The STATA OMNIBUS: Regression and Modelling with STATA

Master linear regression through ordinary least squares (OLS), the most common regression method, used to relate a single continuous variable to multiple continuous or categorical predictors.

Learn to use Stata to demonstrate ordinary least squares regression and interpret the output, using do files and the auto training data set.

Understand regression analysis by linking a dependent variable y to independent variables X with an error term, while recognizing data types and that log transformations can change interpretation.

Explore linear regression and the ordinary least squares method, modeling a linear relationship between a continuous dependent variable and explanatory variables. Differentiate simple regression from multiple regression.

Explore the core regression methods, from ordinary least squares for continuous, cross-sectional data to nonlinear logit and probit, ordered and multinomial variants, and time-based panel, count, and Cox models.

Explore lines of best fit using parametric and non-parametric methods, from local polynomial regression to linear and quadratic forms, and extend to the plane of best fit in multidimensional data.

Explore how regression analysis reveals relationships in data while distinguishing causality from correlation, and learn how time elements and theoretical reasoning influence causal inferences in different settings.

Explain ordinary least squares, a regression method that fits a line of best fit by minimizing the sum of squared residuals to avoid cancellation.

Explore how Stata displays regression output, focusing on coefficients and the role of standard errors, t statistics, p values, confidence intervals, and R squared in assessing fit.

Explain the sum of squares—explained, residual, and total—and how R-squared and adjusted R-squared quantify model fit; show how noise alters R-squared even when the underlying relationship remains the same.

Explore the best linear unbiased estimator under Gauss–Markov assumptions, compare efficient and inefficient ordinary least squares estimators, and understand unbiasedness and the role of standard errors.

Explain how the homoskedasticity assumption keeps residual variance stable and why violations affect hypothesis testing, and show how robust standard errors mitigate this issue.

Explain how regression models can be linear in parameters while using non-linear transformations like polynomials and interactions to improve fit, illustrated with residuals and a quadratic example.

Explore the zero conditional mean exogeneity assumption, ensuring no correlation between x and the error term to prevent bias in ols estimates and endogeneity.

Test and correct for endogeneity by improving data quality and model building, exploring different functional forms, and guarding against data mining that undermines exogeneity and biases ordinary least squares results.

Apply Stata to regression analysis with the Auto data, building and diagnosing ordinary least squares models, interpreting foreign status, mileage, weight, and price through diagnostics and transformations.

Explore nonlinear regression through easy statistics in Stata, focusing on intuitive concepts, practical interpretation, and application with minimal equations for learners with no prior background.

Explore nonlinear regression and its focus on nonlinear parameters, examine logit and probit models, and understand non-continuous dependent variables across social sciences.

Target students at all levels and professionals in business and government who want an easy introduction to non-linear regression using Stata.

Identify the prerequisites for this course, noting that no math or statistics are required, but basic knowledge helps with practical applications. Explore how Stata estimates many regression models using data.

Explore nonlinear regression analysis as an extension of linear regression, where the dependent variable relates to one or more independent variables across continuous, integer, binary, ordinal, and nominal data.

Explore how nonlinear regression models relate parameters to the dependent variable in non-linear ways. Learn to transform nonlinear regression coefficients into meaningful measures using marginal effects computation.

Discover how nonlinear regression provides quantitative evidence, enables hypothesis testing, and predicts outcomes while controlling for other factors. It avoids out-of-bounds predictions for binary or time-to-event data with nonlinear transformations.

Explore the linear probability model, an ordinary least squares approach to binary outcomes, its limitations, heteroskedasticity, robust standard errors, and its relation to logit or probit models.

Use logit or probit transformations to create nonlinear models that bound Y between 0 and 1, producing similar logit and probit fits for reliable predictions.

Explore how latent variables underlie nonlinear models like logit and probit, illustrating the unseen y star and the observed outcome. Learn how to interpret coefficients via marginal effects.

