The study aimed to develop a method for predicting the age of human remains based on measurements of the occipital condyles. Measurements of length, width, and height were taken from 68 juvenile specimens and used to generate linear regression models. The best model predicted age based on right condyle length and width, explaining 15% of variation, though neither model met the accuracy standard for legal admissibility. Limitations included a small sample size and age range, suggesting a larger, more diverse sample could improve predictive power.

1. Predicting Age of Adolescent Remains through Occipital
Condyle Measurements
By:
Paul Perrin
Justin Pierce
Grand Valley State University

2. March 21, 2013
2

3. Table of Contents
Abstract ………………………………. 3
Introduction ……………………………… 4
Terms & Definitions ……………………………… 4
Materials & Methods ……………………………… 5
Results ……………………………… 6
Discussion ……………………………… 7
Conclusion ……………………………… 8
Appendix ……………………………… 9
A.1: Occipital Shape Data …………. 9
A.2: Subject Demographics …………. 10
A.3: Delimited Coordinates with distances ….. 11
A.4: SAS Code Program …………. 12
A.5: SAS Output …………. 14
3

4. Abstract
In order to determine a new method for predicting the age of a human based on
their remains, the remains of 68 juveniles from the Hamann-Todd Collection in
Cleveland, Ohio underwent extensive metric analysis and documentation including
recorded known age at time of death.
As humans age, they undergo massive skull metamorphisms including changes in
a pair of oblong boney structures called Occipital Condyles. These condyles are typically
located inside the skull, one on either side of where the spinal cord attaches.
A procedure recorded markers on each Occipital Condyle within their skull using
a Microscribe 3D Digitizer. Using algebraic formulas to calculate length, height, and
width of each condyle, a multiple linear regression was used to model the recorded age of
death. The first model indicates a juvenile’s predicted age in years is:
Upon further investigation, the right condyle width and right condyle height were
correlated according to Pearson’s Correlation Coefficient of 0.48 so the model was
amended to not include the height variable with its higher P-value of 0.0951. The final
model generated that passed all diagnostic tests predicts age in years as:
with a significance value of less than 0.0001 and an R2
value of 0.1503.
.
4

5. Introduction
Identifying the age of specimens is a very important part of forensic sciences.
That is, given a skeleton, bones or a skull, it is very useful to be able to identify the age of
the specimen at time of death. Traditional methods of predicting age are based off of
dental information such as calcification levels in teeth. However, oftentimes this system
of identification is not always valid. Sometimes there aren’t any teeth in the specimen at
all. The goal of the project was to find a way to predict the age of a specimen based on
the size and shape of oblong bone structures in the skull called occipital condyles. The
theory is that these condyles change in size and shape in a predictable manner over time
in all human beings.
Terms & Definitions
When recording coordinate markers using the Microscribe 3D Digitizer, skulls
were individually positioned in the stand such that the anterior side of the skull (where
the facial features would be located) face straight up skywards. When relating in terms of
a mathematical 3 dimensional axis, this position would have the subject facing the
positive y-axis.
Once a baseline for orientation has been established, distances of each condyle in
millimeters are defined as follows.
Length: Distance between Anterior and Posterior markers
Width: Distance between Medial and Lateral markers perpendicular to length
Height: Greatest distance between any two different markers along the superior-
inferior axis.
5

6. Materials & Methods
The remains of 68 juveniles from the Humann-Todd cadaver collection in
Cleveland, Ohio were used as a sample population due extensive documentation
including bone measurements and the known recorded age at the time of death. A table
showing the complete set of condyle marker measurements recorded can be seen in
Appendix A.1. Demographic and age variables for each observation are listed in
Appendix A.2.
Using coordinate markers collected from these 68 observations, the length and
width of each condyle can be calculated using the Pythagorean Theorem: a2
+ b2
= c2
where a and b is the changes in x and z coordinates respectively, and c is the distance to
be found.
For finding width in millimeters, the expanded equation would be:
C =
For finding length in millimeters, the expanded equation would be:
C =
For finding the height, take the absolute value of the difference in y coordinates for every
pair of different condyle markers. The greatest value is what would be called the height.
A logical expression for finding the height would be:
MAX( |Anterior y – Posterior y|, |Anterior y – Lateral y|, |Anterior y – Medial y|, |Posterior y –
Lateral y|, |Posterior y – Medial y|, |Lateral y – Medial y|)
6

7. A complete list of height, length, and width condyle measurements is available in Table
A.3 of the Appendix.
Once distance measurements have been collected for each condyle, Statistical
Analysis Software (SAS 9.3) is used to determine a multiple linear regression model to
predict recorded age of death for an observation using their length, width, and height
measurements of the left and right condyles using backwards selection method. All six
variables were included in the model for predicting age and dropped one by one if their
significance level was greater than 0.10. Through this method, the left condyle width was
first to be eliminated (p value = 0.688), followed by left condyle length (p value =
0.2629) and finally left condyle height (p value = 0.2071).
The three remaining variables: right condyle length, height, and width had p-
values less than the 0.1 level of significance. A copy of the SAS program code used to
conduct the analysis is shown in Appendix Figure A.4 while output produced by the code
is available in Appendix Figure A.5.
Results
Using backward selection process with a significance level of 0.10, the predicted
recorded age of remains in years was:
with an overall significance level of 0.0098 and an R2
value of 0.195073.A secondary
model generated using the same backward selection method but without incorporating the
right condyle height predicted the recorded age of remains in years as:
with an overall significance level of less than 0.0001 and an R2
value of 0.1503.
7

8. Discussion
While performing diagnostic tests to verify the first model developed, an issue
arose regarding variables that correlated with each other. In regression, correlated
variables are redundant and provide no further insight when predicting a variable
accurately. In the first model, the right width and height measurements were shown to be
correlated by Pearson’s correlation coefficient of 0.482. In statistics, a coefficient of 1 or
-1 suggests a strong correlation between two variables. When deciding which of the
correlating variables to eliminate, the one with the higher p-value (Right condyle height
had a p-value of 0.0951) should be dropped from the model.
When trying to compare how accurate a model is, the R2
figure reported by SAS
represents the proportion of all predicted values that can be explained using the
regression model. The first model generated in this study has an R2
value of 0.195 and the
secondary model has an R2
value of about 0.15. In order for a method of identifying the
age of human remains to be recognized and admissible in a court of law, a method must
be at least 80% accurate. Both models fail to meet that standard based on the low R2
values of 0.195 and 0.15.
One possible reason why both models have such a low accuracy is due to the
small sample size from which data was obtained from. The Hamann-Todd collection has
over 3,000 individuals with extensive documentation and from that large group, 68 were
sampled. Out of the selected 68, 4 samples were discarded due to having both left and
right condyles damaged. From the sample remaining, 8 observations had no
measurements taken of the left occipital condyle. Once more samples are included, than
8

