THE EFFECT OF SELECTED WEA.THER VARIABLES
ON THE AMOUNT OF STEM RUST DAMAGE
TO WHEAT IN NEBRASKA
by
LAWRENCE MARVIN JACOBSON
A RESEARCH PAPER
submitted to
THE DEPARTMENT OF GEOGRAPHY
OREGON STATE UNIVERSITY
in partial fulfillment of
the requirements for the
degree of
MASTER OF SCIENCE
August 1968
A CKNOWLEDGEMENTS
I wish to express my gratitude to all the people who have helped
me to prepare this research paper. Especially, do I wish to thank
Dr. Richard M. Highsmith, my advisor and major professor, who
not only helped me to prepare this paper, but acted as a guide and
interpreter throughout my stay at Oregon State University.
I am greatly indebted to Mr. Kenneth McRae (Statistics Dept.,
Oregon State University) for his patience and competence in helping
me prepare and understand the statistical methods employed in this
paper. Dr. Robert L. Powelson (Plant Pathology Dept., Oregon
State University) deserves my sincere gratitude for the assistance he
gave me in comprehending the basic principles of plant diseases.
I
am also thankful to Dr. Robert W. Romig and Dr. R. A. Kilpatrick
of the United States Department of Agriculture for the information
and advice they gave me.
TABLE OF CONTENTS
Page
INTRODUCTION ................................
1
STATEMENT OF PROBLEM .......................
2
REVIEW OF LITERATURE ........................
2
HYPOTHESIS ..................................
4
THE STUDY AREA AND DATA. SOURCES ...............
5
ANALYSIS ....................................
7
First Multiple Regression Analysis ...............
7
Prediction Calculations .......................
9
Second Multiple Regression Analysis ..............
10
SUMMARY AND CONCLUSIONS .....................
11
FOOTNOTES ..................................
13
APPENDIX ...................................
Other Bibliography ..........................
16
LIST OF TABLES
Table
I.
II.
III.
IV.
Page
Data
.
17
.......................
19
A.
List of Variables ....................
21
B.
Computer Print Out ...................
23
First Computer Run
Second Computer Rim ......................
A.
List of Variables ....................
24
B.
Computer Print Out ...................
25
Third Computer Run .......................
A. List of Variables ....................
26
Computer Print Out ...................
27
B.
LIST OF FIGURES
Figure
I.
Page
a bar graph: YEARLY STEM RUST DAMAGE TO
NEBRASKA WHEAT .......................
28
THE EFFECT OF SELECTED WEATHER VARIABLES
ON THE AMOUNT OF STEM RUST DAMAGE
TO WHEAT IN NEBRASKA
ABSTRACT: Researchers have long tried to correlate weather
factors with plant disease occurrences. However, inconclusive
results have usually been obtained because most plant diseases
have biologic as well as climatic optimums.
In this study, thirty weather variables were correlated, by the
stepwise regression method in a computer, to the amount of wheat
lost to stem rust in Nebraska over a period of fifty-two years. The
amount of May precipitation was found to be significant at the one
per cent confidence level.
INTRODUCTION
Stem rust (Puccinia graminis tritici) can be a destructive
force to a field of wheat. Some years, up to eighty per cent of a
wheat crop may be taken by this species of fungi. In other years,
almost no damage is done.
According to Dr. Robert Powelson, a phytopathologist at
Oregon State University, there appear to be three main variables
which determine the amount of damage that will be done by Puccinia.
These variables are: (1) the amount of virulent fungus available to
reproduce and spread, (Z) the acreage planted to a susceptable crop,
and (3) the weather.
2
Each variable (of the three) has a complex of elements. It
would be of value if a way were found to predict when infestations
are likely to occur. The challenge of this complex problem was the
stimulation for the research reported in this paper.
STA.TEMENT OF PROBLEM
The object of this research is to discover: (1) if certain
weather elements have an effect on the percentage of the Nebraska
wheat crop lost to stem rust, and (2) if so, whether predictions of
future damage can be made.
REVIEW OF LITERATURE
In the past fifty years there has been a significant amount of
work published correlating crop plant disease damage to weather
factors. The finding of this research has not been entirely conclusive.
Beauverie, for example, reported that stem rust was essentially a wet season disease. 2. Since urediospores require moisture
on the plants for a few hours in order to germinate, he believed
that rust epidemics must be associated with wet weather.
