<p> Regression Analysis Chih-Chiang Yang, Ph.D. [email protected] 27016855x2151</p><p>Correlation Coefficient</p><p> Pearson’s Product-moment Correlation Coefficient</p><p> Spearman’s Correlation Coefficient</p><p> Point-biserial Correlation Coefficient</p><p> Biserial Correlation Coefficient</p><p> Phi Coefficient</p><p>Testing Hypothesis for ρ</p><p>Terms for Regression Analysis</p><p> Regression Analysis</p><p> Dependent Variable/Explained Variable/Regressand/y</p><p> Independent Variable/Explanatory Variable/Predictor/xi</p><p> Simple Regression</p><p> Multiple Regression</p><p> Linear Regression</p><p> Non-linear Regression</p><p> Simple Linear Regression</p><p> Multiple Linear Regression</p><p>Simple Linear Regression</p><p>2  y0   1 x   ；~NID (0,  ) ˆ ˆ  Estimations of Parameters（OLS）： yˆ   0  1 x1</p><p>1 ANOVA for Simple Linear Regression</p><p> ANOVA Table Source SS df MS F P Regression SSR 1 MSR MSR P[F>F*] F *  MSE Residual SSE n-2 MSE Total SST n-1</p><p> Testing Hypothesis for i s</p><p> Testing Hypothesis for 1</p><p> Testing Hypothesis for 0</p><p>2 SSR  Coefficient of Determination： R  SST</p><p>Model Adequacy Checking</p><p> Residual Analysis  Normal Plot</p><p> Plot of Residuals Against yˆi</p><p> Plot of Residuals Against xi  Plot of Residuals Against Times</p><p> Detection of Outliers</p><p> Lack of Fit  Transformation to a Straight Line</p><p>Multiple Linear Regression</p><p>2  y0   1 x 1   2 x 2 ...  k x k   ；~NID (0,  ) ˆ ˆ ˆ ˆ  Estimations of Parameters（OLS）： yˆ   0  1 x1   2 x2  ...   k xk</p><p>ANOVA for Multiple Linear Regression</p><p> ANOVA Table Source SS df MS F P</p><p>2 Regression SSR k MSR MSR P[F>F*] F *  MSE Residual SSE n-k-1 MSE Total SST n-1</p><p> Testing Hypothesis for i s</p><p> Testing Hypothesis for i</p><p>2 SSR  Coefficient of Determination： R  SST</p><p>2n 1 2  Adjusted R1  (1  R ) n p</p><p>Stepwise Regression Selection Procedures</p><p> Forward Selection</p><p> Backward Selection</p><p> Stepwise Selection</p><p>Multicollinearity Diagnostics</p><p> Examination of the Correlation Matrix</p><p> Variance of Inflation Factors (VIF)</p><p> Eigenvalues</p><p>Dealing with Multicollinearity</p><p> Collecting Additional Data</p><p> Model Respecification/Variable Elimination</p><p> Ridge Regression</p><p> Generalized Ridge Regression</p><p> Principal Component Regression</p><p> Latent Root Regression</p><p>3 Other Topics</p><p> Autocorrelation</p><p> Robust Regression</p><p> Nonlinear Regression</p><p> Logistic Regression</p><p>4</p>