代做留学统计作业 STAT 404代写 统计代写 R语言作业代写

STAT 404 – Assignment 4

Total marks: 45 + 1 bonus

代做留学统计作业 The data set in the file PaperHelicopter.txt was contributed by a volunteer student (one of you). Two factors are considered in the experiment: the

1. 代做留学统计作业

The data set in the file PaperHelicopter.txt was contributed by a volunteer student (one of you).

Two factors are considered in the experiment: the length of the wing (in cm) and the number of clippers used as weight. There are n = 4 replicates for each combination of the levels (also called a run or treatment). The response value is the time (in seconds) it takes to reach the ground from a height of 2 meters.

Use a fixed-effects model for data analysis. You may use the following code to read in the data set:

dat = read.table("PaperHelicopter.txt", header=T)
dat$length = factor(dat$length)
dat$clips = factor(dat$clips)

(a) [6] Obtain the estimated treatment effects of both factors and their interactions.

(b) [2] Estimate the variance of the experimental error.

(c) [6] Construct the complete analysis of variance table (including p-values for testing the standard hypotheses).

(d) [6] Construct a two-sided 95% confidence interval for effect difference (may also be called a contrast) α₃ − α₁ for factor length with levels {1, 2, 3} being the lengths {7, 8, 9} cm. Remark: not simultaneous CI.

2. 代做留学统计作业

Repeat the in-class example on “fabricating integrated circuit”. An initial step of this process is to grow an epitaxial layer on polished silicon wafers. It is desired to have the actual thickness as close to 14.5 µm, and within the limits [14, 15].

The data are given in the following table. There are n = 6 replicates in each run. Note the data set may be different from the one in lecture.

ybar = c(14.58, 13.59, 14.29, 14.05, 14.59, 13.97, 14.43, 14.11, 14.81, 13.81, 13.73, 13.90, 14.44, 13.94, 14.36, 14.18)
ss = c(0.272, 0.289, 0.263, 0.196, 0.221, 0.207, 0.226, 0.212, 0.269, 0.268, 0.217, 0.228, 0.224, 0.258, 0.255, 0.195)

(a) [8] Construct the ANOVA table including all effects for the mean response (the class example omitted some for the ease of presentation).

(b) [4] Identify the significant effects based on F-tests.

(c) [4] Create the normal and half-normal plots for the estimated effects.

(d) [4] Construct a 95% two-sided CI for the effect of D.

3.

[5] Under the model assumption for the randomized block design as given in this course, the four terms in the decomposition of the response y_ij are mutually independent. The proof in the lecture slides is not complete nor well-organized (due to the nature of lecturing).

Choose any two pairs of these four terms (same ones are also accepted) and show that they are independent. Be sure to add more concrete details and explanations.

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