Confidence Estimation of an Unknown Component of the Vector of Regressor Variables in Multivariate Linear Regression

The model used in this paper is Y = X β, where withunknown x 0 . Estimators of x 0 are derived by putting β m x 0 =β m+1 regarding β m+1 as a new unknown parameter. Formally we use the model Y = X 1 β + + e where β′ + = (β 0 , …β m+1 andThen β m+1 / β m is a point estimator of x 0 . Assuming normality for e and taking the random variable z=β m x 0 −β m+1 we get a t ‐distributed variable and finally a confidence estimator of x 0 . The formulas are applied in dose response relations in antibiotic assays refering to a standard. Now we can take into account not only the dependence on the dose/concentration but also on the position on the test agar plate where the test solution is filled in. As a consequence the confidence interval of the unknown dose/concentration x 0 becomes shorter and by it the statements more precise.