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The following key concepts from the book "Introduction  to Econometrics" by James  H. Stock ( Harvard University) and  Mark W. Watson ( Princeton University) are available in PDF. You can download them from the Google Drive link given at the end of the list of key concepts provided here. PART ONE Introduction and Review 1.1 Cross-Sectional, Time Series, and Panel Data 53 2.1 Expected Value and the Mean 60 2.2 Variance and Standard Deviation 61 2.3 Means, Variances, and Covariances of Sums of Random Variables 74 2.4 Computing Probabilities and Involving Normal Random Variables 76 2.5 Simple Random Sampling and i.i.d. Random Variables 82 2.6 Convergence in Probability, Consistency, and the Law of Large Numbers 86 2.7 The Central Limit Theorem 89 3.1 Estimators and Estimates 105 3.2 Bias, Consistency, and Efficiency 105 3.3 Efficiency of Y : Y Is BLUE 107 3.4 The Standard Error of Y 113 3.5 The Terminology of Hypothesis Testing 115 3.6 Testing the Hypothesis E(Y) = μY,0 Agai...

These essential research methodology and data analysis books, widely used in Master’s, MS/MPhil, and PhD programmes, are available in PDF format on my Google Drive. You can easily download each book by clicking the link provided below. A Primer on PLS-SEM, 2nd Edition — Joseph F. Hair A Primer on PLS-SEM, 3rd Edition — Joseph F. Hair Discovering Statistics Using IBM SPSS Statistics, 5th Edition — Andy Field Discovering Statistics Using IBM SPSS Statistics, 3rd Edition — Andy Field Introduction to Econometrics, 4th Edition — James H. Stock Multivariate Data Analysis, 7th Edition Multivariate Data Analysis, 8th Edition — Joseph F. Hair PLS-SEM (2016) — G. David Garson Research Methods for Business, 7th Edition SPSS Survival Manual, 4th Edition — Julie Pallant Using Econometrics, 7th Edition — A. H. Studenmund Research Books Available in PDF Click here to download these books

Assumptions of Multiple Regression These are the conditions under which the OLS estimator is valid and has the nice statistical properties we rely on (like unbiasedness and consistency). Assumption 1: Zero Conditional Mean E ( u | X 1 = x 1 ,…, X k = x k ) = 0 Meaning: On average, the omitted factors uuu are unrelated to the included regressors XXX. Put differently: Once you control for the regressors, there’s no leftover systematic relationship between uuu and XXX. Why it matters: If this fails, your regression suffers from omitted variable bias . Example: If PctEL (percent English learners) belongs in the model but you leave it out, and it’s correlated with STR, then the STR coefficient gets biased. Solution: Include the omitted variable (if you can measure it). Assumption 2: i.i.d. Sampling   ( X 1 i ,…, X ki ,Y i ), i =1,…, n , are i.i.d. Meaning: Each observation comes from the same population and ...

Omitted Variable Bias? What is "error u"? Imagine you want to predict students’ grades (Y) using hours studied (X) . But grades are not decided only by study hours. Some students are naturally smarter. Some had better teachers. Some were sick on exam day. All of these extra things (not included in your formula) are captured in the error term (u) . So u = "all the other factors we didn’t include in the equation." Could you please explain why there are always omitted variables?  In real life, it's impossible to include every single factor that affects Y. Example: For grades, you can’t measure “motivation”, “sleep quality”, or “stress” perfectly. So, some variables will always be omitted. Could you please let me know when this might become a concern If the omitted factors are unrelated to X (study hours), it’s not a big deal. OLS (our method) still works fine. BUT if the omitted factors are related ...