Stat 5122
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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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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 Spring '11
 libo
 Statistics, Linear Regression, Normal Distribution, Regression Analysis, Standard Deviation, Prediction interval, PROC GPLOT

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