WAGE1
T Tests with WAGE1
Estimate a wage equation and test education, experience, and tenure with real t statistics.
Module 4
Multiple Regression Inference
Learn how to make statistical inferences in multiple regression using t tests, p-values, confidence intervals, linear restrictions, F tests, and professional regression reporting.
20 lessons8 to 12 hoursIntermediate
Skills
Explain why inference requires a sampling distribution.State the classical linear model assumptions and the role of normality.Interpret t statistics, p-values, confidence intervals, and practical significance.Test zero and nonzero hypotheses about individual coefficients.Test linear combinations and joint restrictions with F tests.Report regression results professionally using Python and careful economic language.
Progress tracking
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Module resources
20 quiz checks23 datasets10 notebooks
Lessons
1Why Inference Matters in Multiple RegressionWhy is an estimate not enough?Open lesson2Classical Linear Model AssumptionsWhat extra assumptions support exact regression tests?Open lesson3Normality and Sampling DistributionsWhat does normality do for OLS inference?Open lesson4The t Distribution in RegressionWhy do regression tests use t instead of z?Open lesson5Testing a Single Coefficient Against ZeroHow do we test whether a regressor has no partial effect?Open lesson6One-Sided t TestsWhen is a one-sided alternative appropriate?Open lesson7Two-Sided t TestsWhy are two-sided tests common in regression tables?Open lesson8Testing Nonzero Hypothesized ValuesHow do we test beta equals one or minus one?Open lesson9p-Values for t TestsWhat does a p-value measure?Open lesson10Statistical Significance versus Practical SignificanceCan a result be statistically significant but not important?Open lesson11Confidence Intervals for Regression CoefficientsHow do intervals summarize uncertainty?Open lesson12Using Confidence Intervals to Test HypothesesHow can an interval answer a hypothesis test?Open lesson13Testing One Linear Combination of ParametersHow do we test beta one equals beta two?Open lesson14Reparameterizing a Model for Linear RestrictionsHow can a transformed model estimate the restriction directly?Open lesson15Introduction to F TestsWhy do we need a joint test?Open lesson16F Tests for Exclusion RestrictionsHow do we test whether a group of variables can be omitted?Open lesson17R-Squared Form of the F StatisticWhen can R-squared compute an F statistic?Open lesson18Overall Significance of a RegressionWhat does the regression F statistic test?Open lesson19General Linear RestrictionsWhat if the restriction is not just omitting variables?Open lesson20Reporting Regression Results ProfessionallyHow do we turn inference into a professional report?Open lesson
Notebook labs
GPA1
One-Sided and Two-Sided Tests
Compare tail choices and hypothesis wording using GPA1.
GPA1
p-Values and Critical Values
Use scipy to compute p-values and critical values from the t distribution.
WAGE1
Confidence Intervals
Build confidence intervals from estimates, standard errors, and t critical values.
WAGE2
Linear Combinations
Test whether two coefficients are equal using WAGE2.
BWGHT
F Tests for Exclusion Restrictions
Compare restricted and unrestricted models and compute an F statistic.
BWGHT
R-Squared F Test
Use R-squared values to compute the F statistic for valid exclusion restrictions.
HPRICE1
General Linear Restrictions
Use statsmodels f_test for restrictions beyond simple variable exclusion.
CEOSAL2
Reporting Regression Results
Assemble coefficient, uncertainty, p-value, fit, and interpretation into a report table.
WAGE1
Applied Inference Project
Run a complete inference workflow and draft a concise empirical report.