Carleton
found that lack of moisture tended to be a limiting factor in rust
3
development.
Lambert, however, found no correlation between a high num-
ber of rainy days during the growing season and severity of stem
rust infection in the Upper Mississippi Valley in the period 1904 to
1925.
He calculated that the odds were six to one that stem rust
epiphytotics would occur during hot growing seasons.
Peltier found in his analysis of weather-rust data for the
period 1921 to 1930 that: (1) stem rust did not become epiphytotic
during years of early heading and ripening of winter wheat in eastern
Nebraska, (2) while low temperature was the limiting factor in pri-
mary infection, moisture limited secondary infection, and (3) rust
epiphytotics were promoted by having a large amount of spores
available when conditions for maximum infection prevailed.
6.
In a biometrical study carried out by Levine, mean temperature and total precipitation in the last two months of the growing
season were found to be correlated with the intensity of stem rust
infection on susceptible varieties of wheat.
However, Levine
pointed out that these were not the sole determinants in predicting
an epiphytotic. Wallin found that the greater the March precipita-
tion in Texas, Oklahoma, and Kansas, the greater the likelihood of
a summer epiphytotic of stem rust in Kansas, North Dakota, South
Dakota, and Minnesota. 8. In another study Wallin found that there
was a correlation between precipitation, temperature, and the
4
occurrence of stem rust outbreaks in the Dakotas, Nebraska, and
Minnesota.
However, Wallin did make clear that long term
temperature and rainfall lines were not always precise in separating
rust years from non-rust years. 1110.
A. tendency toward stem rust epidemics is exhibited, in the
Mississippi Valley, according to Hamilton and Stakman, if rust
spores arrive earlier than they do in a normal year.
They found
that June 5th was the average date of the first Puccinia spore
appearance in eastern Nebraska.
Rowell found, in his dew
chamber experiments with Puccinia graminis, that rapid drying of
the spores after a heavy dew resulted in a great loss in infectivity.13
Most of the variables used in this study were either those sug-
gested in the literature, or alterations thereof.
HYPOTHESIS
Because factors other than weather influence the amount of
stem rust damage to wheat in a particular year, a 100 per cent
correlation is not to be expected between the forementioned varia-
bles considered in this research. Nevertheless, it is believed that
some useful correlations will be obtained through the employment
of the common null hypothesis. The amount of stem rust damage
will equal Y. The equation to be tested is:
5
. +30X30) + (
?
biological
selected climatic influences
influences
Y = (P0+P1X1 +132X2.
.
)
+(
?
amount of
susceptible
host available
Ho: 3i=O
Hi: some
1
O
THE STUDY AREA, AND DATA SOURCES
A. major difficulty encountered in this problem was that of
getting data on stem rust damage to wheat. The data used were ob-
tamed from the Cooperative Rust Laboratory of the University of
Minnesota for the fifty-two year period
1916-67.
Whe weather data
were obtained from the Nebraska sector of the publication, Climatological Data by Section (E. S.S. A..) for the years
1916- 67.
Nebraska was chosen for the place of study because: it is a
major wheat producing state, and the essential data were available.
A study unit about the size of a county would have been more suitable
for this type of work, but no extended period of stem rust damage
data of this type could be found. Another suitable study area would
be a state with little variation in climate and significant production of
a particular variety of wheat. North Dakota comes quite close to
being this ideal type, as it is of moderate size, relatively smooth in
topography, and has a specialty crop of Durum wheat. No long term
damage to only Durum wheat, however, could be found for this or
any other state.
Out of all the states for which data was available, Nebraska
came closest to being a satisfactory study unit. Although there is a
decrease in precipitation as one travels from east to west in this
state, winter wheat is the dominant crop in most parts.
Since the data on stem rust damage were a state average of the
percentage of the crop lost, the weather data were analyzed in the
same manner. A state average for each of the variables was obtamed by averaging these weather stations: Chadron, North Platte,
and Lincoln. In a few cases a station had some missing data for a
short period. In these instances data for a nearby station was substituted. For the 'percentage of possible sunlight, " "average wind
velocity, " and "relative humidity" categories, data were only available for Lincoln and North Platte. During this fifty-two year time
span, the form of presentation of humidity data changed from a
monghly average to a monthly average at various times of the day.