9. the overall model will become more accurate since the linear model will have more data
points to fit a line with.
Conclusion
The linear model failed to give significant evidence to suggest a relationship
between condyle shape/size and age of a particular specimen. The data tell us now that
15% of the variation in condyle shape/size is accounted for by age. Although this was
not the outcome that was hoped for, the model still shows valuable information about
condyle shape/size and age.
There were also several limitations worth addressing in this study. All of our
specimens were from a population with little variability. For example, most of the
specimens were all of the same race (African American), and relatively small age range
(about 0-18). It is possible that with a larger more diverse sample, a more effective
model could have been created. Also, to come up with condyle shape and size
approximations, all there was to work with were four 3D coordinates per condyle. The
problem with this is it is impossible to tell the true shape and size of condyles by just
these coordinates. If further research were to be done, things like total volume and
surface area of condyles would we essential to creating an effective model.
9

10. Appendix
Table A.1: Occipital Shape Data
IDnumber Rt Occip condyle A Rt Occip Condyle P Rt Occipital Condyle L Rt Occipital Condyle M Lft Occipital Condyle A Lft Occipital Condyle P Left Occipital Condyle L Lft Occipital Condyle M
HTH0710 168.90184.10128.17 183.48 140.0993.33 176.88187.00123.70 174.69 183.10120.62 189.15210.20130.29 175.01166.97103.72 183.90221.05123.53 183.90171.20117.40
HTH0624 159.37184.87122.88 168.60 132.0996.19 147.97177.35117.11 152.77 176.81114.90 144.63170.07120.75 150.88150.23108.65 152.24166.53120.88 153.75164.55120.98
HTH0645 140.17171.04110.30 159.08 188.04125.18 161.27190.37125.49 159.72 190.76125.55
HTH0526 152.15169.32116.78 163.21 160.63121.14 164.51165.60126.75 159.03 166.60124.54 244.67180.26126.47 220.44144.16129.30 240.77178.23124.84 206.04166.65132.04
HTH0632 197.53110.47112.79 200.78 106.9495.05 203.90120.16108.55 210.71 116.24105.91 185.78115.22113.37 210.05113.36100.69 196.22130.99119.22 189.03128.49118.87
HTH0633 X_117.14Y_208.32Z_136.17 X_156.62Y_217.81Z_141.06 137.20211.17141.28 135.92 181.32139.51 121.81199.98120.15 154.77209.78138.76 158.84219.62139.23 160.10226.85141.04
HTH0527 110.63202.75111.73 124.67 165.19115.29 136.64212.11119.03 132.56 212.16121.01 210.90189.40121.58 240.22166.10130.94 240.87166.04130.56 220.17218.06126.91
HTH0245 178.71179.9656.37 200.79 100.9455.00 202.45108.7254.96 196.29 112.2753.50 197.92120.2551.95 200.37104.8344.32 197.01112.2749.07 194.21116.2043.00
HTH0485 137.34206.21130.25 156.10 188.89130.72 152.21201.97129.05 147.02 200.03133.10 194.34159.19132.72 200.65145.55131.27 199.78178.01131.32 196.47173.53138.61
HTH0404 194.17179.60128.84 205.98 135.5711.55 200.58177.06129.32 202.05 175.88129.24 234.11180.90122.51 220.88141.47102.00 220.00172.84112.43 230.37175.12115.64
HTH1385 225.48155.6339.17 234.87 124.4133.08 224.17126.4637.99 229.45 142.5735.68 194.45134.8734.33 201.86121.6236.98 196.10122.8242.00 201.42122.6542.11
HTH1583 176.44145.3165.72 174.50 114.1958.34 177.20104.7154.21 181.89 104.1450.94
HTH1557 170.57166.17124.58 202.64 119.82102.38 187.61142.84112.62 179.75 141.01115.68 175.51178.70130.42 197.98145.20119.62 173.98181.20130.12 182.70178.57129.76
HTH1074 177.28187.7042.25 184.66 163.4145.17 187.52170.3040.84 185.80 172.2440.71 220.32127.26136.42 223.04141.23133.59 217.75137.32133.23 221.07127.20135.54
HTH1156 210.46192.97118.46 229.81 201.88109.45 214.20208.79112.61 212.97 202.08112.16 209.26188.1529.10 203.81200.4619.72 201.71193.6324.52 208.95198.7122.12
HTH1115 149.30159.8060.85 175.27 92.0646.68 175.57103.9552.59 182.69 110.2451.22 198.87134.78108.23 198.60123.6699.46 189.75132.68112.83 196.53127.09109.52
HTH1098 179.58212.03125.93 184.37 185.61117.78 179.33202.37118.22 182.74 201.43122.04 284.67157.91126.15 299.43120.66126.96 298.03115.74131.81 293.61127.46130.54
HTH1240 147.62200.33114.36 163.03 110.12130.49 164.65142.30129.09 171.08 130.35134.34 201.67175.52119.23 213.88150.0998.01 213.51163.59102.17 215.87159.87104.51
HTH0872 272.7142.99120.60 238.97 71.70102.36 254.0169.2593.61 269.33 57.8085.89 263.3135.7391.00 256.8939.3493.82 261.1139.7690.90 250.0246.2193.47
HTH0816 247.69-51.6237.59 234.87 -42.5433.37 235.70-44.3136.06 259.42 -63.6435.21 256.96-58.3134.99 237.28-44.9932.20 243.00-47.4834.31 244.11-55.4931.85
HTH1768 245.6219.96111.29 239.51 27.75108.64 228.4019.41118.25 233.83 10.51129.44
HTH1772 270.1529.72126.79 224.34 96.87135.38 256.5065.73132.40 249.74 62.00136.39 234.40-37.29142.66 203.85-18.55140.57 201.55-63.61141.32 195.86-66.52141.43
HTH1784 236.81-59.0133.76 222.55 -61.0852.07 223.15-71.7235.83 224.70 -81.9834.62 219.76-79.98132.25 214.71-57.79127.39 226.84-78.02131.03 223.33-86.95133.03
HTH2141 243.91263.76122.61 227.30 249.70113.22 232.65267.94110.20 233.10 268.21109.05 239.27251.43123.36 212.19261.30113.74 220.84254.89119.31 230.11252.47117.53
HTH2075 289.41-8.45 95.07 277.13 1.7881.20 331.02-48.4198.17 307.91 15.0259.94
HTH2118 298.89-16.34117.92 284.80 -0.88115.79 284.57-7.24121.17 288.89 -1.67121.11 193.88-43.49121.63 198.27-28.43118.82 210.98-23.50122.30 198.54-19.02125.09
HTH2370 319.23-59.6831.83 306.63 -46.2934.63 314.59-65.8631.05 296.88 -41.3837.25 297.07-47.2737.70 273.08-25.0737.32 282.89-29.8937.37 278.87-34.1734.20
HTH2144 292.30-19.15108.92 291.83 -18.53107.84 278.07-16.9998.57 288.08 -14.3899.70 305.89-2.66 99.76 300.033.34 80.30 306.14-10.4797.30 300.20-13.1698.37
HTH2074 331.98-17.77132.13 306.58 -15.71127.57 307.02-1.32133.10 306.19 2.34132.68 261.39-6.89 135.66 265.08-13.93123.34 272.38-9.59129.46 272.65-19.75128.82
HTH1379 239.982.1338.22 228.48 -2.5534.76 225.15-1.4438.21 228.38 0.1535.94 227.124.2724.59 230.28-5.5622.75 233.99-9.8728.48 229.71-8.5324.45
HTH1509 294.1011.26112.70 284.72 -48.4596.52 299.78-40.47108.14 255.04 -35.19114.59
HTH1441 321.588.5998.25 294.71 16.7588.07 318.47-5.70102.73 308.30 6.4396.07 315.85-4.84 109.07 321.1011.5893.12 319.9415.01100.65 309.7710.3599.25
HTH1168 277.74-39.7164.83 213.24 -13.2862.82 212.95-17.1663.17 243.21 -27.3763.79 279.01-38.9753.83 208.42-23.4745.58 204.82-21.5746.53 245.27-35.8149.44
HTH1453 248.81-2.32 108.33 240.16 7.44106.07 242.400.45108.57 247.56 2.28106.56 271.56-24.98103.64 255.8912.2492.01 262.57-14.25104.00 264.28-9.7299.82
HTH1232 318.47-3.15 113.69 277.97 -19.26127.20 308.40-11.28126.28 289.88 -3.60135.58 242.34-67.76132.21 265.32-35.57127.76 273.81-39.67131.31 258.34-36.77134.83
HTH1867 220.968.2629.22 225.99 -2.2425.48 322.64-47.7329.70 314.09 -49.9360.21
HTH1886 226.12-7.62 35.11 217.06 -11.6330.55 277.22-56.4438.28 246.62 -27.4441.54 259.47-42.7744.03 238.05-14.3534.50 239.49-13.5440.54 245.28-25.8334.33
HTH1861 na
HTH1894 283.0066.8985.16 237.12 24.72100.81 258.4214.31113.03 256.42 16.63109.07 292.198.06100.59 294.384.26 95.54 298.242.11100.98 289.724.5298.29
HTH1845 273.1337.3646.38 256.83 63.0940.26 280.97-26.1743.29 276.54 29.0442.93 292.1818.3851.86 268.6337.0134.71 275.0021.4633.60 276.383.4937.19
HTH1688 332.7967.08128.63 331.12 52.31128.01 302.4267.31136.90 305.83 65.20137.92 278.6434.72142.06 325.2210.42141.39 315.06-11.62139.99 321.9755.01143.97
HTH2135 270.4878.68132.87 254.47 70.44126.14 266.8848.99131.84 271.77 54.93133.40 224.16-9.63 136.23 242.98-13.96123.16 241.10-6.21131.82 234.40-9.60133.37
HTH3112 332.6960.58138.31 316.30 58.18133.84 321.6254.09136.12 328.09 57.94135.09 328.1957.64135.09 308.7752.32139.19 310.4451.54129.97 306.2251.73135.93
HTH3455 352.4051.43134.50 322.13 59.11131.11 331.6953.97135.34 341.39 57.65135.58 328.0725.99132.97 323.3741.97127.44 328.0238.61132.56 319.6733.09133.39
HTH3470 306.1823.33133.11 275.88 49.20130.49 290.4747.14137.61 295.07 49.99135.62 284.9634.86134.46 276.0151.04132.94 277.3248.96138.25 270.4645.66139.84
HTH1140 269.75-25.19141.48 251.62 -28.99129.59 253.26-31.22135.06 259.25 -28.98138.11 259.43-21.29140.32 254.93-20.04132.88 268.42-37.21132.53 257.04-40.20134.80
HTH0098 382.0644.28114.79 367.56 52.91106.14 354.4325.83114.27 361.08 28.94113.95 344.21-7.02 109.62 333.9347.6381.76 342.0852.6084.82 333.6752.8288.79
HTH0437 328.0152.58121.76 298.99 87.04132.95 328.7054.64119.10 324.98 56.69120.71 265.416.73118.05 290.6445.26121.85 292.5218.84117.23 287.8014.71118.14
HTH1041 313.7738.41130.71 228,31 191.60129.07 256.7491.07129.78 255.97 96.02130.53 248.5140.43123.499 256.0763.01118.48 259.2641.40118.32 255.2139.79122.90
HTH0548 307.37-5.99 133.78 214.56 83.26137.21 234.5569.29127.43 235.12 72.97129.79 223.1624.54136.15 232.3519.71116.51 241.8611.66120.72 239.257.64122.83
HTH1590 302.3017.45131.08 302.83 33.78122.81 302.0338.11131.93 308.64 38.62131.91 268.49-0.83 131.06 273.7310.74126.79 270.71-2.05129.98 264.08-7.313131.31
HTH1606 339.0932.13130.11 313.07 55.04127.94 328.5545.41130.99 334.90 49.83132.58 318.98-1.97 123.50 319.2236.83125.64 312.914.91126.30 312.753.62127.06
HTH1589 not available
HTH1097 248.83182.76136.42 214.98 178.54132.65 222.31179.10136.66 220.02 185.77139.94 217.80185.14137.47 223.37191.42130.47 238.99179.20130.22 233.96174.78134.45
HTH1012 240.02162.36114.51 205.15 168.05115.02 216.33169.01117.16 214.62 174.04119.45 231.53164.66118.95 224.76172.92113.43 236.51170.30116.31 234.26162.24116.48
HTH1836 265.7574.2836.02 255.48 78.3234.17 255.7276.5832.36 259.50 76.6732.55 285.8249.1530.01 262.3983.4034.03 268.6171.5331.27 267. 62 69.9826.81
HTH1834 288.2742.29125.30 294.53 50.23116.86 277.9935.37125.40 283.81 37.29124.03 273.0236.06131.21 281.8712.07122.79 292.7811.36125.48 288.237.27125.35
HTH1950 284.0747.50106.35 279.04 47.8696.65 278.6652.1798.37 285.10 44.1298.89 283.0723.93105.02 284.1633.0691.38 297.9924.2196.28 306.4422.0090.37
HTH1878 286.1569.4648.98 249.82 95.0648.775 249.3194.5248.26 251.90 95.1548.26
HTH2548 315.00-16.76112.24 303.93 -17.42108.39 305.07-12.85109.15 302.39 -13.56110.79 243.00-60.83119.66 241.44-49.58115.66 244.77-56.94116.85 247.90-45.25114.94
HTH2714 na
HTH1974 292.66176.47116.86 247.17 189.67126.78 272.07179.66122.04 276.59 186.44123.53 273.55170.75117.70 257.65192.05122.48 269.66188.60122.49 264.27180.66125.00
HTH0721 na 232.36207.56138.19 245.87242.59135.60 252.34223.50135.60 248.02216.69137.92
HTH1711 222.17181.6190.62 228.42 166.9378.32 222.30169.0386.34 227.14 175.3487.08
HTH0576 289.86220.35112.37 242.33 223.27119.52 264.49215.96120.52 268.01 221.64120.49 252.99198.99120.97 228.32228.08122.09 249.55205.62123.32 245.13200.10127.11
HTH0695 279.67172.31139.13 243.33 182.10138.37 259.66168.22139.41 252.47 158.16141.78 241.44155.13143.29 239.36168.72135.23 258.28162.21135.68 250.03156.68138.60
HTH2310 226.73183.38105.63 245.58 178.5699.00 235.75175.33100.33 235.46 182.45104.22 187.89123.49101.95 204.06110.8990.40 200.57118.1096.57 196.50113.3099.31
HTH0410 309.82200.00129.48 294.45 194.53126.37 291.33196.53133.86 289.42 201.30134.85 277.34162.59129.30 262.24196.77132.86 284.90169.19130.14 280.85164.00132.40
10

