Assignment Total 9 questions

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

Question 1

An analyst fitted normal error regression model (2.1) and conducted an \(F\) test of \(\beta_{\mathrm{I}}=0\) versus \(\beta_{1} \neq 0\). The \(P\) -value of the test was .033, and the analyst concluded \(H_{a}: \beta_{1} \neq 0\). Was the \(\alpha\) level used by the analyst greater than or smaller than .033? If the \(\alpha\) level had been .01, what would have been the appropriate conclusion?

Throughout this chapter (excluding Section 2.11), and in the remainder of Part I unless otherwise stated, we assume that the normal error regression model (1.24) is applicable. This model is:

\(Y_{i}=\beta_{0}+\beta_{1} X_{i}+\varepsilon_{i}\)

where:

\(\beta_{0}\) and \(\beta_{1}\) are parameters

\(X_{i}\) are known constants

\(\varepsilon_{i}\) are independent \(N\left(0, \sigma^{2}\right)\)

Question 2

Using the normal error regression model (2.1) in an engineering safety experiment, a researcher found for the first 10 cases that \(R^{2}\) was zero. Is it possible that for the complete set of 30 cases \(R^{2}\) will not be zero? Could \(R^{2}\) not be zero for the first 10 cases, yet equal zero for all 30 cases? Explain.

Throughout this chapter (excluding Section 2.11), and in the remainder of Part I unless otherwise stated, we assume that the normal error regression model (1.24) is applicable. This model is:

\(Y_{i}=\beta_{0}+\beta_{1} X_{i}+\varepsilon_{i}\)

where:

\(\beta_{0}\) and \(\beta_{1}\) are parameters

\(X_{i}\) are known constants

\(\varepsilon_{i}\) are independent \(N\left(0, \sigma^{2}\right)\)

Question 3

Calculate power for the slope using the results of text Problem 1.22 as follows. Assume n = 16, 𝜎2 = MSE, and SSX = 1280. (Note: this last value could be obtained with SAS using

proc univariate data = (dataset name);

var time;

and looking at the output titled "Corrected SS" in the Moments section.)

1. Find the power for rejecting the null hypothesis that the regression slope is zero using alpha = 0.08 significance test when the alternative is 𝛽1 = 0.9.
2. Plot the power as a function of 𝛽1 for values of 𝛽1 between -2.7 and +2.7 in increments of 0.3.

The next 5 problems continue the analysis of the plastic hardness data begun in the first assignment , question 1.22

Question 4

Plot the data using proc gplot. Include a smoothed function on the plot by using the i = smnn option on the symbol1 statement, where nn is a number between 1 and 99. Is the relationship approximately linear?

Question 5

Plot the 85% bounds (confidence band) for the mean (use i=rlclm on the symbol1 statement).

Question 6

Plot the 85% bounds for individual observations (using i=rlcli).

Question 7

Give an estimate of the mean hardness that you would expect after 37 and 41 hours; and an 85% confidence interval for each estimate. Which confidence interval is wider and why is it wider?

Question 8

Give a prediction for the hardness that you would expect for an individual piece of plastic after 41 hours; give an 85% prediction interval for this quantity.

Question 9

Given that \(R^{2}=\mathrm{SSM} / \mathrm{SST}\), it can be shown that \(\frac{R^{2}}{1-R^{2}}=S S M / S S E\). If you have \(\mathrm{n}=25\) cases and \(R^{2}=0.35\), what is the F-statistic for the test that the slope is equal to zero?

Price: $31.87

Solution: The downloadable solution consists of 19 pages, 1287 words and 20 charts.
Deliverable: Word Document