Regression Analysis: Linear and Quadratic Relationship between Distance and Height, Study notes of Statistics

Download Regression Analysis: Linear and Quadratic Relationship between Distance and Height and more Study notes Statistics in PDF only on Docsity! Stat 333 Spring 2004 2/26/2004 Discussion 5 1 Matrix Let Ap×q = {aik} Bp×q = {bik} Cq×p = {cjl} Show (A′)′ = A, (A + B)′ = A′ + B′, (AC)′ = C′A′, and (A−1)′ = (A′)−1. 2 General Linear Regression Consider Galileo’s data. Horizontal Distance Initial Height (punti) (punti) 253 100 337 200 395 300 451 450 495 600 534 800 573 1000 Determine the matrices, X′Y, X′X, (X′X)−1, and β̂ = (X′X)−1X′Y for the following models. a. (distance)i = β0 + β1(height)i + i. b. (distance)i = β0 + β1(height)i + β2(height) 2 i + i. Now fit the model using Minitab. a. (distance)i = β0 + β1(height)i + i. Regression Analysis: Distance versus Height The regression equation is Distance = 270 + 0.333 Height Predictor Coef SE Coef T P Constant 269.71 24.31 11.09 0.000 Height 0.33334 0.04203 7.93 0.001 S = 33.6785 R-Sq = 92.6% R-Sq(adj) = 91.2% Analysis of Variance Source DF SS MS F P Regression 1 71351 71351 62.91 0.001 Residual Error 5 5671 1134 Total 6 77022 4268 CSSC ting-li@stat.wisc.edu Ting-Li Lin