In the latter case, the 6 a. m. average and the 6 p. m. average were
averaged in order to get comparable data.
It should be noted that the selected representative weather
statio's show a lack of representation from the northeastern and
north central parts of the state. This is an intentional bias, because
comparatively little of the state's wheat production comes from these
7
two areas. 14.
ANALYSIS
A. stepwise multiple regression was done by computer compar-
ing stem rust damage to the thirty weather variables. (See table 1
for complete list of variables and data.) This seemed to be the best
available method for segregating the most significant variables and
forming a usable prediction equation.
No data was transformed, even though the stem rust data was
not normally distributed. This was because more than half of that
data either showed no damage at all or only a one tenth of a per cent
of crop loss. Since the data range was from zero to thirty per cent
crop loss, quite an irregular pattern was formed when graphed. (see
figure 1) No transformation was able to make the pattern more
regular. 15. It must then be assumed, then, that the 'Student's T
test and the "Table of five per cent and one per cent points for r
and R" are valid indicators of the reliability of the computed results.
The results of the first regression test were quite interesting.
Simple correlations revealed the following variables to be correlated
at the one per cent confidence level with stem rust losses:
A.
total May precipitation, with a 43348 correlation
.
c oe ffi ci e nt,
B
precipitation fromMay 21-31 with a .41103 correlation
coefficient,
C
(total May precipitation) (percentage of possible May
sunlight) with a . 42858 correlation coefficient,
D
(total May precipitation) (May mean temperature) with a
correlation coefficient of .47196,
E
(percentage of possible June sunlight) (average June
relative humidity) with a correlation coefficient of
45620, and
F
(total May precipitation)2 with a .46531 correlation
coefficient.
The multiple correlation was also significant at the one per
cent confidence level, having an R- square of .51272 for the six
variables which were deemed significant at the five per cent confidence level by the Student's T test. Variable twenty-three, (May 131 precipitation) . (May mean temperature) was the most significant
member in the equation, accounting for approximately 22. 3 per cent
of the variations in stem rust damage. 16.
This prediction equation comes from the first multiple regression.
= -.10416 - .1936 X3 +.0285X4 +.0024X3'X5
stem
May 1-31 May 21-31 (May precip.)'
rust
(May mean temp.)
precip.
precip.
Y
+ .000118 X2'X8 + .00002457 X 7x 8
(% poss. June sunlight)
(last frost)'
(May wind vel.) (June relative humidity)
+ .0107 X3
(May 1-31 precip.)
Approximate yearly predictions of crop loss due to the actions
of Puccinia graminis were calculated by computer and compared to
the actual crop losses. 17. Most of the predictions came fairly
close to the actual wheat losses. The three notable exceptions were
the years 1919, 1920, and 1944. These years had ten, twelve, and
twenty per cent crop losses respectively. However, the prediction
equation only predicted slightly more than one, one, and five per
cent losses for these same years.
But there were some notably good predictions. The years
1923, 1935, 1959, 1960, 1961, 1962, and 1965 were also "bad rust
years, ' and were predicted so. The prediction equation made only
one bad prediction after 1920. Also, all of the years with no rust
damage at all were predicted at less than five tenths of one per cent
damage.
A. curious attribute of this prediction equation is that the precipitation from May 21-3 1 has a positive effect on the prediction
10
equation, whereas the May 1-31 precipitation has a negative effect
on this same equation. This occurred even though both of these
variables had positive simple correlations of significance.
Since most of the significant variables in both the simple and
multiple correlations were related to May precipitation in some
way, it seemed that a better multiple correlation could be obtained
by a more detailed examination of this variable. Thus, the effects
of May 1-20 and May 21-31 precipitation were examined separately. 18.
A. stepwise multiple regression was also done on these vanables. However, only a . 38634 R- square was obtained on this run,
with the only significant variables being May 21-31 precipitation and
(May 1-31 precipitation). (May 21-31 precipitation. 19.
11
SUMMARY AND CONCLUSIONS
It seems as if certain weather elements do have an affect on
the percentage of the Nebraska wheat crop lost to stem rust. The
most important of these variables seems to be the amount of precipitation in May. Especially toward the end of May, when wheat
"heads, " does this relationship between moisture and stem rust
damage seem most critical. This finding, in general, seems to be
in agreement with what some other researchers have found.
