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ECONOMETRICS Chapter # 1: Introduction Domodar N. Gujarati

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ECONOMETRICS Chapter # 1: Introduction Domodar N. Gujarati

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ECONOMETRICS I

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ECONOMETRICS I. CHAPTER 4: CLASSICAL NORMAL LINEAR REGRESSION MODEL. Textbook: Damodar N. Gujarati (2004)  Basic Econometrics , 4th edition, The McGraw-Hill Companies. 4.1 THE PROBABILITY DISTRIBUTION OF DISTURBANCES u i.

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ECONOMETRICS I CHAPTER 4: CLASSICAL NORMAL LINEAR REGRESSION MODEL • Textbook: Damodar N. Gujarati (2004) Basic Econometrics, 4th edition, The McGraw-Hill Companies

4.1 THE PROBABILITY DISTRIBUTION OF DISTURBANCES ui • The OLS estimators of and are both linear functions of ui, which is random by assumption. Therefore, the sampling or probability distributions of the OLS estimators will depend upon the assumptions made about the probability distribution of ui.

4.2 THE NORMALITY ASSUMPTION

Why the normality assumtion? • By the central limit theorem (CLT) of statistics statistics, it can be shown that if there are a large number of independent and identically distributed random variables, then, with a few exceptions, the distribution of their sum tends to a normal distribution as the number of such variables increase indefinitely. It is the CLT that provides a theoretical justification for the assumption of normality of ui .

Why the normality assumption? • A variant of the CLT states that, even if the number of variables is not very large or if these variables are not strictly independent, their sum may still be normally distributed. • With the normality assumption, the probability distributions of OLS estimators can be easily derived because one property of the normal distribution is that any linear function of normally distributed variables is itself normally distributed. OLS estimators and are linear functions of ui . Therefore, if ui are normally distributed, so are and , which makes our task of hypothesis testing very straightforward.

Why the normality assumtion? • The normal distribution is a comparatively simple distribution involving only two parameters (mean and variance); it is very well known and its theoretical properties have been extensively studied in mathematical statistics. Besides, many phenomena seem to follow the normal distribution. • Finally, if we are dealing with a small, or finite, sample size, say data of less than 100 observations, the normality assumption assumes a critical role. It not only helps us to derive the exact probability distributions of OLS estimators but also enables us to use the t, F, and χ2 statistical tests for regression models. As we will show subsequently, if the sample size is reasonably large, we may be able to relax the normality assumption.

4.3 PROPERTIES OF OLS ESTIMATORS UNDER THE NORMALITY ASSUMPTION • With the assumption that ui follow the normal distribution, the OLS estimators have the following properties:

4.3 PROPERTIES OF OLS ESTIMATORS UNDER THE NORMALITY ASSUMPTION

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INTRODUCTION TO ECONOMICS- ECONOMICS SIMPLIFIED

INTRODUCTION TO ECONOMICS- ECONOMICS SIMPLIFIED

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Bridging to the Space Solar Power Economy – Staging the Enabling Addressable Markets and Financial Instruments for Economical Viability Jim Keravala – CEO, Offworld

SBSP in the context of the Energy Transition Dr Edward Tate – CTO and Founder, Virtus Solis Technologies, Inc.

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Video recording - Keynote 10: Defense Advanced Research Projects Agency Dr Paul Jaffe - Programme Manager, Tactical Technology Office, DARPA

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THREE ESSAYS ON THE ECONOMICS OF EDUCATIONAL OPPORTUNITY

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  • K-12 educational outcomes are a powerful reflection of social opportunity, both by meaningfully predicting adult wellbeing across measures like health and income, and by encapsulating the breadth of factors that contribute to a child’s preparedness, ability, and opportunity to learn and persist in school. In this light, the persistent deficits in educational outcomes experienced by individuals from traditionally disadvantaged identity groups and classes reflect systemic failures to meaningfully address the numerous shortcomings of education and social policy to create equal educational opportunities for all students. The three papers that comprise this dissertation aim to promote more equitable education and social policy by contributing valuable insights into three vital areas of policy that substantively shape the educational opportunities and outcomes of students in the United States. In the first, I extend the existing literature on how air pollutants can contribute to educational inequality by measuring the association between students’ proximity to hog farms, their feces lagoons, and fecal fertilizer spraying, and educational outcomes in North Carolina. In the second, I examine the most important school–level resource for student achievement –– teachers –– and how the processes by which students are assigned to classrooms enables the disproportionate assignment of lower performing, nonwhite, and low-income students to less effective teachers within their schools. And finally, I examine districts’ proposed spending of federal COVID–19 relief funds, what differences in spending strategies existed for these extremely flexible dollars, and what potential equity implications may exist for student academic learning recovery in the wake of the pandemic. Collectively, these papers contribute new knowledge in three important areas of education and social policy and foreground several promising future research directions by which greater educational equity and equality of social opportunity can be promoted.
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  • https://doi.org/10.17615/c3d5-1b73
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  • Domina, Thurston
  • Springer, Matthew G.
  • Sartain, Lauren
  • Lindsay, Constance A.
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  • University of North Carolina at Chapel Hill Graduate School

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