Question 1:

Program a function, making use oflm()to fit the linear regression model, that outputs the six coefficient estimates.Set R's seed to 2:

set.seed(2, sample.kind = "Rounding")

and then useboot()to produceR= 1000 bootstrap estimates for each of?(0), ?(1),?(2),?(3),?(4), and?(5)

Enter your R code below.

Use your bootstrap estimates to estimate the standard error,SE(?(hat)i), for each ofi= 0, 1, 2, 3, 4, 5.

Question 2:

SE(?(hat)0) =

Question 3:

SE(?(hat)1) =

Question 4:

SE(?(hat)2) =

Question 5:

SE(?(hat)3) =

Question 6:

SE(?(hat)4) =

Question 7:

SE(?(hat)5) =

Question 8:

The standard errors estimated from usual linear regression methods are shown in the R output below:

Coefficients:

Estimate Std.Error t value PR(>|t|)

(Intercept) 48.914179 90.852925 0.538 0.595

Girth -8.228180 13.803580 -0.596 0.556

Height -0.616152 1.250446 -0.493 0.626

GirthHeight 0.103075 0.180291 0.572 0.573

Girth2 0.311160 0.536379 0.580 0.567

Girth2Height -0.001764 0.006621 -0.266 0.792

How do these values compare to the standard errors computed in the previous set of questions?

Choose one of the following:

1. The estimates from usual linear regression methods aregreater.
2. The estimates from usual linear regression methods areless.
3. The two sets of estimates areabout the same.

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