Econ 299 Chapter3a -...

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1 Chapter 3 – Statistical Review This chapter will conduct a brief review of  statistical concepts.  It is NOT a replacement  for a statistics course.  Concepts will include: -Models -Random and non-random variables -Probabilities -Expected Values -Variance -Distributions and Tables (Normal, t, F, chi-squared) -Covariance and Correlation -Estimators (Including OLS) -Confidence Intervals and Hypothesis Testing
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2 3.1 Simple Economic Models  and Random Components Consider the linear economic model: Y i  = b 1  + b 2 X i  +  є i Where the variable Y (such as utility) is  related to another variable X (such as  House episodes watched) Є (or  epsilon ) represents error; everything  included in Y that is not explained by X Ie: Quality of House Episode, Quality of  Popcorn, Other Facts of Life
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3 3.1 Observed or Random Components Є (or  epsilon ) is the RANDOM ERROR TERM;  it takes on values according to chance Since Y i  depends on  Є i , it is also random   b 1  + b 2 X is assumed to be fixed in most simple  models (which simplifies everything) Referred to as the deterministic part of the  model Non-Random b 1  and b 2  are unknown, and must be estimated
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4 3.1 Example Consider the function: Utility = b 1  + b 2 Sisters +  є i Here happiness depends on the number of  one’s sisters є captures such concepts as number of  brothers, income, and other factors Utility and Sisters are Observable Utility and  є are random b 1  and b 2  must be estimated (< or > 0?)
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5 3.2 Random Variables and Probabilities Random Variable A variable whose value is determined by  the outcome of a chance experiment Ie: Sum of a dice roll, card taken out of a deck,  performance of a stock, oil discovered in  Alberta, gender of a new baby, etc. Some outcomes can be more likely than others  (ie: more chance of some oil discovered than  none)
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6 3.2 Random Variables Discrete Variable Can take on a finite # of values Ie: Dice roll, card picked Continuous Variable Can take on any value within a range Ie: Height, weight, time Variables are often considered discrete to aid in  calculations and economic assumptions (ie:  Money in increments of 1 cent)
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7 3.2 Probabilities Probabilities are assigned to the various  outcomes of random variables Terminology : Sample Space – set of all possible outcomes  from a random experiment -ie S = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} -ie E = {Pass exam, Fail exam, Fail horribly} Event – a subset of the sample space -ie B = {3, 6, 9, 12}  ε  S -ie F = {Fail exam, Fail horribly}  ε  E
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8 3.2 Probabilities
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