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Lecture

Simple Linear Regression and Correlation (2).docx

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Department
Statistics
Course
STATS 2B03
Professor
Aaron Childs
Semester
Fall

Description
November 9 , 2012 Stats 2B03: Statistical Methods for Science Simple Linear Regression and Correlation (2) Single-Variable Regression - notation:  n = # of *x, y) pairs  ∑  ∑  ∑ - result: the least square estimates0of β a1d β are and - Example (continued) x y X2 xy Y2 3 7 9 21 49 5 9 25 45 81 1 6 1 6 36 2 5 4 10 25 11 27 39∑ 82 ∑ 191 ∑  ( )  ( )( )   ( )   when x = 4, hat 4.314 + .8857(4) = 7.8568 9.4 Evaluating the Regression Equation - 9.4.1 some notation and terminology:  y-values predicted by the regression line are called predicted values or fitted values and are denoted haty  the y-variable is called the response or dependent variable, and the x- variable is called the predictor or the independent variable  the i’s are called residuals, and they are estimated by the observed residuals  example (continued) x y
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