WAGE1
WAGE1 Multiple Regression
Estimate log wage on education, experience, and tenure when the WAGE1 file is installed.
Module 3
Multiple Regression Analysis
Learn how multiple regression estimates partial relationships, controls for observed differences, diagnoses omitted-variable bias and collinearity, and supports responsible Python analysis.
20 lessons8 to 12 hoursIntermediate
Skills
Explain why simple regression can be misleading.Write and interpret a multiple linear regression model.Interpret coefficients while holding controls fixed.Compare simple and multiple-regression estimates.Explain partialling out, omitted-variable bias, multicollinearity, VIF, precision, and BLUE.Estimate and interpret multiple regression in Python with statsmodels.
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Module resources
20 quiz checks17 datasets8 notebooks
Lessons
1Why Multiple Regression?Why can a one-variable regression give a misleading answer?Open lesson2The Model with Two Explanatory VariablesHow do we read a regression with two explanatory variables?Open lesson3The General Multiple-Regression ModelWhat changes when the model has many explanatory variables?Open lesson4Holding Other Factors FixedWhat does ceteris paribus mean in a regression sentence?Open lesson5Changing Several Variables at the Same TimeHow do predictions change when more than one x changes?Open lesson6How OLS Estimates Multiple RegressionHow does OLS choose all coefficients at once?Open lesson7Fitted Values and ResidualsHow do fitted values and residuals work with several x variables?Open lesson8The Partialling-Out InterpretationHow can one coefficient isolate the leftover part of x1?Open lesson9Simple Regression versus Multiple RegressionWhy do coefficients change after controls are added?Open lesson10Goodness of Fit in Multiple RegressionDoes a higher R-squared mean a better causal model?Open lesson11The Multiple-Regression AssumptionsWhat conditions make OLS easier to interpret?Open lesson12Perfect CollinearityWhen can a multiple-regression model not be estimated?Open lesson13Omitted-Variable BiasHow can leaving out a variable push a slope up or down?Open lesson14Including Irrelevant VariablesWhat happens when we include a variable with no true partial effect?Open lesson15Multicollinearity and VIFWhy can highly related regressors make estimates imprecise?Open lesson16Variance, Standard Errors, and Degrees of FreedomWhat makes a coefficient estimate more or less precise?Open lesson17The Gauss-Markov TheoremWhat does it mean that OLS is BLUE?Open lesson18Model versus Estimation MethodWhy is OLS a method rather than the model itself?Open lesson19Multiple Regression in PythonHow do we estimate and read a multiple regression in statsmodels?Open lesson20Module 3 Applied ProjectWhat determines wages, and how cautious should our interpretation be?Open lesson
Notebook labs
GPA1
GPA1 Multiple Regression
Estimate college GPA on high-school GPA and ACT when the GPA1 file is installed.
WAGE1
Simple vs Multiple Regression
Compare the education coefficient before and after adding experience and tenure controls.
WAGE1
Partialling-Out Demonstration
Recover a multiple-regression coefficient by using the leftover part of education after controls.
WAGE1
Omitted-Variable Bias Example
Compare a short wage model with a controlled model and discuss the direction of omitted-variable bias.
WAGE1
VIF Calculation
Calculate variance inflation factors for education, experience, and tenure.
WAGE1
Residuals and Fitted Values
Create fitted values and residuals from a multiple-regression wage model.
WAGE1
R-squared Comparison
Compare R-squared across nested models and separate fit from causal interpretation.