HW3.Solutions

# HW3.Solutions - Name Section Biological Statistics II...

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Name: Biological Statistics II Section: Biometry 3020 / Natural Resources 4130 / Statistical Science 3200 Homework 3 Due on Thursday February 18 1. (4 points) KNNL 6.23 a. Consider the multiple regression model n i X X Y i i i i ,..., 1 2 2 1 1 = + + = ε β β where the i ε are uncorrelated, with 0 } { = i E ε and 2 2 } { σ ε σ = i . State the least squares criterion and derive the least squares estimators of 1 β and 2 β and their corresponding variance. Make sure to define all terms 2. Zinc lozenges having a positive Zinc Ion Availability (ZIA) value reduce the duration of common colds in a dose-response manner. Lozenges with ZIA = = = - - = - - = = 2 1 2 1 21 11 1 1 2 2 2 1 1 ) ,..., ( ) ( )' ( ) ( β β β β β X Y Y Y n n t n n i i i i X X X X Y Y Q X X Y Q X Y X X Y X β X β Y X β Y Y Y Y ' ' ' 2 ' 2 ' ' ' ' 2 ' ) ( )' ( = + - = + - = - - = d dQ Q 1 1 1 1 1 1 1 ) ' ( ) ' ( ' ) ' ( ) ' ( ) ( ' ) ' ( ) ' ) ' (( ) ( ' ) ' ( - - - - - - - = = = = = X X X X X X X X X X X X X X Y X X X b Y X X X b MSE MSE Y V V V

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of 25 reduced duration of colds by about 1-1/2 day, while lozenges having a ZIA value of 44 reduced the duration of colds by 4.8 days, and lozenges having a ZIA value of 100 reduced the duration of colds by 7 days. Lozenges having a zero ZIA did not have any effect on colds. Zinc lozenges releasing negatively charged zinc species at physiologic pH and increased the duration and severity of common colds in a dose-response manner.
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