Introduction to Statistics, Lecture 11 - Regression Analysis (Chapter ...

Inferences for the Regression ModelInference for intercept and slopeInference for intercept and slopeInferences for the Regression ModelInferences for intercept and slopeInference for intercept and slopeWe want to test the hypotheses about the intercept withthe y-axisThe test statistic ist =H 0 :H 1 :α = aα ≠ a√(a − α) nS xxs e S xx + n(¯x) 2The critical value is found in the t-distribution, t α/2 (n − 2)We want to test a hypothesis about the slope βThe test statistic ist =H 0 :H 1 :β = bβ ≠ b(b − β) √Sxxs eThe critical value is found in the t-distribution, t α/2 (n − 2)Per Bruun Brockhoff (pbb@imm.dtu.dk) Introduction to Statistics, Lecture 11 Fall 2012 22 / 32Per Bruun Brockhoff (pbb@imm.dtu.dk) Introduction to Statistics, Lecture 11 Fall 2012 23 / 32Inferences for the Regression ModelConfidence Intervals for α and βInference for intercept and slopeInferences for the Regression ModelConfidence Interval for α + βx 0Confidence interval for the lineConfidence interval for αConfidence interval for βa ± t α/2 · s e√1n + (¯x)2S xxb ± t α/2 · s e1√SxxA confidence interval for α + βx 0 corresponds to aconfidence interval at the point x 0√1(a + bx 0 ) ± t α/2 · s en + (x 0 − ¯x) 2S xxPer Bruun Brockhoff (pbb@imm.dtu.dk) Introduction to Statistics, Lecture 11 Fall 2012 24 / 32Per Bruun Brockhoff (pbb@imm.dtu.dk) Introduction to Statistics, Lecture 11 Fall 2012 25 / 32