Final Exam Essay

Final Exam Essay Final Exam Essay Chapter 11 – Simple linear regression Types of Regression Models (Sec. 11-1) Linear Regression: - Outcome of Dependent Variable (response) for ith experimental/sampling unit - Level of the Independent (predictor) variable for ith experimental/sampling unit - Linear (systematic) relation between Yi and Xi (aka conditional mean) - Mean of Y when X=0 (Y-intercept) - Change in mean of Y when X increases by 1 (slope) - Random error term Note that and are unknown parameters. We estimate them by the least squares method. Polynomial (Nonlinear) Regression: This model allows for a curvilinear (as opposed to straight line) relation. Both linear and polynomial regression are susceptible to problems when predictions of Y are made outside the range of the X values used to fit the model. This is referred to as extrapolation. Least Squares Estimation (Sec. 11-2) 1. Obtain a sample of n pairs (X1,Y1)†¦(Xn,Yn). 2. Plot the Y values on the vertical (up/down) axis versus their corresponding X values on the horizontal (left/right) axis. 3. Choose the line that minimizes the sum of squared vertical distances from observed values (Yi) to their fitted values ( ) Note: 4. b0 is the Y-intercept for the estimated regression equation 5. b1 is the slope of the estimated regression equation Measures of Variation (Sec. 11-3) Sums of Squares ï‚ § Total sum of squares = Regression sum of squares + Error sum of squares ï‚ § Total variation = Explained variation + Unexplained variation ï‚ § Total sum of squares (Total Variation): ï‚ § Regression sum of squares (Explained Variation): ï‚ § Error sum of squares (Unexplained Variation): Coefficients of Determination and Correlation Coefficient of Determination ï‚ § Proportion of variation in Y â€Å"explained† by the regression on X ï‚ § Coefficient of Correlation ï‚ § Measure of the direction and strength of the linear association between Y and X ï‚ § Standard Error of the Estimate (Residual Standard Deviation) ï‚ § Estimated standard