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Tilastollinen tietojenk¨asittely Exercise 3 7.11.2006 1. Maindonald 3.9.6. 2. Maindonald 3.9.8. 3. Maindonald 3.9.10. 4. Fibonacci series is defined as follows:  a

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Jaa "Tilastollinen tietojenk¨asittely Exercise 3 7.11.2006 1. Maindonald 3.9.6. 2. Maindonald 3.9.8. 3. Maindonald 3.9.10. 4. Fibonacci series is defined as follows:  a"

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Tilastollinen tietojenk¨asittely Exercise 3

7.11.2006

1. Maindonald 3.9.6.

2. Maindonald 3.9.8.

3. Maindonald 3.9.10.

4. Fibonacci series is defined as follows:

 a1= 1 a2= 1

an+2=an+an+1.

Make a function, which calculates the terms a) rekursively b) iteratively.

5. Inwtlosdata (Library MASS) test the degree of polynomial model needed when the dependent variable is Weight and the explanatory variable is Days. Investigate the distribution of residuals and make the appropriate tranformations if needed.

6. Write a function which generatesnvectors from the regression model y=Xβ+,

where ∼N(0, σ2I). Numbern, X, β andσ2 should be given as argu- ments. Hint: Use rnorm().

7. Use your function forn= 1000 and for some appropriate choices ofX,β andσ2. Investigate now the distribution of the estimates ˆβ.

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