, models such as Poisson or negative binomial regression may be considered depending on the data-generating process.

For example:

poisson number_of_visits age income

The regression model should therefore be selected according to the measurement and distribution of the dependent variable, rather than simply because regress is available.

26. Run the Final Regression Model

After data cleaning, descriptive analysis, diagnostics, and model specification, run the final model.

For example:

regress performance credit experience education business_size, vce(robust)

Then run relevant diagnostics:

estat vif
estat hettest
estat ovtest
rvfplot, yline(0)

The exact diagnostics should correspond to the assumptions and structure of the model.

27. Compare Regression Models

Researchers often estimate several models.

For example:

Model 1: Basic model

regress performance credit

Model 2: Add demographic variables

regress performance credit age gender education

Model 3: Add business characteristics

regress performance credit age gender education experience business_size

This allows the researcher to examine whether coefficients change when additional theoretically relevant variables are introduced.

28. Save Regression Results

For repeated analysis, it is useful to save estimation results.

For example:

estimates store model1

Then estimate another model:

regress performance credit experience education business_size
estimates store model2

The models can subsequently be compared or exported using appropriate reporting tools.

29. Save the Stata Do-File

A good research practice is to keep a complete record of the commands used during analysis.

For example:

* Import data
import excel "researchdata.xlsx", firstrow clear

* Descriptive statistics
summarize performance credit experience education business_size

* Correlation
pwcorr performance credit experience education business_size, sig

* Regression
regress performance credit experience education business_size

* Multicollinearity
estat vif

* Heteroskedasticity
estat hettest

* Robust regression
regress performance credit experience education business_size, vce(robust)

Keeping a do-file improves reproducibility because the analysis can be rerun after data corrections or model changes.

30. Report Regression Results in a Thesis or Research Report

A regression results table can contain:

The report should also provide:

• Number of observations
• R-squared
• Adjusted R-squared
• F-statistic
• Model p-value
• Standard-error specification
• Relevant diagnostic results

31. Example of Interpretation

Suppose the regression produces:

Credit access
Coefficient = 0.452
p-value = 0.001

A suitable interpretation would be:

“Holding the other variables in the model constant, a one-unit increase in the credit-access measure is associated with an estimated 0.452-unit increase in business performance. The coefficient is statistically distinguishable from zero at the 5% significance level.”

Avoid writing that credit access causes higher business performance unless the research design supports a causal interpretation.

32. Complete Stata Regression Workflow

A practical workflow can therefore be summarized as:

Step 1

Define the research question.

Step 2

Identify the dependent and independent variables.

Step 3

Prepare and code the dataset.

Step 4

Import the data into Stata.

Step 5

Inspect the dataset.

describe
codebook
browse

Step 6

Check missing observations.

misstable summarize

Step 7

Conduct descriptive statistics.

summarize
tabulate gender

Step 8

Examine correlations.

pwcorr y x1 x2 x3, sig

Step 9

Examine graphical relationships.

scatter y x1

Step 10

Run the initial regression.

regress y x1 x2 x3

Step 11

Interpret coefficients, p-values and confidence intervals.

Step 12

Assess model fit.

Examine:

• R-squared
• Adjusted R-squared
• F-statistic
• Root MSE

Step 13

Check multicollinearity.

estat vif

Step 14

Check heteroskedasticity.

estat hettest

Step 15

Examine residuals.

rvfplot, yline(0)

Step 16

Check model specification.

estat ovtest

Step 17

Investigate influential observations.

predict cooksd, cooksd

Step 18

Use robust or clustered standard errors where justified.

regress y x1 x2 x3, vce(robust)

or:

regress y x1 x2 x3, vce(cluster group)

Step 19

Estimate the final theoretically justified model.

Step 20

Export and report the results.

33. Common Mistakes to Avoid

Researchers conducting regression analysis in Stata should avoid:

1. Running regression before cleaning the dataset.
2. Treating categorical variables as continuous without justification.
3. Ignoring missing observations.
4. Automatically deleting outliers.
5. Reporting only p-values without coefficients.
6. Ignoring confidence intervals.
7. Treating correlation as proof of causation.
8. Using linear regression when the dependent variable requires another model.
9. Ignoring multicollinearity.
10. Ignoring heteroskedasticity.
11. Running many models without theoretical justification.
12. Changing the model simply to obtain statistical significance.
13. Failing to retain the Stata do-fi