732G21/732G28/732A35 Lecture 3

Properties of the model errors ε 4. ε are assumed to be normally distributed

Properties of the residuals e The residuals shall be approximately normally distributed The residuals can not be considered as independent random variables. This is due to that the calculation of all residuals involves the fitted values, which are based on the same equation.

1. Non-linearity of the regression function  Residuals against the predictor variable (X)  Residuals against the fitted values ( ) 4 2. Nonconstancy of error variance  Residuals against the predictor variable (X)  Residuals against the fitted values ( )

3. Presence of outliers  Residuals against the predictor variable (X)  Residuals against the fitted values ( )  Dot plots of the residuals Nonindependecy of error terms  Residuals against time (the order in which observations were made)

5. Non-normality of error terms  Normality plot of residuals  Histogram of residuals 6 6. Omission of important predictors  Plotting the residuals versus those potentially important variables

Four in one plot from Minitab 7

An experiment for investigating the effect of the number of days of training (X) on performance in sales situations (Y) has been conducted. 8 Days of training (X)Performance score (Y)

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Family confidence coefficient for estimation of β 0 and β 1 Let Then,  Interval estimate for β 0  Interval estimate for β 1 12

Family confidence coefficient for confidence intervals  The Working-Hotelling procedure:  The Bonferroni procedure: 13 where

Family confidence coefficient for prediction intervals  The Scheffé procedure:  The Bonferroni procedure: 14 where