11. Table A.2: Subject Demographics
ID number Recorded Age Dental Age Sex Ethnicity
HTH 0710 10 10 M B
HTH 0624 6 6 F B
HTH 0645 12 12 F W
HTH 0526 11 10 F B
HTH 0632 10 7 F B
HTH 0633 14 10 F B
HTH 0527 16 18 F W
HTH 0245 0 6 mon M W
HTH 0485 16 15 F B
HTH 0404 11 10 M B
HTH 1385 1 18 mon M B
HTH 1583 1 9 mon M W
HTH 1557 3 3 M B
HTH 1074 4 4 F B
HTH 1156 8 7 F B
HTH 1115 5 5 F B
HTH 1098 5 6 F B
HTH 1240 12 12 F W
HTH 0872 8 11 F B
HTH 0816 0 9 mon M W
HTH 1768 1 1 M B
HTH 1772 12 11 F W
HTH 1784 6 7 M B
HTH 2141 4 4 F B
HTH 2075 1 1.5 M B
HTH 2118 13 11 F B
HTH 2370 1 1 M B
HTH 2144 6 6 M B
HTH 2074 8 9 F B
HTH 1379 1 6 mon M B
HTH 1509 3 3 F B
HTH 1441 10 10 M B
HTH 1168 1 9 mon M B
HTH 1453 0 6 mon F B
HTH 1232 16 18 F B
HTH 1867 0 0 M W
HTH 1886 0 0.5 M B
HTH 1861 0 0.5 F W
HTH 1894 1 1 M B
HTH 1845 0 8 fetal mon F W
HTH 1688 10 11 M B
HTH 2135 14 F B
HTH 3112 15 15 M B
HTH 3455 18 18 M B
HTH 3470 18 18 M B
HTH 1140 18 18 M B
HTH 0098 18 18 M W
HTH 0437 18 18 F W
HTH 1041 17 17 F B
HTH 0548 17 M B
HTH 1590 18 18 F B
HTH 1606 17 17 F B
HTH 1589 17 15 M B
HTH 1097 18 18 M B
HTH 1012 18 20 F B
HTH 1836 0 9 fetal mon M W
HTH 1834 8 8 M B
HTH 1950 4 4 M B
HTH 1878 0 7 fetal mon M W
HTH 2548 0 9 mon M B
HTH 2714 1 1 F B
HTH 1974 18 18 M B
HTH 0721 18 18 M B
HTH 1711 17 17 M B
HTH 0576 16 18 F B
HTH 0695 18 18 M B
HTH 2310 15 15 M B
HTH 0410 18 16 M W
11

