Assignment # 1 2

Note: All answers to be completed in SAS. All SAS input and output must pasted in to the solutions.

Other Statistical software, such as Minitab, JMP, SPSS, R, and MATLAB, are also allowed to use .

1. Consider the data set and setting described in Montgomery Problem 5-7.

1. Construct an interaction plot and describe what the plot tells you in regards to main effects and interaction.
2. Analyze the residuals, making sure to comment on each of the model assumptions.
3. Statistically assess the main effects and interaction using \(\alpha=.05\).
4. Based on the results in c), perform any appropriate pairwise comparisons and draw conclusions.

DATA set file chap05prob07.dat is attached with the email.

[1] 5.7. Johnson and Leone (Statistics and Experimental Design in Engineering and the Physical Sciences, Wiley, 1977) describe an experiment to investigate warping of copper plates. The two factors studied were the temperature and the copper content of the plates. The response variable was a measure of the amount of warping. The data were as follows:

2. Suppose prior information suggests that warping is linearly related to the copper content. Do these data support this? Test if the full model used in \(\# 1\) is necessary or whether a reduced one assuming a linear relationship (possibly differing by temperature) with copper content is acceptable. Make sure to specify the \(F\) statistic, its degrees of freedom, and \(P\) -value.

3. A three-factor study involves \(a=4\) levels of Factor \(\mathrm{A}, b=3\) levels of Factor \(\mathrm{B}\) and \(c=2\) levels of Factor C. Each combinations is observed \(n=5\) times. All factors are fixed so the MSE is our estimate of the only error term. What is the standard error of

\(\bar{y}_{i j k} ?\)

- \(\bar{y} \ldots ?\)

- \(\bar{y}_{i j . .}-\bar{y}_{i^{\prime} j . .} ?\)

- \(\bar{y}_{. j . .} ?\)

- \(\bar{y}_{i \ldots}-\bar{y}_{i^{\prime} \ldots} ?\)

4. Suppose another experiment was performed to assess the capability of a measurement system. Ten parts were randomly selected from the production line and five randomly selected operators measured each part three times. The data set can be found on the course webpage titled hw9.dat. Let's analyze the data from this experiment assuming both part and operator are random.

1. Analyze the residuals.
2. Provide variance estimates for all model variances.
3. What is the estimated percent of total variability that is due to part variability?

6. Refer to Exercise #4. Reanalyze the data now assuming that the operators are fixed, using both the restricted and unrestricted forms of the mixed model. Compare the results obtained from the two models. Given that operator is now fixed, your analysis should perform pairwise comparisons if the \(F\) test for operator is significant. Likewise for significant random factors, you should provide variance estimates and \(95 \%\) confidence intervals.

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Solution: The downloadable solution consists of 12 pages, 1114 words and 5 charts.
Deliverable: Word Document