Beauverie (1923), Moreland (1906), Carleton (1905), Peltier
(1933), Levine (1928), and Wallin (1964b) all found some relation
between moisture and damage by stem rust.
But, the results
obtained in this study seem to indicate that the time the moisture
arrives is as important as the amount of moisture itself. This
probably has to do with moisture availability at a time when the
Puccinia spores can get an early start at germination and reproduction.
Although some researchers found relationships between
temperature and stem rust damage (some of which were conflicting),
no temperature correlations, as such, were found in this study.
The prediction equation computed in the first multiple regression run was fairly successful. For most of the years in this study,
the predicted crop losses were reasonably close to the actual crop
12
losses. Yet, there were a few years in which little damage was
predicted, but significant losses occurred.
Although other variables, in addition to unmodified rainfall
variables, correlated by computer with stem rust damage, some of
these may have been TichancelT correlations. Considering an original
sample size of thirty and a five per cent confidence level on the
StudentTs T test, it is quite possible that one or two of these varia-
bles is correlated only by coincidence.
It seems, then, that in order to better predict and understand
the depredations of Puccinia graminis, biological - as well as
physical - variables should be taken into consideration.
13
FOOTNOTES
1.
Powelson, Robert L. Associate Professor, Oregon State
University, Department of Botany and Plant Pathology.
Personal Communication.
2.
Corvallis, Oregon. May 25, 1968.
Beauverie, J. 1923. On the development of wheat rusts in
relation to climatic conditions. Report of the International
Conference of Phytopathology and Economic Entomology,
Holland: page 202.
3.
Carleton, M. A..
of 1904.
1905.
Lessons from the grain-rust epidemic
24p. (United States Department of Agriculture.
Washington, D. C. Farmer's Bulletin 219. page 24.
4.
Lambert, Edmund B. 1929. The relation of weather to the
development of stem rust in the Mississippi Valley. Phytopathology 57: page 68.
page 48.
5.
Ibid.
6.
Peltier, George L. 1933. Relation of weather to the prevalence of wheat stem rust in Nebraska. Journal of Agricultural
Research 46: page 72.
7.
Levine, Moses N.
1928.
Biometrical studies on the variation
of physiologic forms of Puccinia graminis tritici and the effects of ecological factors on the susceptibility of wheat
varieties. Phytopathology 18: page 120.
14
8.
Wallin, Jack R. 1964. Texas, Oklahoma, and Kansas winter
temperatures and rainfall, and summer occurrence of Puccinia
graminis tritici in Kansas, Dakotas, Nebraska, and Minnesota.
International Journal of Biometeorology 7: page 243.
9.
Wallin, Jack R. 1964. Summer weather conditions and wheat
stem rust in the Dakotas, Nebraska, and Minnesota. International Journal of biometeorology 8: page 42.
10.
Ibid. page 44.
11.
Hamilton, Laura M. and E. C. Stakman. 1967. Time of stem
rust appearance on wheat in the Western Mississippi Basin in
relation to epidemics from 1921 to 1962. Phytopathology 57:
page 609.
12.
Ibid. page 604.
13.
Rowell, 3. B., C. R. Olien, and R. D. Wilcoxson. 1958.
Effect of certain environmental conditions on infection of wheat
during the growing season in the spring wheat area of the
United States to the occurrence of stem rust epidemics.
Phytopathology 18: page 377.
14.
Nebraska. Department of Agriculture. Nebraska agricultural
statistics; centennial edition 1967.
Lincoln, Nebraska, pages
70, 71, and 78.
15.
The cube, square, square root, log and loglog of the stem
rust data were unsuccessfully tried.
15
16.
See computer run #1, Table II B.
17.
Note computer run #2, Table III B.
18.
For a complete list of these variables see Table II A..
19.
For more details see computer run #3, Table IV B.
APPENDIX
16
OTHER BIBLIOGRAPHY
DeWeille, G. A..
1965.
The epidemiology of plant disease as consid-
ered within the scope of agrometeorology. Agricultural
Meteorology 2:1-15.
Loegering, W. Q. The rust diseases of wheat. Washington, D. C.
United States Department of Agriculture. 1967. 22p. (Agricultural Handbook 334)
Moreland, W. H. 1906.