12. Table A.3: Delimited Coordinates with Distances
ID rocax rocay rocaz rocpx rocpy rocpz roclx rocly roclz rocmx rocmy rocmz locax locay locaz locpx locpy locpz loclx locly loclz locmx locmy locmz recage Rwidth Rlength Rheight Lwidth Llength Lheight
710 168.9 184.1 128.17 183.48 140.09 93.33 176.88 187 123.7 174.69 183.1 120.62 189.15 210.2 130.29 175.01 166.97 103.72 183.9 221.05 123.53 183.9 171.2 117.4 10 3.78 37.77 46.91 6.13 30.10 54.08
624 159.37 184.87 122.88 168.6 132.09 96.19 147.97 177.35 117.11 152.77 176.81 114.9 144.63 170.07 120.75 150.88 150.23 108.65 152.24 166.53 120.88 153.75 164.55 120.98 6 5.28 28.24 52.78 1.51 13.62 19.84
645 140.17 171.04 110.3 159.08 188.04 125.18 161.27 190.37 125.49 159.72 190.76 125.55 12 1.55 24.06 19.33
526 152.15 169.32 116.78 163.21 160.63 121.14 164.51 165.6 126.75 159.03 166.6 124.54 244.67 180.26 126.47 220.44 144.16 129.3 240.77 178.23 124.84 206.04 166.65 132.04 11 5.91 11.89 8.69 35.47 24.39 36.1
632 197.53 110.47 112.79 200.78 106.94 95.05 203.9 120.16 108.55 210.71 116.24 105.91 185.78 115.22 113.37 210.05 113.36 100.69 196.22 130.99 119.22 189.03 128.49 118.87 10 7.30 18.04 13.22 7.20 27.38 17.63
633 117.14 208.32 136.17 156.62 217.81 141.06 137.2 211.17 141.28 135.92 181.32 139.51 121.81 199.98 120.15 154.77 209.78 138.76 158.84 219.62 139.23 160.1 226.85 141.04 14 2.18 39.78 36.49 2.21 37.85 19.64
527 110.63 202.75 111.73 124.67 165.19 115.29 136.64 212.11 119.03 132.56 212.16 121.01 210.9 189.4 121.58 240.22 166.1 130.94 240.87 166.04 130.56 220.17 218.06 126.91 16 4.54 14.48 46.97 21.02 30.78 52.02
245 178.71 179.96 56.37 200.79 100.94 55 202.45 108.72 54.96 196.29 112.27 53.5 197.92 120.25 51.95 200.37 104.83 44.32 197.01 112.27 49.07 194.21 116.2 43 0 6.33 22.12 79.02 6.68 8.01 15.42
485 137.34 206.21 130.25 156.1 188.89 130.72 152.21 201.97 129.05 147.02 200.03 133.1 194.34 159.19 132.72 200.65 145.55 131.27 199.78 178.01 131.32 196.47 173.53 138.61 16 6.58 18.77 17.32 8.01 6.47 32.46
404 194.17 179.6 128.84 205.98 135.57 11.55 200.58 177.06 129.32 202.05 175.88 129.24 234.11 180.9 122.51 220.88 141.47 102 220 172.84 112.43 230.37 175.12 115.64 11 1.47 117.88 44.03 10.86 24.41 39.43
1385 225.48 155.63 39.17 234.87 124.41 33.08 224.17 126.46 37.99 229.45 142.57 35.68 194.45 134.87 34.33 201.86 121.62 36.98 196.1 122.82 42 201.42 122.65 42.11 1 5.76 11.19 31.22 5.32 7.87 13.25
1583 176.44 145.31 65.72 174.5 114.19 58.34 177.2 104.71 54.21 181.89 104.14 50.94 1 5.72 7.63 40.6
1557 170.57 166.17 124.58 202.64 119.82 102.38 187.61 142.84 112.62 179.75 141.01 115.68 175.51 178.7 130.42 197.98 145.2 119.62 173.98 181.2 130.12 182.7 178.57 129.76 3 8.43 39.00 46.35 8.73 24.93 36
1074 177.28 187.7 42.25 184.66 163.41 45.17 187.52 170.3 40.84 185.8 172.24 40.71 220.32 127.26 136.42 223.04 141.23 133.59 217.75 137.32 133.23 221.07 127.2 135.54 4 1.72 7.94 24.29 4.04 3.93 14.03
1156 210.46 192.97 118.46 229.81 201.88 109.45 214.2 208.79 112.61 212.97 202.08 112.16 209.26 188.15 29.1 203.81 200.46 19.72 201.71 193.63 24.52 208.95 198.71 22.12 8 1.31 21.34 15.82 7.63 10.85 12.31
1115 149.3 159.8 60.85 175.27 92.06 46.68 175.57 103.95 52.59 182.69 110.24 51.22 198.87 134.78 108.23 198.6 123.66 99.46 189.75 132.68 112.83 196.53 127.09 109.52 5 7.25 29.58 67.74 7.54 8.77 11.12
1098 179.58 212.03 125.93 184.37 185.61 117.78 179.33 202.37 118.22 182.74 201.43 122.04 284.67 157.91 126.15 299.43 120.66 126.96 298.03 115.74 131.81 293.61 127.46 130.54 5 5.12 9.45 26.42 4.60 14.78 42.17
1240 147.62 200.33 114.36 163.03 110.12 130.49 164.65 142.3 129.09 171.08 130.35 134.34 201.67 175.52 119.23 213.88 150.09 98.01 213.51 163.59 102.17 215.87 159.87 104.51 12 8.30 22.31 90.21 3.32 24.48 25.43
872 272.71 42.99 120.6 238.97 71.7 102.36 254.01 69.25 93.61 269.33 57.8 85.89 263.31 35.73 91 256.89 39.34 93.82 261.11 39.76 90.9 250.02 46.21 93.47 8 17.16 38.35 28.71 11.38 7.01 6.87
816 247.69 -51.62 37.59 234.87 -42.54 33.37 235.7 -44.31 36.06 259.42 -63.64 35.21 256.96 -58.31 34.99 237.28 -44.99 32.2 243 -47.48 34.31 244.11 -55.49 31.85 0 23.74 13.50 21.1 2.70 19.88 13.32
1768 245.62 19.96 111.29 239.51 27.75 108.64 228.4 19.41 118.25 233.83 10.51 129.44 1 12.44 6.66 17.24
1772 270.15 29.72 126.79 224.34 96.87 135.38 256.5 65.73 132.4 249.74 62 136.39 234.4 -37.29 142.66 203.85 -18.55 140.57 201.55 -63.61 141.32 195.86 -66.52 141.43 12 7.85 46.61 67.15 5.69 30.62 47.97
1784 236.81 -59.01 33.76 222.55 -61.08 52.07 223.15 -71.72 35.83 224.7 -81.98 34.62 219.76 -79.98 132.25 214.71 -57.79 127.39 226.84 -78.02 131.03 223.33 -86.95 133.03 6 1.97 23.21 22.97 4.04 7.01 29.16
2141 243.91 263.76 122.61 227.3 249.7 113.22 232.65 267.94 110.2 233.1 268.21 109.05 239.27 251.43 123.36 212.19 261.3 113.74 220.84 254.89 119.31 230.11 252.47 117.53 4 1.23 19.08 18.51 9.44 28.74 9.87
2075 289.41 -8.45 95.07 277.13 1.78 81.2 331.02 -48.41 98.17 307.91 15.02 59.94 1 44.67 18.52 63.43
2118 298.89 -16.34 117.92 284.8 -0.88 115.79 284.57 -7.24 121.17 288.89 -1.67 121.11 193.88 -43.49 121.63 198.27 -28.43 118.82 210.98 -23.5 122.3 198.54 -19.02 125.09 13 4.32 14.25 15.46 12.75 5.21 19.99
2370 319.23 -59.68 31.83 306.63 -46.29 34.63 314.59 -65.86 31.05 296.88 -41.38 37.25 297.07 -47.27 37.7 273.08 -25.07 37.32 282.89 -29.89 37.37 278.87 -34.17 34.2 1 18.76 12.91 24.48 5.12 23.99 22.2
2144 292.3 -19.15 108.92 291.83 -18.53 107.84 278.07 -16.99 98.57 288.08 -14.38 99.7 305.89 -2.66 99.76 300.03 3.34 80.3 306.14 -10.47 97.3 300.2 -13.16 98.37 6 10.07 1.18 4.77 6.04 20.32 16.5
2074 331.98 -17.77 132.13 306.58 -15.71 127.57 307.02 -1.32 133.1 306.19 2.34 132.68 261.39 -6.89 135.66 265.08 -13.93 123.34 272.38 -9.59 129.46 272.65 -19.75 128.82 8 0.93 25.81 20.11 0.69 12.86 10.16
1379 239.98 2.13 38.22 228.48 -2.55 34.76 225.15 -1.44 38.21 228.38 0.15 35.94 227.12 4.27 24.59 230.28 -5.56 22.75 233.99 -9.87 28.48 229.71 -8.53 24.45 1 3.95 12.01 4.68 5.88 3.66 14.14
1509 294.1 11.26 112.7 284.72 -48.45 96.52 299.78 -40.47 108.14 255.04 -35.19 114.59 3 45.20 18.70 59.71
1441 321.58 8.59 98.25 294.71 16.75 88.07 318.47 -5.7 102.73 308.3 6.43 96.07 315.85 -4.84 109.07 321.1 11.58 93.12 319.94 15.01 100.65 309.77 10.35 99.25 10 12.16 28.73 22.45 10.27 16.79 19.85
