Course Notes - Department of Mathematics and Statistics

Extra sum of squares modelSource of variation SS DF MS FRegression(age,ht) 41.703 2Regression(sex| age,ht) (2.602) (1) 2.602 1.950Regression(sex,age,ht) 44.305 3 14.768Residual (Error) 37.407 28 1.336Total 81.712 31• This F statistic is not significant, meaning there is no evidencethat sex affects TLC after allowing for age and height.• The effect of sex was contained in the residual when TLC was expressedin terms of age and height only. The effect of the residualwas therefore greater.• The real effect of intersect can be hidden by residual variabilityreducingthis residual variability by including more predictors inthe model can improve the analysis (and therefore the study).The p-values associated with hypothesis tests for the parametersof interest will generally be smaller.• Confounders can affect the parameter estimates of the predictorvariables of interest as well as the residual variability. Thereforeincluding confounders in the model is important for obtainingvalid estimates of the coefficients of interest regardless of the reductionin the residual variability.Rule of Thumb• For multiple linear regression, we should not perform the analysisif the number of variables in the model is greater than the numberof individuals divided by 10.243