The relation of the weather to rust on
cereals. India. Department of Agriculture. Memoirs.
Botanical Series 1 (2):53-57.
Nuttonson, M.Y. Wheat-climate relationships and the use of
phenology in ascertaining the thermal and photo-thermal
requirements of wheat. Washington, D. C.
,
American Institute
of Crop Ecology, 1955. 388p.
Peterson, R. F. Wheat. New York, Interscience Publishers Inc.
1965.
422p.
Stakman, E. C. and E. B. Lambert. 1928. The relation of temperature during the growing season in the spring wheat area of the
United States to the occurrence of stem rust epidemics.
Phytopathology 18:369-379.
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92 720 (57 104
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085 630 770 236
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798 570 68? 325
96? 575 70? 2o3
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19
Table hA
All of the variables used in the regression tests were used
because it was thought that variations in each one of these variables
would cause variations in the amount of stem rust damage to wheat in
Nebraska.
The variables concerning temperature were chosen because it
was believed that abnormally cold or hot weather would tend to limit
the growth of the Puccinia spores. The data of the last frost seemed
to be a good way to find out whether a late frost would retard the
damage caused by stem rust.
Since many researchers found correlations between precipita-
tion and rust damage, many precipitation variables were used in this
study. This was done in order to see if any hicriticalT! periods in the
life cycles of either Puccinia or wheat could be discerned, and if
discernible, the extent of criticalnessTT of these periods. Humidity
variables were used because it was believed that low relative
humidities would tend to dry out the spores, making them less viable.
Wind variables were used because it was thought that higher
wind speeds would mean greater spreading of spores. The percentage of sunlight variables were used because it was hypothesized
that excessive light would render Puccinia spores inviable. Variables were squared and multiplied with one another in order to see
20
Table hA. cont.
if more subtle relationships could be brought out.
21
Table II Part A cont.
List of Variables for the First Computer Run
Xl
(May mean temperature)2
X2 = date of last frost, April 1 = 1
X3 = May 1-31 precipitation
X4 = May 21-31 precipitation
X5 = mean May temperature
X6
average daily maximum temperature in May
X7 = average daily minimum temperature in May
X8 = average May wind velocity
X9 = percentage of possible May sunlight
Xl0 = average May relative humidity
Xli = June 1-30 precipitation
X12 = June 1-10 precipitation
X13 = mean June temperature
X14 = average daily maximum temperature in June
X15 = average daily minimum temperature in June
Xl6 = average June wind velocity
X17 = percentage of possible June sunlight
X18 = average June relative humidity
X19 = average July precipitation
Table II Part A. cant.
X2O = mean July temperature
X21 = average July relative humidity
X22 = (X3) (X9)
X23 = (X3y(X5)
X24 = (X3).(Xll)
X25 = (X2)(X8)
XZ6 = (X8)(X1O)
X27 = (Xll)(X13)
X28 = (X17Y(X18)
X29 = (X19) (X2O)
X30 = (X3)2
24
Table III, Part A
List of Variables for the Second Computer Run
Xl = (X3)2
X2 = (date of last frost) (average May wind velocity)
X3 = May 1-31 precipitation
X4 = May 21-31 precipitation
X5 = (May 1-31 precipitation). (mean May temperature)
X6 = (percent of possible June sunlight). (June relative humidity)
26
Table IV, Part A.
List of Variables for the Third Computer Run
Xl = May 1-20 precipitation
X2 = May 1-31 precipitation
X3 = May 21-31 precipitation
X4 = (Xl) (X2)
X5 = (X1) (X3)
x6 = (X2) (X3)
=
(X1)2
X8 = (X2)2
X9 = (X3)3
YEARLY STEM RUST DAMAGE
TO NEBRASKA WHEAT
I6
26
36
46
YEARS
56
66
a
a
a
.
a
.
ACCT
7OiOB/o1
DATE
07/15/68
DEPT: 197
CLASSa ç
IDa LMJ
TIME INI 17/41/OS
TIME 01)1* 17/4/32!
TIME USED
CGMP* 00/00/12,189
CHAN* Oo/oO/07433
FACILITIES; REQUESTED
COREsO30
CUTaO1000
PONoO000
ScR:*oO3:
!t'1psOO1 12
JOB!