1168 277.74 -39.71 64.83 213.24 -13.28 62.82 212.95 -17.16 63.17 243.21 -27.37 63.79 279.01 -38.97 53.83 208.42 -23.47 45.58 204.82 -21.57 46.53 245.27 -35.81 49.44 1 30.27 64.53 26.43 40.55 71.07 17.4
1453 248.81 -2.32 108.33 240.16 7.44 106.07 242.4 0.45 108.57 247.56 2.28 106.56 271.56 -24.98 103.64 255.89 12.24 92.01 262.57 -14.25 104 264.28 -9.72 99.82 0 5.54 8.94 9.76 4.52 19.51 37.22
1232 318.47 -3.15 113.69 277.97 -19.26 127.2 308.4 -11.28 126.28 289.88 -3.6 135.58 242.34 -67.76 132.21 265.32 -35.57 127.76 273.81 -39.67 131.31 258.34 -36.77 134.83 16 20.72 42.69 16.11 15.87 23.41 32.19
1867 220.96 8.26 29.22 225.99 -2.24 25.48 322.64 -47.73 29.7 314.09 -49.93 60.21 0 31.69 6.27 55.99
1886 226.12 -7.62 35.11 217.06 -11.63 30.55 277.22 -56.44 38.28 246.62 -27.44 41.54 259.47 -42.77 44.03 238.05 -14.35 34.5 239.49 -13.54 40.54 245.28 -25.83 34.33 0 30.77 10.14 48.82 8.49 23.44 29.23
1894 283 66.89 85.16 237.12 24.72 100.81 258.42 14.31 113.03 256.42 16.63 109.07 292.19 8.06 100.59 294.38 4.26 95.54 298.24 2.11 100.98 289.72 4.52 98.29 1 4.44 48.48 52.58 8.93 5.50 5.95
1845 273.13 37.36 46.38 256.83 63.09 40.26 280.97 -26.17 43.29 276.54 29.04 42.93 292.18 18.38 51.86 268.63 37.01 34.71 275 21.46 33.6 276.38 3.49 37.19 0 4.44 17.41 89.26 3.85 29.13 33.52
1688 332.79 67.08 128.63 331.12 52.31 128.01 302.42 67.31 136.9 305.83 65.2 137.92 278.64 34.72 142.06 325.22 10.42 141.39 315.06 -11.62 139.99 321.97 55.01 143.97 10 3.56 1.78 15 7.97 46.58 66.63
2135 270.48 78.68 132.87 254.47 70.44 126.14 266.88 48.99 131.84 271.77 54.93 133.4 224.16 -9.63 136.23 242.98 -13.96 123.16 241.1 -6.21 131.82 234.4 -9.6 133.37 14 5.13 17.37 29.69 6.88 22.91 7.75
3112 332.69 60.58 138.31 316.3 58.18 133.84 321.62 54.09 136.12 328.09 57.94 135.09 328.19 57.64 135.09 308.77 52.32 139.19 310.44 51.54 129.97 306.22 51.73 135.93 15 6.55 16.99 6.49 7.30 19.85 6.1
3455 352.4 51.43 134.5 322.13 59.11 131.11 331.69 53.97 135.34 341.39 57.65 135.58 328.07 25.99 132.97 323.37 41.97 127.44 328.02 38.61 132.56 319.67 33.09 133.39 18 9.70 30.46 7.68 8.39 7.26 15.98
3470 306.18 23.33 133.11 275.88 49.2 130.49 290.47 47.14 137.61 295.07 49.99 135.62 284.96 34.86 134.46 276.01 51.04 132.94 277.32 48.96 138.25 270.46 45.66 139.84 18 5.01 30.41 26.66 7.04 9.08 16.18
1140 269.75 -25.19 141.48 251.62 -28.99 129.59 253.26 -31.22 135.06 259.25 -28.98 138.11 259.43 -21.29 140.32 254.93 -20.04 132.88 268.42 -37.21 132.53 257.04 -40.2 134.8 18 6.72 21.68 6.03 11.60 8.70 20.16
98 382.06 44.28 114.79 367.56 52.91 106.14 354.43 25.83 114.27 361.08 28.94 113.95 344.21 -7.02 109.62 333.93 47.63 81.76 342.08 52.6 84.82 333.67 52.82 88.79 18 6.66 16.88 27.08 9.30 29.70 59.62
437 328.01 52.58 121.76 298.99 87.04 132.95 328.7 54.64 119.1 324.98 56.69 120.71 265.41 6.73 118.05 290.64 45.26 121.85 292.52 18.84 117.23 287.8 14.71 118.14 18 4.05 31.10 34.46 4.81 25.51 38.53
1041 313.77 38.41 130.71 228.31 191.6 129.07 256.74 91.07 129.78 255.97 96.02 130.53 248.51 40.43 123.499 256.07 63.01 118.48 259.26 41.4 118.32 255.21 39.79 122.9 17 1.07 85.48 153.19 6.11 9.07 23.22
548 307.37 -5.99 133.78 214.56 83.26 137.21 234.55 69.29 127.43 235.12 72.97 129.79 223.16 24.54 136.15 232.35 19.71 116.51 241.86 11.66 120.72 239.25 7.64 122.83 17 2.43 92.87 89.25 3.36 21.68 12.88
1590 302.3 17.45 131.08 302.83 33.78 122.81 302.03 38.11 131.93 308.64 38.62 131.91 268.49 -0.83 131.06 273.73 10.74 126.79 270.71 -2.05 129.98 264.08 -7.313 131.31 18 6.61 8.29 21.17 6.76 6.76 18.053
1606 339.09 32.13 130.11 313.07 55.04 127.94 328.55 45.41 130.99 334.9 49.83 132.58 318.98 -1.97 123.5 319.22 36.83 125.64 312.91 4.91 126.3 312.75 3.62 127.06 17 6.55 26.11 22.91 0.78 2.15 38.8
1097 248.83 182.76 136.42 214.98 178.54 132.65 222.31 179.1 136.66 220.02 185.77 139.94 217.8 185.14 137.47 223.37 191.42 130.47 238.99 179.2 130.22 233.96 174.78 134.45 18 4.00 34.06 7.23 6.57 8.95 16.64
1012 240.02 162.36 114.51 205.15 168.05 115.02 216.33 169.01 117.16 214.62 174.04 119.45 231.53 164.66 118.95 224.76 172.92 113.43 236.51 170.3 116.31 234.26 162.24 116.48 18 2.86 34.87 11.68 2.26 8.74 10.68
1836 265.75 74.28 36.02 255.48 78.32 34.17 255.72 76.58 32.36 259.5 76.67 32.55 285.82 49.15 30.01 262.39 83.4 34.03 268.61 71.53 31.27 267.62 69.98 26.81 0 3.78 10.44 4.04 4.57 23.77 34.25
1834 288.27 42.29 125.3 294.53 50.23 116.86 277.99 35.37 125.4 283.81 37.29 124.03 273.02 36.06 131.21 281.87 12.07 122.79 292.78 11.36 125.48 288.23 7.27 125.35 8 5.98 10.51 14.86 4.55 12.22 24.7
1950 284.07 47.5 106.35 279.04 47.86 96.65 278.66 52.17 98.37 285.1 44.12 98.89 283.07 23.93 105.02 284.16 33.06 91.38 297.99 24.21 96.28 306.44 22 90.37 4 6.46 10.93 8.05 10.31 13.68 11.06
1878 286.15 69.46 48.98 249.82 95.06 48.775 249.31 94.52 48.26 251.9 95.15 48.26 0 2.59 36.33 25.6
2548 315 -16.76 112.24 303.93 -17.42 108.39 305.07 -12.85 109.15 302.39 -13.56 110.79 243 -60.83 119.66 241.44 -49.58 115.66 244.77 -56.94 116.85 247.9 -45.25 114.94 0 3.14 11.72 4.57 3.67 4.29 11.69
1974 292.66 176.47 116.86 247.17 189.67 126.78 272.07 179.66 122.04 276.59 186.44 123.53 273.55 170.75 117.7 257.65 192.05 122.48 269.66 188.6 122.49 264.27 180.66 125 18 4.76 46.56 13.2 5.95 16.60 21.3
721 232.36 207.56 138.19 245.87 242.59 135.6 252.34 223.5 135.6 248.02 216.69 137.92 18 4.90 13.76 35.03
1711 222.17 181.61 90.62 228.42 166.93 78.32 222.3 169.03 86.34 227.14 175.34 87.08 17 4.90 13.80 14.68
576 289.86 220.35 112.37 242.33 223.27 119.52 264.49 215.96 120.52 268.01 221.64 120.49 252.99 198.99 120.97 228.32 228.08 122.09 249.55 205.62 123.32 245.13 200.1 127.11 16 3.52 48.06 7.31 5.82 24.70 29.09
695 279.67 172.31 139.13 243.33 182.1 138.37 259.66 168.22 139.41 252.47 158.16 141.78 241.44 155.13 143.29 239.36 168.72 135.23 258.28 162.21 135.68 250.03 156.68 138.6 18 7.57 36.35 23.94 8.75 8.32 13.59
2310 226.73 183.38 105.63 245.58 178.56 99 235.75 175.33 100.33 235.46 182.45 104.22 187.89 123.49 101.95 204.06 110.89 90.4 200.57 118.1 96.57 196.5 113.3 99.31 15 3.90 19.98 8.05 4.91 19.87 12.6
410 309.82 200 129.48 294.45 194.53 126.37 291.33 196.53 133.86 289.42 201.3 134.85 277.34 162.59 129.3 262.24 196.77 132.86 284.9 169.19 130.14 280.85 164 132.4 18 2.15 15.68 6.77 4.64 15.51 34.18
12