Discover marginal effects as slope or partial effects in linear and nonlinear regressions, computed at mean x, showing how a unit change in x shifts Y's probability of being one.

Examine how dummy explanatory variables shift the nonlinear y–x relationship in regression. Observe that the intercept effect of a 0/1 dummy varies with x under a logistic transformation.

Explain multiple nonlinear regression with several continuous predictors and a dummy variable, highlighting how each beta depends on all x-values, and compare logit versus linear model fits.

Assess goodness of fit for nonlinear models like logit and probit by comparing full and null models with log-likelihood, using pseudo R-squared and classification tables, and noting cut-point effects.

Explain how logit coefficients relate to log odds and how exponentiating them yields odds ratios, while noting that odds hide the probability magnitude and marginal effects reveal it.

Explore logit and probit regression, including robustness to small samples, comparable predictions and marginal effects, and practical options like reporting average marginal effects or using a linear probability model.

Explore how the linear probability model can mirror marginal effects from logit and probit, and compare its slope estimates to OLS in binary outcomes.

Explore regression modeling with intuitive concepts, focusing on interpretation and transferable skills across methods. Observe practical demonstrations in Stata, emphasize application over equations, and learn to build better models.

Focus on thoughtful planning, theory-driven explanatory modeling, and careful variable selection before regression; balance prediction and explanation with iterative checks, sensitivity analyses, and data quality considerations in Stata.

Explore how linear regression can model non-linear relationships by adding polynomial terms, testing functional form, and interpreting coefficients, with examples like age-related U-shaped and quadratic effects.

Explore functional form in regression with stata by modeling hourly pay as a function of age and schooling, then quadratic and cubic terms, and assess multicollinearity with vif.

Explore how interaction effects in regression models reveal differing trends across groups, including continuous by continuous, categorical by continuous, and categorical by categorical interactions in Stata.

Explore how to incorporate time information into regression models, including long and wide data forms, time trends, lags, leads, and finite distributed lag models, with practical Stata examples.

Learn to code and interpret categorical explanatory variables in regression using dummy variables, reference categories, intercept shifts, and group tests, with practical examples in Stata.

In Stata, convert the categorical Rep 78 into dummy variables, run regressions with miles per gallon, and assess reference category effects and group significance via margins.

Explore how multicollinearity inflates standard errors and degrades regression estimates as perfect and imperfect collinearity emerge. Identify warning signs and remedies, including variance inflation factor, variable exclusion, and centering.

Explore multicollinearity in regression with Stata by examining pairwise correlations, assessing VIF, and using backward selection, PCA, or demeaning to stabilize coefficients.

Identify how missing data in y or X reduces regression sample size and learn when to delete rows, delete variables, or impute values using mean, regression, and multiple imputation.

Learn to handle missing values in Stata with miss table and patterns, run MCAR tests, and apply deletion and imputation (mean, categorical, regression) to compare models.

Explore Stata, a versatile statistical software for data management and analysis, including file handling, merging, and manipulation. It offers wide statistical options, graphing, and multi-core processing.

Open the Stata interface and explore the results, command, variable, and properties windows, then customize layouts, menus, and preferences using the set command.

Explore stata's help features by using the help command, the help menu, and online resources to access the PDF manual, getting started guides, and the Stata Journal.

Explore Stata command syntax and how it structures interactions beyond the graphical interface. Learn by prefix, variable list, expression, if, in, weights, and options, plus help and regress shortcuts.

Explore do files and ado files in Stata, including how to create, edit, and execute do files, and why this modular coding supports reproducible data analysis.

Start and manage log files in Stata to record your data sessions, view and amend logs, append or replace them, and translate logs to plain text for editors.

Learn to load and import data in Stata with clear, use, system use, and import, and import Excel data with first row variable names and sheet option.

View raw data in Stata with Browse and Edit, inspect data via the data editor, filter with if and in, and view the first ten observations.