LMJ!7O108/Oi,197,?,1000
SCHEO ,CCREa3O, SCR*3
STEP
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PROBLEM NO,
DATE
2
NO OF DATA a
7 12 68
52
NO OF VARIABLES a
8
NO OF CASE a 2
TRANSFORMATIONS
2s
5*
6*
8*
2(3)6
3(3)5
t(3
1(0)0
1 a
a:
3
3) 3
TNPUT FORMAT
(3x,r4.4,r#,2,2r4.3,r4,2.,8x,r4.2,,,31x,2,4.2
INPUT VAR!ABLES
2,30000000E-02 2.90000cE 01
2.l0000000E 00
2.ø00000oo-o1 5,89øOOO 01
2,700000Ô0E 00
2.Ø0000000E-o1
8.T000000oE 00
b.95000000E 01
6,g8000000E o
4.8O2S0OOE
6,95000000E 01
?.0000000E.O2;
VARIABLES A!ER+ TRANSFORMATIONS
7,e900óooôE: 00
2,52!oó00002
1.S9*oOOO
o?
S
VERSUS X 1) THRU X( 8)
8.77357076E 03 i.13510580E 05 2.10557422E 03
X( 2) VERSUS X( 2) THRU Xl 8)
6.30155516E 06 4.90956450E 04 1192498723E 04
X( 3) VERSUS: XC!) THRU X(8)
5,45723700E 02: 2.14604800E 02
.0S9?!8 °!
2.$750707
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.9R14573
X( 4) VERSU8 XC 4) THRU X 8)
i.01756800E 02 1,?558649?E 04 2,8S382227E 05
4.34195000
XC 5) VERSUS
1.87575680E: 06
X
5) THRU X( 8)
4.0!98?628t 07 6.29413925E 03
X( 6) VERSUS XC 6) THRU X( 8)
1.05711182E 09 1.1a25floE 07 1,3824586óE 03
THRU XC 8)
XC 7) VERSUS X(
I,08368000E 02
)
2.53393000E: 05
XC 8) VERSUS XC
2 a 3?303000Eu0
S
$S PRODUCTS
RAW SUMS 0! SQUARES AND
THRU XC A)
!.8?16?
0
05
0
2,411407U 06
3,68394537E 04
09
i.0971!E 08
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6.52366000E 00
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?.074f271
2,86847000E 00
2.8214?708E 01
[.
RESIDUAL
SUMS
or
SQuARES
CROSS PRODUCTS
AND
1) THRU Xi 8
3.0463160E: 03: 9.0407615?E Ô3
4.6o95894E 02
1.4I8842!3
0
2.599576!!E 04 22345002E 04
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1.57497583E
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2.13o76076L 03 -1,45442499E 02
1.60238327E 06
XC 1) VERSUS'
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XC 2) THRU X
XC 3) VERSUS: X
7.3454ÔÔ58E oI
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2.37199654E ot 4.13565055E 03
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2.46038OflE Oli ,3194e9SE 63
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4.02375000E 03 .4,71925O00E 00
XC 8) VERSUS XC 8) THRU X
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8)
8.51 719924
01
4.43450001
01
9,93916166E 01
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XC 1) VERSUS XC 1) THRU X( 8)
1.00000000E 00 t.OS1?869Eo1 90?444296oEOj
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1.00000000E 00 5.S1962673E.O1 9.88270343E.O1 .5,7433970*O
2.67527291E-OI
4,334
XC 2 VERSUS
1.00000000E 00
XC 4) VERSUS
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X
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1,08919870E01 i,4093!97E-0I
XC 5) VERSUS X( 5) THRU X 8)
t.00000000E 00 .4 .10845329E.01 -3,09085386E-01
XC 8) VERSUS XC
1 ,00000000E 00
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8)
3.50O171E.01
X( 7) VERSUS: X( 7) THRU X( 8)
1,00000000E 00 4,724952i9E,O1
XC 8) VERSUS Xl 8) THRU X( 8)
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4,562O09?2E02
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1.S877440O
3
t.56710000E
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6.33400000E
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2.32369200E
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1.63300000E
TYPE 3 TAPE oUl'PUT
I
N0BAStCS?A1
02
04
02
01
03
05
03
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MEAN
1,04946865E
3,01489231E
3,01365385E
1,21807692E
1.7744t115E
01
02
00
00
02
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7.72869823E 00
1.i5?24O8E 02
6,925b0000E 01
li?0011442E 00
6,945?0084E-01
6,83t15211E ot
6.06142990E 02
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3.14038462E'-02
6 03942 146F"02
4,46863M6t 03
PROBLEM NO,
NO O
2
DATA
OF VARIABLES a
NO OF CASE
:
8
2.