13. A.4: SAS Code
/*
Occipital Condyle Measurements
By: Justin Pierce
STA 319 Project
2/25/2013
*/
options nodate nonumber;
*Reads in Excel spreadsheet containing all condyle measurements;
proc import datafile="N:MY DOCUMENTSWinter 2013STA
319ClientOccypital_Condyle_Data_Final.xls" out=condylemeas
dbms=EXCEL97
replace; getnames=yes;
run;
/* Displays All variables imported from excel */
proc print data=condylemeas;
title 'Data Import Test';
run;
/* Generate a Multiple Linear Regression model using measurements of
each condyle to predict recorded age using backward selection
(alpha=0.1) */
proc reg;
model recage = Rlength Rwidth Rheight Llength Lwidth Lheight /
selection=backward;
title 'Recorded Age model';
run;
/* Checking Model Adequacy */
proc glm;
model recage = Rlength Rwidth Rheight;
title 'Model Adequacy';
run;
/* Residual Tests and Diagnostic Tools */
ods graphics on;
proc glm plots=all;
title 'Diagnostic Tests';
model recage = Rlength Rwidth Rheight/ P ;
output out = stat
P=pred R=residual RSTUDENT=r1 DFFITS=diffits COOKD=cookd
H=hatvalue PRESS=res_del ;
run;
ods graphics off;
13

