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Unformatted text preview: E(Y|x)= μ Y|x = β + β 1 x Simple Linear Regression Model : Y= β + β 1 x+ – Assumes random, independent, mean 0, ε constant variance Method of Least Squares: Y i = β + β 1 x i + ε i , i=1, 2, …, n where: Estimated regression line is Residuals: Residual sum of squares: Unbiased estimators , meaning distributions are centered at true values of β 1 and β and are normal. (coefficient of determination) Regression models are used primarily for interpolation . That is, when predicting a new observation on the response (or estimating the mean response) at a particular value of the regressor x, we should only use values of x that are within the range of the x’s used to fit the model. Testing Hypotheses in Simple Linear Regression H : β 1 = β 1,0 , H 1 : β 1 ≠β 1,0 Test stat: (for our purposes, B 1,0 =0 usually) Reject H if To test β =/ 0: ≠ Reject null for same reason as above....
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- Spring '06
- Regression Analysis, one j, Y. ANOVA