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# statistics - Descriptive Statistics Regression Basics...

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Descriptive Statistics Regression Basics 06E:071:SCA Statistics for Strategy Problems Thomas Parker Fall 2011 T. Parker () Review 1 / 15

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Descriptive Statistics Regression Basics Review : Outline Descriptive statistics The center of the data The spread of the data Associations between populations Regression basics Conditional Probability Regression estimate formulas T. Parker () Review 2 / 15
Descriptive Statistics Regression Basics The center of the data Suppose there is a population of things that have numerical values attached to them, and call them a population X = { X 1 ,... X N } . What are some ways we can describe the population? The mean probably needs no introduction, but just in case, μ = 1 N Σ N i = 1 X i We will call the population mean μ . This is also known as the expected value of the population, and we write μ = E [ X ] , where the E reminds us that this is the value that you “expect” if you choose one value from X at random. Other ways of defining “the middle” of the data? T. Parker () Review 3 / 15

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Descriptive Statistics Regression Basics Median and mode? When are they different from the mean? symmetric asymmetric T. Parker () Review 4 / 15
Descriptive Statistics Regression Basics Median and mode? When are they different from the mean? symmetric asymmetric mean median mode T. Parker () Review 5 / 15

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Descriptive Statistics Regression Basics The spread of the data We will use the variance and the standard deviation. They are two ways of telling you the same thing: what is the dispersion of the observations? The variance Var ( X ) = σ 2 is defined by σ 2 = 1 N Σ N i = 1 ( X i - μ ) 2 The standard deviation is the square root of the variance. Why do we use the standard deviation? Given a sample, how do you calculate the variance by hand? T. Parker () Review 6 / 15
Descriptive Statistics Regression Basics Expectation, variance and constants Let c be a constant and let X be random: E [ c ] = T. Parker () Review 7 / 15

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Descriptive Statistics Regression Basics Expectation, variance and constants Let c be a constant and let X be random: E [ c ] = c E [ X + c ] = T. Parker () Review 7 / 15
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statistics - Descriptive Statistics Regression Basics...

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