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STAT 350 – Fall 2008
Lab #10
Solution
DUE:
Friday, December 12
th
@ 4:30 p.m.
For her senior thesis, an undergraduate in biology wanted to study the effect of crowding (population
density) on fecundity (egg production) using
Tribolium
(flour) beetles.
She had 80 jars of flour.
She
controlled the density (number of beetles per jar) in her experiment and then would measure the
number of eggs produced.
Dividing the number of eggs by the number of adults would give a measure
of the fecundity of the population (she decided it would be impossible to sex all the beetles which is
why she is not measuring fecundity as #eggs per female).
She used density levels ranging from 100 to
2000 beetles per jar and replicated each density level 4 times.
The results of her experiment are given
in the accompanying Excel file.
Unless otherwise indicated, all plots and analyses for this lab are to be done using SAS.
Please put all
SAS input (contents of the editor window) and all SAS output (contents of the Output window) as an
appendix.
Nothing pasted directly from SAS should be given as an answer to the questions below
(
except for graphs
)!
1.
This part should not
be done in SAS
.
One thing that she is interested in is estimating the
fecundity when the population density is 1000.
Using the 4 observations for fecundity when
density was 1000, give a point estimate for the predicted # eggs/female and give a 90% prediction
interval (be sure to show your work).
Consider this early review – this has nothing to do with
regression
.
The 4 fecundities with density = 1000, were 1.32, 1.14, 1.45, and 1.37
the average of these 4 fecundities is 1.32, the standard deviation is 0.131403
The sum of the 4 observations is 5.28, the sum of the squares is 7.0214
SS
yy
= 7.0214 – 5.28
2
/4 = 0.0518
90% PI:
N
1
1.32
2.353
0.131403 1
4
with df=3
t
±+
→
0.97431 to 1.66569
2.
No transformations:
Use density as the independent variable (
x
) and fecundity as the dependent
variable (
y
).
a.
Using SAS, find the least squares regression equation to predict fecundity from density.
ˆ
4.79201 0.00254
f
d
=−
b.
Using SAS, give a point estimate for the predicted fecundity (# eggs/female) and give a 90%
prediction interval for the fecundity (# of eggs/adult) when the density is 1000.
Point Estimate:
2.2505
90% PI:
0.5002
to
4.0007
Lab #10 Solution
Page 1 of 13
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View Full Document c.
Is this regression "significant"?
Give the value of the appropriate test statistic, along with its
degrees of freedom.
Yes.
F
= 157.37,
df
1
= 1,
df
2
= 78,
p
< 0.0001
OR
Yes.
t
= 12.55,
df
= 78,
p
< 0.0001
d.
Using the plot option in PROC REG, give a scatter plot of fecundity versus density with the
fitted regression line.
f ecundi t y = 4. 792  0. 0025 densi t y
N
80
Rsq
0. 6686
Adj Rsq
0. 6644
RMSE
1. 0449
0
1
2
3
4
5
6
7
8
9
densi t y
0
250
500
750
1000
1250
1500
1750
2000
e.
Using the plot option in PROC REG, give the residual plot from this regression analysis.
What
does this plot tell you about your analysis?
N
80
2
1
0
1
2
3
4
0
Lab #10 Solution
Page 2 of 13
f.
Using PROC UNIVARIATE, give a QQ plot of the residuals.
What does this plot tell you
about your analysis?
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This note was uploaded on 02/23/2009 for the course STAT 350 taught by Professor Staff during the Fall '08 term at Purdue University.
 Fall '08
 Staff

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