STATGU4206Homework3 sol - STAT GU4205/5205 Homework 3[100...

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STAT GU4205/5205 Homework 3 [100 pts]Due 6:10 pm Thursday, October 20thProblem 1[15 pts]Consider the modelYi=μ+ii= 1,2, . . . , niiidN(0, σ2).The sample mean and sample variance are defined respectively as¯Y=1nnXi=1YiandS2Y=1n-1nXi=1(Yi-¯Y)2.Prove that the sample mean¯Yand sample varianceS2Yare independent random vari-ables.
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Problem 2[36 pts]Consider thesingle factor anova modelwith three groups. The three groups are drug dose1, drug dose 2 and control. Letn1and ¯y1respectively denote the number of respondentsand sample mean response for drug dose 1 group. Letn2and ¯y2respectively denote thenumber of respondents and sample mean response for drug dose 2 group.Letn3and ¯y3respectively denote the number of respondents and sample mean response for the controlgroup. Note that
i. Write down the design matrix and response vector describing model (1).(6 pts)
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ii. Compute (XTX)-1and simplify the result. This requires inverting a 3
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