F LEVEL TO ENTER VARIABLES s
F LEVEL To REMOVE VARIABLES
0
0
7
8VAR!A8LES
ELIMINATE
SYV al.86020519E.O1DEG, FREE, a 5.j0000000E 01
STANDARD ERROR OF
6.034215E'02
S
"w
S
S
VARIARLE ENTERTNG
SSE
1.44504421E-01
F LEVEL
1.3294
S
S
S
R"SQUARE
2.22750146Euoi
DEG, FREE
5.00000000E 0
STANDARD ERRCR C!Y
5.7422E-O2
CONSTANT
-4.2513379EO2
VARIARLE
X 5
S
5
CCEFF!C!ENT
STUDENTS
4,1689?3Ea04 3,78416SE 00
.
Ij#
iu
VARIABLE ENTERING
3
SSE
RNSQUARE
2,6928?832EO1
1 .35927494EuO1
.
.
F LEVEL
3.120?
STANDARD ERROR OF Y a
VARIABL2
xu
S
S
5,2669066t.02
CCNSTANT 4.1159434E02
CCEFflCIENT
3-7,1oe7Sa1Eô2
x S
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DEG, FREE
4,90000000E 01
1.6500503Ee03
STUDENTS
I
t.?665S14E 00
2.336050TE 00
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STEP NC, i
VARIABLE ENTERING
2
SSE
1,24688812EmO1
r LEVEL
4.3264
R-SQUARE
3.29703987EO1
STANDARD ERROR 0F V
5.Oq67476E-02
CONSTANT -6.79?5912E-02
VARIABL
COEF!cIENT
STUDENTS
0
Xa
xX.
DEG, FRE
4.40000000E 01
T
2
8.695?9E.0S 2,08O005! 00
3
5
B.289$31ÔE02 a2,1065510E 00
1,8212022Eiu03 2.6453395E 00
STEP NO. 4
VARIARLE ENTERtNG
SSE
1,13641205E.O1
LEVEL
4.5663
.
R-SQUARE
3.R9060491E-01
DEG. FRU
4.70000000E 01
STANDARD ERROR OF Y a 4.9173441E-02
CONSTANT -7,6806532E-02
VAR1ABL
STUDENTS T
COEFFICIENT
xxi
.
.4
Xi
X-
9.44e28t2E-oS 2.34i88a5E 00
3 i9.6550270E.02 -2.5077224E 00
4
2.5678154EiÔ2 2.136e9e9E 00
S
1.912?724E-03 2.8?37300E 00
2
STEP NO.
VARIABLE ENTERING
SSE
1.o09451llE-0l
F LEVEL
5,7883
STANDARD ERROR OF? a
I
RSQUARE
4.57344213E-ol
4,6945052E-02
CONSTANT -E.8539144E-03
VARIABLE
COEFFICIENT
XX.
X.
.
STUDENTS
I
!.333136?E"03 2.4058e74E 00
1,1118561E-04 2,8538622E 00
3 '1.5542184E.01 -3.5249882E 00
4
2.9938749E-02 2.5845522E 00
5
1.8862413E.03 2.9742832E 00
1
X'
DEG, FREE
4.60000000E 01
2
STEP NO,
6
VARIABLE ENTERING
6
SSE
RsSQU*RE
9.3499t9o2
4.97371E,08E'O1
F LEVEL
3,5836
STANDARD ERRCR or Y a
DEe, FREE
4.S0000000E O
4.5!82451E'.02
CONSTANT u.9.2233717F-'02
VARXABLt
x,.
I
X-'
2
x.,
COEFFICIENT
1.1064492E'.02
1,0949343E-04
3 '1,89O7i53E*O1
2.7040285E-02
X 4
r
x- 5
.3.198042E-03
6
2,2316532E.o5
SYD ERROR OF COEF
T VALUE
38395j TE-03
2.0487718E
3,7920 166EO5 2. 8874724
4.6439619E"02 4.07t341 E
1. t3?5O32E02 2.3771613E
6.5822114E-o4
1. 1788603E*05
1.e!3b4?IE
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STD. COEPT
0$
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0o -3.7571Ô60E 0O
0o 3, 1O97967EO1
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00 2, 2397a5iE.oi
.
