732G21/732G28/732A35 Lecture 2

Inference concerning β 1  Confidence interval for β 1 : where  Test concerning β 1 : H 0 : β 1 = 0 H a : β 1 ≠ 0 Reject H 0 if |t*| > t(1-α/2;n-2) 2

Inference concerning β 0  Confidence interval för β 0 : where 3

4 POINT ESTIMATE CONFIDENCE INTERVAL The expected response E(Y h ) for all units in the population with X = X h In our example: expected salary for all 25-year olds in the population PREDICTION INTERVAL The expected response Y h(new) for one specific unit in the population with X = X h In our example: expected salary for one specific 25-year old in the population

Confidence interval for E(Y h ) 5 where

Prediction interval of Y h(new) 6 where

ANOVA table 7 Source of variation SSdfMS Regression1 Errorn - 2 Totaln - 1

F Test H 0 : β 1 = 0 H a : β 1 ≠ 0 Reject H 0 if F* > F(1-α;1, n-2) 8

Measures of linear association  Coefficient of determination:  Coefficient of correlation: 9