14. /* Checking for Multicollinearity, correlation coefficent is close to 1
or -1 */
proc corr;
title 'Checking for Multicollinearity';
var Rlength Rwidth Rheight;
run;
/* Model Attempt #2: RHeight and RLength are correlated, dropping
Rheight due to highest p value */
proc reg;
model recage = Rlength Rwidth;
title 'Model #2';
run;
/* Checking Model #2 Adequacy */
proc glm;
model recage = Rlength Rwidth;
title 'Model #2 Adequacy';
run;
/* Residual Tests and Diagnostic Tools for Model #2 */
ods graphics on;
proc glm plots=all;
title 'Diagnostic Tests for Model #2';
model recage = Rlength Rwidth/ P ;
output out = stat
P=pred R=residual RSTUDENT=r1 DFFITS=diffits COOKD=cookd
H=hatvalue PRESS=res_del ;
run;
ods graphics off;
quit;
14

15. A.5: SAS Output
Summary of Backward Elimination
Step Variable
Removed
Label Number
Vars In
Partial
R-Square
Model
R-Square
C(p) F Value Pr > F
1 Lwidth Lwidth 5 0.0025 0.2395 5.164
7
0.16 0.686
6
2 Llength Llength 4 0.0195 0.2200 4.425
3
1.28 0.262
9
3 Lheight Lheight 3 0.0250 0.1951 4.039
9
1.63 0.207
1
Model Adequacy
The GLM Procedure
Dependent Variable: recage recage
Source DF Sum of Squares Mean
Square
F Value Pr > F
Model 3 481.873250 160.624417 4.20 0.009
8
Error 52 1988.341036 38.237328
Corrected Total 55 2470.214286
R-Square Coeff Var Root MSE recage Mean
0.195073 62.96064 6.183634 9.821429
Source DF Type I SS Mean
Square
F Value Pr > F
Rlength 1 190.148915
4
190.1489154 4.97 0.0301
Rwidth 1 181.244146
9
181.2441469 4.74 0.0340
Rheight 1 110.480187
5
110.4801875 2.89 0.0951
15

