Easy Statistics: Linear and Non-Linear Regression

Explore easy statistics and nonlinear regression through an intuitive course with almost no equations that emphasizes application and interpretation of statistical results for learners with no prior knowledge.

Explore non-linear regression, a regression technology using non-linear parameters, contrasting with linear regression and its curve fitting, and examine its use across economics, sociology, psychology, politics, and medicine.

Learn the statistical intuition behind nonlinear regression without heavy equations, apply regression models to data, interpret outputs, and gain tips for working with nonlinear regression.

Designed for academic students of any level and practitioners such as business users and government policy analysts, this course offers an easy introduction to nonlinear regression.

No math or statistics background is required to follow this course. Stator demonstrates many regression models with data, guiding you to measure quantitative variables against each other.

Learn to interpret outputs from stator, a purchasable statistical software, with data demonstrations. Access attached code and training data to replicate examples.

Learn non linear regression analysis, linking a dependent variable Y to one or more independent variables via nonlinear models and an error term E, with Y often not continuous.

Explore how non-linear regression links parameters to the dependent variable nonlinearly, and learn to interpret nonlinear coefficients through transformations and marginal effects.

Explore why nonlinear regression provides quantitative evidence, hypothesis testing, and predictions; it excels with certain data types like binary and time outcomes, avoiding out of bounds prediction through nonlinear transformations.

Explore nonlinear regression models, including logistic and probit for binary outcomes, ordered and multinomial variants, count models, and Cox proportional hazards for time as a dependent variable.

Learn how maximum likelihood estimates nonlinear models by iteratively maximizing likelihood, with guidance on sample size, observations per parameter, and issues like collinearity and little variation in the dependent variable.

Explore the linear probability model for a binary y, illustrating why linear regression on binary data is problematic, with a ~0.23 slope and out-of-bounds predictions, noting robust standard errors.

Apply logit and probit transformations to produce nonlinear models that bound predictions between zero and one for wine x. Reject linear probability in favor of nonlinear models.

Explain how latent variables underlie nonlinear models, making coefficients hard to interpret, and how marginal effects reveal the relationship between inputs and hidden hunger y*.

Explore marginal effects and slope coefficients in linear and nonlinear regression. Learn to compute effects at the mean of X and as averages across X, illustrated by a 0.30 slope.

Explore how dummy explanatory variables, taking values 0 or 1, shift the nonlinear regression intercept via X under a logistic transformation to keep predictions within bounds.

Explore multiple nonlinear regression with several continuous predictors and a dummy variable. The model shows each coefficient's effect depends on all X values, producing nonlinear planes of best fit.

Assess goodness of fit for nonlinear regression using pseudo r-squared and classification tables, and note how the 0.5 cut point affects accuracy.

Explain how loaded coefficients relate to latent scores, how exponential coefficients convert to log odds and odds ratios, and why marginal effects are needed to quantify probability changes.

Explore logit and probit regression, noting non-linear models may need more data but remain robust with small samples; compare coefficients and report effects at the mean.

Explore how the linear probability model can yield similar marginal effects to logistic and linear regression for binary outcomes, with average marginal effects close to standard estimates.

Explore applied logit and probit in Stata, using binary union data to estimate models, compare marginal effects with linear probability models, and illustrate latent variables with a simulated example.

Explore regression modelling with an intuitive, equation-light approach that uses explanatory variables x to explain a dependent variable y, blending theory and practical data demonstrations in a statistics program.

Learn to balance predictive and explanatory regression, plan carefully, rely on theory and data quality, and address common issues like missing values and multicollinearity.

Explore how regression models capture non-linear shapes by adding polynomial terms (quadratic and cubic) to Y on X, test linearity, and interpret coefficients in hourly earnings and age relationships.

Examine how interaction effects in regression create new terms such as polynomials and dummy, continuous, and categorical groupings that alter relationships and slopes.

Explore how interaction effects reshape regression results, using mpg, foreign status, weight, and categorical groups to reveal how car prices respond to mileage, origin, and other factors with margins visualization.

Explore how time information shapes regression analyses, from long and wide data forms and panel data to time lags, leads, and distributed lag models, including difference transformations.

Explore how time in regression shapes analysis with panel data, including lagged effects, linear and nonlinear time specifications, and difference-based estimates to reveal dynamic wage patterns in unbalanced datasets.

Learn how to encode categorical data as dummy variables, include them in regression, and interpret intercept shifts relative to a reference category.

Learn to handle categorical explanatory variables in regression by coding dummies, selecting a reference category, and interpreting coefficients with post-estimation graphs and group tests.

Explore how multicollinearity inflates standard errors and distorts coefficients when explanatory variables measure the same thing, with perfect and imperfect linearity.

Explore practical strategies to manage multicollinearity in regression using variance inflation factor, backward stepwise selection, principal component analysis, and demeaning to stabilize coefficients.

Understand how missing data in y or x reduces regression sample size and apply deletion or imputation, including structural, MAR, and MNAR patterns.

Learn how to include a categorical variable in regression using dummy variables in Stata, interpret coefficients, perform a group test, and compare different reference categories.