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### 65 Cards in this Set

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 4 main assumptions of linear model and their assumtpions 1. Fixed X 2. Sum of errors=0 leads to unbiasedness 3. Homoscdeastacity 4. No Autocorrellation makes estimators efficient 5th assumption of linear model errors are normally distributed Solution for OLS in Linear Algebra B=(X'X)^-1(X'Y) What does SER do Best overall indicator of regression effectiveness Blue best linear unbiased estimator What does GOF tell us How well the model fits the data Variance avg deviation from the mean -> how spread out the distribution is Central Tendency ->E(X) the mean, median, and mode Dispersion range, variation, and SD -> distribution about the mean Covariance measure of how two variables vary together correllation standard covariance standard error measure of accuracy -> standard deviation of the sampling distribution of that statistic probability measure of uncertainty Random variable assigns outcome to event mutually exclusive when one thing happens another cannot conditional probability ratio of joint to marginal parameters defines what distributions look like 2 ways to define distributions 1. probability distrabution function 2. cumlative density function Central limit theory bigger the scale the better the data 3 hypothesis tests 1. compare mean to some hypothetical value 2. standardize its deviation 3. use properties of normal curve hypothesis statement that something is true Null a hypothesis to be tested Point estimate value of a statistic used to estimate a parameter P value requirement 5 or below to reject null T-test requirement outside of +- 2 standard deviations reject null T value number of SD's away from the mean Identity Matrix matrix with 1's alone the diagnol Regression Analysis process of estimating parameters from samlpe data Residuals difference between regression and actual results RSS Sum of squared residuals 4 measure of GOF 1. standard error of regression 2. test on each individual slope coeficient 3. R^2 4. F-test Total variance absence of any other info other then mean Two parts of TSS 1. ESS 2. RSS ESS Error sum of Squares What is ESS variation in Y not accounted for by X RSS difference between regression line an mean What does a large RSS tell us means more Y variation explained by X R^2 coefficient of determination What does a large RSS with respect to TSS tell us how much variation of Y is explained by X OLS ordinary least squares What is OLS process by which we turn data into theoretical quantities Diagnostics warn us of inappropiate uses of OLS Problems with data to focus on 1. unusual data 2. non-constant variation 3. non-normal errors b1 b1=sum((xi-meanx)(yi-meany))/sum(xi-meanx)^2 b0 b0=Y-b1(meanx) Null hypothesis no difference between hypothesis and reality...where you fail to reject null skew where the tail in a set of data is elongated 3 units of linear algebra analysis 1. scalar 2. vector 3. matix singularity when one column is a linear function of another -> when variables are perfectly correlated Linear model tells us the trend between variables Regression analysis process of estimating parameters from sample data Regression coefficients b0 and b1 Residuals difference between regression and actual results P(Y|X) probability distribution of Y for specific values of x...probability of seeing value of Y conditional on X OLS process by which we turn data into theoretical quantities Influence Leverage * Discrepancy Outlier ususual Y for level of X -> does not mean seperate from data cloud Method of deletion 1. remove outlier 2. calculate line 3. calculate residual as if influential case had been present How do you fix heteroscedascity transform the Y variable Leverage how much influence does a point Y exert on all fitted fields discrepancy how far from regression is outlier 4 elements of modeling 1. question 2. DV 3. IV 4. Unit of analysis Bias the amount of error that arises when estimating a quantity Complementarity probability of something not happening -> 1-P heteroscedascity constant error variance