16. Source DF Type III SS Mean
Square
F Value Pr > F
Rlength 1 276.683208
1
276.6832081 7.24 0.0096
Rwidth 1 187.687833
0
187.6878330 4.91 0.0311
Rheight 1 110.480187
5
110.4801875 2.89 0.0951
Parameter Estimate Standard
Error
t Valu
e
Pr > |t|
Intercept 10.3351341
4
1.69614503 6.09 <.0001
Rlength 0.11690006 0.04345774 2.69 0.0096
Rwidth -0.28477666 0.12853758 -2.22 0.0311
Rheight -0.05726150 0.03368715 -1.70 0.0951
Diagnostic Tests
The GLM Procedure
Dependent Variable: recage recage
Source DF Sum of Squares Mean
Square
F Value Pr > F
Model 3 481.873250 160.624417 4.20 0.009
8
Error 52 1988.341036 38.237328
Corrected Total 55 2470.214286
R-Square Coeff Var Root MSE recage Mean
0.195073 62.96064 6.183634 9.821429
Source DF Type I SS Mean
Square
F Value Pr > F
Rlength 1 190.148915
4
190.1489154 4.97 0.0301
Rwidth 1 181.244146 181.2441469 4.74 0.0340
16

17. Source DF Type I SS Mean
Square
F Value Pr > F
9
Rheight 1 110.480187
5
110.4801875 2.89 0.0951
Source DF Type III SS Mean
Square
F Value Pr > F
Rlength 1 276.683208
1
276.6832081 7.24 0.0096
Rwidth 1 187.687833
0
187.6878330 4.91 0.0311
Rheight 1 110.480187
5
110.4801875 2.89 0.0951
Parameter Estimate Standard
Error
t Valu
e
Pr > |t|
Intercept 10.3351341
4
1.69614503 6.09 <.0001
Rlength 0.11690006 0.04345774 2.69 0.0096
Rwidth -0.28477666 0.12853758 -2.22 0.0311
Rheight -0.05726150 0.03368715 -1.70 0.0951
Sum of Residuals -0.000000
Sum of Squared Residuals 1988.34103
6
Sum of Squared Residuals - Error SS -0.000000
First Order Autocorrelation 0.318036
Durbin-Watson D 1.339962
17

18. Checking for Multicollinearity
The CORR Procedure
3 Variables: Rlength Rwidth Rheight
18

19. Simple Statistics
Variable N Mean Std Dev Sum Minimum Maximum Label
Rlength 5
6
27.4322
0
21.9139
6
1536 1.17784 117.88308 Rlength
Rwidth 5
6
6.99607 6.49442 391.7799
5
0.93022 30.77316 Rwidth
Rheight 5
6
30.1810
7
28.2675
1
1690 4.04000 153.19000 Rheight
Pearson Correlation Coefficients, N = 56
Prob > |r| under H0: Rho=0
Rlength Rwidth Rheight
Rlength
Rlength
1.00000 -
0.04260
0.7552
0.48260
0.0002
Rwidth
Rwidth
-
0.04260
0.7552
1.00000 -
0.04060
0.7664
Rheight
Rheight
0.48260
0.0002
-
0.04060
0.7664
1.00000
Model #2
The REG Procedure
Model: MODEL1
Dependent Variable: recage recage
Number of Observations Read 65
Number of Observations Used 56
Number of Observations with Missing Values 9
19

20. Analysis of Variance
Source DF Sum of
Squares
Mean
Square
F Value Pr > F
Model 2 371.39306 185.6965
3
4.69 0.013
3
Error 53 2098.8212
2
39.60040
Corrected Total 55 2470.2142
9
Root MSE 6.29288 R-Square 0.1503
Dependent Mean 9.82143 Adj R-Sq 0.1183
Coeff Var 64.0730
1
Parameter Estimates
Variable Label DF Parameter
Estimate
Standard
Error
t Valu
e
Pr > |t|
Intercept Intercept 1 9.54804 1.66054 5.75 <.0001
Rlength Rlength 1 0.08132 0.03876 2.10 0.0407
Rwidth Rwidth 1 -0.27977 0.13077 -2.14 0.0370
Model #2 Adequacy
The GLM Procedure
Dependent Variable: recage recage
Source DF Sum of Squares Mean
Square
F Value Pr > F
Model 2 371.393062 185.696531 4.69 0.013
3
Error 53 2098.821223 39.600400
Corrected Total 55 2470.214286
R-Square Coeff Var Root MSE recage Mean
0.150349 64.07301 6.292885 9.821429
20

21. Source DF Type I SS Mean
Square
F Value Pr > F
Rlength 1 190.148915
4
190.1489154 4.80 0.0328
Rwidth 1 181.244146
9
181.2441469 4.58 0.0370
Source DF Type III SS Mean
Square
F Value Pr > F
Rlength 1 174.330706
6
174.3307066 4.40 0.0407
Rwidth 1 181.244146
9
181.2441469 4.58 0.0370
Parameter Estimate Standard
Error
t Valu
e
Pr > |t|
Intercept 9.548040859 1.66054345 5.75 <.0001
Rlength 0.081316603 0.03875628 2.10 0.0407
Rwidth -
0.279772082
0.13077423 -2.14 0.0370
Diagnostic Tests for Model #2
The GLM Procedure
Dependent Variable: recage recage
Source DF Sum of Squares Mean
Square
F Value Pr > F
Model 2 371.393062 185.696531 4.69 0.013
3
Error 53 2098.821223 39.600400
Corrected Total 55 2470.214286
R-Square Coeff Var Root MSE recage Mean
0.150349 64.07301 6.292885 9.821429
21

22. Source DF Type I SS Mean
Square
F Value Pr > F
Rlength 1 190.148915
4
190.1489154 4.80 0.0328
Rwidth 1 181.244146
9
181.2441469 4.58 0.0370
Source DF Type III SS Mean
Square
F Value Pr > F
Rlength 1 174.330706
6
174.3307066 4.40 0.0407
Rwidth 1 181.244146
9
181.2441469 4.58 0.0370
Parameter Estimate Standard Error t Valu
e
Pr > |t|
Intercept 9.548040859 1.66054345 5.75 <.0001
Rlength 0.081316603 0.03875628 2.10 0.0407
Rwidth -0.279772082 0.13077423 -2.14 0.0370
Sum of Residuals 0.000000
Sum of Squared Residuals 2098.821223
Sum of Squared Residuals - Error SS -0.000000
First Order Autocorrelation 0.328108
Durbin-Watson D 1.313792
22

23. 23

24. 24