Explore how missing values are coded as full stops in Stata and treated as positive infinity, and learn to identify, recode, and analyze them with ms table, summarize, and encode/decode.

Analyze distributional statistics for a continuous variable using inspect, stem, and summarize detail to reveal shape, skew, and tails, then test normality with skewness and kurtosis on price data.

In Stata, apply frequency, sampling, analytical, and importance weights to adjust survey data toward population totals, and learn bracket syntax for weighted descriptive stats, regressions, and graphs.

Explore the new Stata 17 table command to build custom two-way tables, compute descriptive, frequency, and summary statistics, and export results to Excel, PDF, or Latex.

Explore renaming single or grouped variables, changing variable labels, and creating value labels in Stata using rename and label commands, with a quick tour of the variables manager.

Learn to create indicator variables in Stata with generate, replace, or recode, using else rules and tabulate, and utilize auto code and enlist for efficient categorization.

Learn to save Stata datasets safely by using cd and save, avoid overwriting with replace, and export to formats like Excel, always working on a copy.

Learn how to combine data sets in Stata by appending observations and merging variables using a merge key or ID variable, including 1 to 1 and other merge types.

Explore double loops in Stata that multiply each variable by iterative factors to generate many new variables, speeding repetitive data manipulation shown with the auto data.

Learn to handle date information in Stata by converting string dates to numeric, handling varied formats (mdy, dmy, ymd), combining separate year, month, day fields, and formatting for analysis.

Learn to analyze data across groups in Stata by using underscore variables, subscripts, and the by prefix or bysort, generating new variables and extracting group max or min.

Learn to create bar graphs and dot charts in Stata, compare frequencies across categories, and interpret summary statistics such as the average price and its standard deviation.

Explore how to graph distributions in Stata with histogram, kernel density, quantile plots, and box plots, and see how bin width, bandwidth, and glider transforms reveal skewness and outliers.

Create pie charts in Stata via the graphical user interface and the graph pie command. Explore categorical data, customize slices, include missing values, and compare domestic and foreign cars.

Explore scatter plots and lines of best fit to visualize relationships between two variables, assess linear and non-linear forms, and overlay fitted plots using the two way command in Stata.

Learn to graph custom functions in Stata with the two way function command, plotting sine waves, quadratics, and logistic curves over chosen x ranges, including regression coefficients.

Contour plots visualize a third dimension in two dimensions, useful for bivariate distributions and continuous by continuous interactions; build with two way contour in Stata using levels and margins.

Learn how sunflower plots in Stata visualize two-variable density, using hexagons and petals to show high, medium, and low density and revealing structure in large data distributions.

Learn to merge multiple graphs into a single Stata figure using graph combine, storing graphs in status memory and applying options like y common, x common, and alt shrink.

learn to create category-based scatter plots in Stata by using the separate and overlay techniques, and to generate and plot mean statistics with collapse across groups.

Explore how to test relationships between two categorical variables in Stata with two-way tabulations, chi square, and fisher exact tests using the auto data.

Learn to test means in Stata using one-sample and two-sample t tests, assess standard deviations and proportions, and compare multiple groups with Hotelling's t-squared and mean by visuals.

Explore one-way and two-way anova in Stata to test mean differences across groups, check equal variances with Bartlett's test, and inspect regression coefficients after anova.

Explore Stata's diagnostic tools for ordinary least squares regression, including post estimation statistics, diagnostic plots, multicollinearity checks, outlier detection, and heteroskedasticity tests.

Transform and model car prices in Stata to improve fit by applying log transformation, adding a quadratic relation with miles per gallon, and using margins plots to visualize interactions.

Explore standardized regression coefficients (beta) to compare variable effects by standardizing to mean zero and a standard deviation of one, using Stata beta or std beta, with cautions for interactions.

Explore constrained linear regression by presetting parameters with the constraint command and estimating with reg using constraint options; assess model fit and diagnostics across different constraints.