2103 Ch10 SIMPLE REGR Nov24,29,Dec1 FALL 2010(V1)

2103 Ch10 SIMPLE REGR Nov24,29,Dec1 FALL 2010(V1) - Chapter...

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Chapter 10: Simple Linear Regression Introduction to Regression Using X to Predict Y Regression: Extent to which one can improve prediction of How do Colleges predict future performance of applicants? Job Applicants: Section 10.1: Probabilistic Models First Order (straight-Line) Probabilistic Model (p. 563) Y= Dependent or Response variable (variable to be modele X= Independent Variable or Predictor Variable (variable use Beta Zero = Y intercept of the line Beta One = Slope of the line E = Epsilon = random error component
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Section 10.2: Fitting the Model: The Least Squares Approach The Least Squares Line Y hat = Beta Zero + (Beta One * X) 1) Sum of the Predictive Errors equals "Zero" 2) The Sum of Squared Errors (SSE) is smaller than for any Interpreting Estimates of Beta Zero and Beta One in Simple Beta Zero = Y intercept represents the predicted value of Y Beta One = Slope represents the change in Y (increase or d Section 10.3: Model Assumptions Section 10.4: Assessing the Utility of the Model: Making Inferences Section 10.5: The Coefficients of Correlation, Coefficient of Determ Section 10.6: Using the Model for Estimation and Prediction
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f Y "beyond" merely guessing the Mean of Y (worst case) ed) ed as a predictor of Y)
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has these Properties y other straight-line model one could use e Linear Regression Y when X = Zero decrease) for every unit increase in X s about the Slope Coefficient mination, and Coefficient of Non-Determination
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Learning Objectives for Simple Regression and Corr 1) Learn concepts of regression and correlation e.g., Correlation, regression, Coe and, Std. Error of Estimate, Predi 2) Learn when regression methods are applied eg. For Simple Regression, it inv both X and Y are NUMERIC rando We want to develop a "model" fo We want to assess Significance a 3) Learn how to interpret results of regression analys 1) e.g., are X and Y appropriate v 2) is X a statistically significant p 3) if X meets above, is it also suff Statistical significance is "necess an "accurate" predict In Class Example with Data, and the Excel Regressio Research Scenario: Can Ad length (X=sec's) predict X=Length of commercial (sec's) Y=Recall Test score (recalling message of commerci Does Recall Vary as a function of Commercials' Leng Is there a statistically significant relationship betwee n=60 "X,Y" pairs Remember for Chapter 7: On Exam, all T test Statistics, and their Pvalues and C Incl T test for 2 Indep Sample Me On Exam, you need to calculate Z test for 2 Sample P
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Chapter 10: Nearly all Statistics are Provided Using Excel to obtain Regression Analysis Output Go to 1) Data, 2) Data Analysis, 3) Regression, follow For Scatterplot: you can use Line Fit option in "Regre Using Insert Menu Graphs, First, go to : Insert Menu, Scatter, selec Examine the Scatterplot: Check for Linearity (should 25 30
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For Dec 1 Class: from Excel Regression Analysis Below: Coefficients andard Err t Stat Intercept 3.64 2.23 1.63 (X)Length 0.27 0.06 4.86 Today's Learning Objectives 1) Write out the Regression Equation from Excel Out 2) Test Slope Coefficient(s) for statistical Significanc Slope Coeff is Not Signif Diff from Ze
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