Midterm 2
Biometry 333
Fall 2006
Name:____________
You are allowed a calculator, clean probability tables, Minitab, R, a 3-by-5 inch note card of
notes. No use of neighbors or internet is allowed.
Show all work. Ask the instructor if a question is not clear.
Each problem is worth 4 points.
(1) DDT levels were measured in falcons captured at nesting sites in the US, Canada, and near the
Arctic. The age of the falcons were also recorded as young, old, or middle-aged. The word
formula for the fitted model was DDT = NESTING + AGE.
(1a) What is the coefficient value for “young” falcons? Show your work.
(1b) What is the expected DDT level of the “old” falcons found at Arctic nest sites?
(1c) Was there a statistically significant difference in mean levels of DDT between different
nesting sites? (Yes or No.) Very specifically explain how you reached your decision.
(1d) One of the F-statistics in the ANOVA table has been replaced by FFFFF. Calculate the Fstatistic that belongs in the place of FFFFF.
(1e) The fitted model was DDT = NESTING + AGE + N(0,  2 ), where N(0,  2 ) is the normally
distributed error term. Estimate the standard deviation  and explain how you derived your
answer.
(1f) Which falcons have the greatest DDT concentrations?
(1g) The adjusted mean squares for NESTING was replaced by AAAAAA. Calculate the value
for AAAAAA. Show your work.
(1h) If an interaction model DDT = NESTING|AGE were fit, how many degrees of freedom
would the NESTING*AGE interaction component of the model use?
1
(2) The weight, height, gender, and brain size (kilopixel count from MRIs) were measured on
volunteer college students. The word formula for the fitted model is: kilopixel = Height +
Weight + Gender.
(2a) In kilopixels, what is the expected difference in brain sizes between men and women of the
same height and weight? Which gender has the greater kilopixel count? Show your work.
(2b) Calculate the R-square value for this model. Show your work.
(2c) A female weighed 140 pounds and was 68 inches tall. Calculate her expected kilopixel
count.
(2d) The p-value for Gender has been replaced with XXXXX in the ANOVA table. Calculate the
p-value. Show your work.
(2e) Calculate a 95% confidence interval for the Height coefficient. Show your work.
(2f) Calculate the t-statistic and p-value for the Weight coefficient. They have been replaced by
TTTT and YYYYY in the Coefficient table. Show your work.
(2g) Write the equation for the line that represents the males and another equation that represents
the females. (Have your equations in the y=a+bx format.)
2
(2h) For each inch increase in height, how much does the expected kilopixel count
increase(decrease)?
(2i) What would be the sum of squares error for the model with the word formula:
kilopixel=Height + Gender? Show your work.
(3) The systolic blood pressure (mm Hg), age (years), and calf skin fold (mm, a measure of body
fat) were measured on Peruvian men. Age, calf skin fold, and their interaction were used to
predict blood pressure. The word formula for the fitted model was Systol=Age|Calf.
(3a) A man aged 32 years had a calf skin fold of 6mm. Calculate his predicted blood pressure.
Show your work.
(3b) Explain how the total sum of squares, 6531.4, was calculated. Be very specific. (You do not
have the information available to actually do the calculation.)
(3c) Calculate the sum of squares error for the model: Systol   0  1Calf ? Show your work.
3
(4) Various characteristics of flowering trillium plants were measured: leaf length (cm), stem
length (cm), and flower type (p=pink, s=seeded, or w=white). Leaf length, flower type, and their
interaction were used to predict stem length. The word formula for the fitted model was: stem =
leaf|flower.
(4a) Provide the equations for the predicted stem length when given the leaf length for each of the
three flower types. (Use the line equation y=a+bx format.)
(4b) Test whether the leaf coefficient is equal to 0.4. Show your work and provide a p-value.
(5) In general, explain how the sum of squares error for a model is calculated.
(6) Suppose you have a model: y   0  1 x1   2 x2   3 x3 .
(6a) In general, how is the sequential sum of squares calculated for x 2 ?
(6b) In general, how is the adjusted sum of squares calculated for x 2 ?
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Problem 1
General Linear Model: DDT versus NESTING, AGE
Factor
NESTING
AGE
Type
fixed
fixed
Levels
3
3
Values
Arctic, Canada, US
middleAged, old, young
Analysis of Variance for DDT, using Adjusted SS for Tests
Source
NESTING
AGE
Error
Total
DF
2
2
22
26
Term
Constant
NESTING
Arctic
Canada
AGE
middleAged
old
Seq SS
17785.4
1721.2
79.7
19586.3
Adj SS
17785.4
1721.2
79.7
Adj MS
AAAAAA
860.6
3.6
F
2454.58
FFFFF
Coef
44.3704
SE Coef
0.3663
T
121.13
P
0.000
36.2963
-18.2593
0.5180
0.5180
70.07
-35.25
0.000
0.000
-0.1481
9.8519
0.5180
0.5180
-0.29
19.02
0.778
0.000
P
0.000
0.000
Problem 2
General Linear Model: kilopixel versus Gender
Factor
Gender
Type
fixed
Levels
2
Values
Female, Male
Analysis of Variance for kilopixel, using Adjusted SS for Tests
Source
Height
Weight
Gender
Error
Total
Term
Constant
Height
Weight
Gender
Female
DF
1
1
1
34
37
Seq SS
67442
3950
17721
105700
194813
Adj SS
3492
641
17721
105700
Adj MS
3492
641
17721
3109
F
P
1.12 0.297
fffff YYYYY
5.70 XXXXX
Coef
603.1
3.895
0.2574
SE Coef
225.8
3.675
0.5667
T
2.67
1.06
TTTT
P
0.012
0.297
YYYYY
-31.87
AAAAA
BBBB
XXXXX
5
Problem 3
General Linear Model: Systol versus
Factor
Type
Levels
Values
Analysis of Variance for Systol, using Adjusted SS for Tests
Source
Calf
Age
Age*Calf
Error
Total
DF
1
1
1
35
38
Seq SS
410.8
0.3
188.9
5931.4
6531.4
Term
Constant
Calf
Age
Age*Calf
Coef
100.53
3.058
0.5944
-0.06660
Adj SS
329.8
157.8
188.9
5931.4
SE Coef
21.77
2.192
0.6160
0.06308
Adj MS
329.8
157.8
188.9
169.5
T
4.62
1.39
0.96
-1.06
F
1.95
0.93
1.11
P
0.172
0.341
0.298
P
0.000
0.172
0.341
0.298
Problem 4
General Linear Model: stem versus flower
Factor
flower
Type
fixed
Levels
3
Values
p, s, w
Analysis of Variance for stem, using Adjusted SS for Tests
Source
leaf
flower
flower*leaf
Error
Total
Term
Constant
leaf
flower
p
s
leaf*flower
p
s
DF
1
2
2
576
581
Seq SS
396.610
1.846
2.618
639.580
1040.654
Adj SS
119.879
2.761
2.618
639.580
Adj MS
119.879
1.381
1.309
1.110
Coef
0.5538
0.31318
SE Coef
0.3735
0.03014
T
1.48
10.39
P
0.139
0.000
0.3457
0.0679
0.4309
0.6927
0.80
0.10
0.423
0.922
-0.01754
-0.01930
0.03396
0.05648
-0.52
-0.34
0.606
0.733
F
107.96
1.24
1.18
P
0.000
0.289
0.308
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