Homework02Solns - Stat 512-2 Solutions to Homework#2 Dr...

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Stat 512-2 Solutions to Homework #2 Dr. Simonsen Due Wednesday, September 7, 2005. The next 5 problems continue the analysis of the plastic hardness data begun on HW #1 (CH01PR22.DAT) . 1. Give an estimate of the mean hardness that you would expect after 36 and 43 hours; and a 95% confidence interval for each estimate. Which confidence interval is wider and why is it wider? Output Statistics Dep Var Predicted Std Error Obs time hard Value Mean Predict 95% CL Mean 95% CL Predict 17 36 . 241.8375 1.0847 239.5110 244.1640 234.5214 249.1536 18 43 . 256.0781 1.5787 252.6922 259.4640 248.3595 263.7967 X = 36: , CI for the mean is [239.5110, 244.1640] ˆ 241.8375 Y = X = 43: , CI for the mean is [252.6922, 259.4640] ˆ 256.0781 Y = The confidence interval for X = 43 is wider because 43 is farther away from the mean X than is 36, and so the standard error for the prediction is larger. 2. Give a prediction for the hardness that you would expect for an individual piece of plastic after 43 hours; and a 95% prediction interval for this quantity. X = 43: , CI for an individual observation is [248.3595, 263.7967] ˆ 256.0781 Y = 3. Plot the data using PROC GPLOT with (a) the 95% bounds (confidence band) for the mean (use i=RLCLM on the SYMBOL1 statement). Conf i dence band f or t he mean 190 200 210 220 230 240 250 260 time ( hour s) 10 20 30 40
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(b) the 95% bounds (confidence band) for individual observations (use i=RLCLI ) Conf i dence band f or i ndi vi dual obser vat i ons 190 200 210 220 230 240 250 260 time ( hour s) 10 20 30 40 4. NKNW Problem 2.26. To change the axis on a plot, add an “order” statement to the axis definition. For example, to make the vertical axis go from -30 to 30 in increments of 10, do axis3 label=(angle=90 ‘Residuals’) order=(-30 to 30 by 10); Then use vaxis=axis3 as an option to the plot statement, along with haxis and vref=0 . The mean value of Y appears as Dependent Mean in the output from proc reg . 2.26: Refer to Plastic hardness Problem 1.22. (a) Set up the ANOVA table. Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 5297.51250 5297.51250 506.51 <.0001 Error 14 146.42500 10.45893 Corrected Total 15 5443.93750 (b) Test by means of an F test whether or not there is a linear association between the hardness of the plastic and the elapsed time. Use a = .01. State the alternatives, decision rule, and conclusion.
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Homework02Solns - Stat 512-2 Solutions to Homework#2 Dr...

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