Transcription of Chapter 2: Simple Linear Regression - Purdue University
{{id}} {{{paragraph}}}
Example: bachelor of science
Chapter 2: Simple Linear Regression - Purdue University
Chapter 2: Simple Linear Regression1 The modelThesimple Linear regressionmodel fornobser-vations can be written asyi= 0+ 1xi+ei, i= 1,2, ,n.(1)The designationsimpleindicates that there is onlyone predictor variablex, andlinearmeans thatthe model is Linear in 0and 1. The intercept 0and the slope 1are unknown constants, andthey are both calledregression coefficients;ei sare random errors. For model (1), we have thefollowing (ei) = 0fori= 1,2, ,n, or, equiva-lentlyE(yi) = 0+ var(ei) = 2fori= 1,2, ,n, or, equiva-lently, var(yi)) = (ei,ej) = 0for alli6=j, or, equivalently,cov(yi,yj) = Ordinary Least Square EstimationThemethod of least squaresis to estimate 0and 1so that the sum of the squares of the differ-ence between the observationsyiand the straightline is a minimum, , minimizeS( 0, 1) =n i=1(yi 0 1xi) = XE(Y|X=x) 1=Slope 0=Intercept1 Figure 1: Equation of a straight lineE(Y|X=x) = 0+ least-squares estimators of 0and 1, say 0and 1, must satisfy 2n i=1(yi 0 1xi) = 0(2) 2n i=1(yi 0
Variation Squares Freedom Square Regress SS R =βˆ1S xy 1 MS R MS R MS Res Residual SS Res =SS T −βˆ1S xy n−2 MS Res Total SS T n−1 Table 1: Analysis of Variance (ANOVA) for testing significance of regression that is, it is likely that the slope β 1 6= 0 if the ob-served value of F 0 is large. The analysis of variance is summarized ...
Loading..
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document: