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review_of_basic_statistics

review_of_basic_statistics - Econometrics Review of Basic...

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Econometrics Review of Basic Statistics

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Topics 1. Descriptive Statistics: - 1 variable: Mean and Variance - 2 variables: Covariance, Correlation 2. Hypothesis Testing

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Descriptive Statistics
Inferential Statistics Involves: - Estimation - Hypothesis Testing Purpose: - Make decisions about population characteristics

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Descriptive Statistics
Mean Measure of central tendency Affected by extreme values Formula:

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Median Measure of central tendency Middle value in ordered series - If odd n, mean of the 2 middle values Value that splits the distribution into two halves Not affected by extreme values Raw Data: 17 16 21 18 13 16 12 11 Ordered: 11 12 13 16 16 17 18 21 Position: 1 2 3 4 5 6 7 8
Mode Measure of central tendency Value that occurs most often Not Affected by Extreme Values There may be more than one mode Raw Data: 17 16 21 18 13 16 12 11 Ordered: 11 12 13 16 16 17 18 21

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Sample Variance Measure of Dispersion around the Mean Formula:
Sample Standard Deviation Measure of Dispersion around the Mean Has the same unit of measurement as the variable itself Formula:

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Radom Variables Random variable: numerical summary of a random outcome 1. Discrete: only a discrete set of possible values => summarized by probability distribution: list of all possible values of the variable and the probability that each value will occur. 2. Continuous: continuum of possible values => summarized by the probability density function (pdf)
Probability Distribution 1. List of pairs [ Xi, P(Xi) ] • Xi = Value of Random Variable (Outcome) • P(Xi) = Probability Associated with Value 2. 0 ≤ P(Xi) ≤ 1 - Mutually exclusive (no overlap) 3. Σ P(Xi) = 1 - Collectively exhaustive

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Mean and Variance: Discrete Case Mean, or Expected Value – Weighted Average of All Possible Values E (X) = μ X = ΣX i P(X i ) Variance – Weighted Average Squared Deviation about the Mean E (X) = μ X = Σ(X i - μ X ) 2 P(Xi)
Covariance - measures joint variability of X and Y

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