PREDICTED VS ACTUAL RESULTS
RUN NC.
ACTUAL
PREDICTED
2
.
.
.
S
S
.
.
.
S
8.982293E-02
1 .026879E-02
1 128879-02
ii
1 ,000000E.03
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4.713310E-03 -4.713310!-03
5,065424E'03
1 .000000E'.03 -4.065424E-03
I 000000E-03 '.9 8938 87E.03 I .089389E-02
0
1 ,Oo0OOOE.O3
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19
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1 .Ô00000E'.03
1 ,400000E'.Ol
21
I .oC0000E*03
22
6, O00000Ee02
23
24
25
S. O000OOE.02
26
27
1 ,000O0o-O3
1.300000E-02
1 .000000E.03
1 .000000E.03
1, 000000E.'03
28
29
2, 000000E'.O 1
30
31
32
33:
1 ,000000E'.03
I ,O000O0E03
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I .000000E'.03
34'
35'
36
37
38
39
40
41
4:2
43
44'
45
4.
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1 .O17707E-02
I 304366 E-02
8.615212E-03 '.7.61521E'O3
5,O0O000E03 4.955513E.O2 '.4,45551 3E-02
A
4. o00000E.02 3 .068563E.02 9.3143?2E03
9'
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20'
S
1, 100253E-02
I .200000E'.Ol
1 .000000E'.03
14
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8.997471E-03
2 .000000E.02
1 .000000E'.Ol
12
S
3.!15732E-02
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6
1
13:
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2.300000E"02 '.1 ,015732E'.O2
1 .0000E.'03 6.617461E-02 -6,517461E-02
lo
.
DEVIATION
47
48
5o
51
1 ,000000E03
1 .000000E.03
1O00O00E.03
1 ,000000E"03
2 .000000E-02
5.O00000E02
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1 .000000EwO3
2,000000E.'02
I .000000E-03
5 ,400000E'.02
5 ,000000E.O2
I ,S00000E.Ot
-5, 32S941E-03
6, 325 941E-03
a .483042E-O2
u'l ,983042E-02
9.035498E..03 .8,03548E-O3
3 .878241E-02 -3,078241E'.02
.6 899O86EuuO3
8, 8990B6E-03
'.1 tS000lE.u02
I .2500ô1E-02
9.213170E'.02 4.786B30E"02
1 592? 09E-03 -6, 592709E-03
S 502085E.03
5.449793E"02
1 .883917E'.02 3.1 16083E-02
A 023624E-03 ..7.023624E-03
1 .066214E-02 2. 337859E-03
2.148993E-02 ..2,048993E.02
2. 129374E-02 .2,029514E'.02
7 .405239E.03
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5.303525E-02 1 .469648E-01
5. 004645E'03
2.379745E-03 -1 .379745E-03
4 .682592E'.02 -2, I82S2E-02
3, 0242 84E-02 -2, 924284E"02
6.217055E-02 '.6.1 17055E-02
3.606502E'.02 -3 .506502E'.02
6.970578E'02 -6, 870578E-02
6 ,3172Ô7E-02 .6 217207E-02
I .4o7483E..02 5,925172E-03
3.4 10528E'.02 1.58 14?2E-02
4, 805546E'.02 .4 7a5546E'.02
5 .476292E.02 -5 376292E'02
8.822547E02 '.6.822547E-02
9 .34430S-O3 -8. 344305E.o3
8.016682E.02 .2,j8682E-02
4 .062ô 1 6E'.02
9. 79865E.O3
1 .246781E-01 2,532185E-02
2.231760E-01 7,682396E-02
1 .553410E-02 -1 .4s34ioE-0a
5 000000E-03 4,227028E'.02 -3 ,72?O8E-02
1 .S00000E-01 1 120072E-01 3, 7992?BE-02
1Oc0000E'.03 -1 ,252044E-03 2, 252044E-03
3 ,000000E.O1
1 .000000E-03
52;
DEVIATtON MEAN,
0
4.3?638?'.c3 .4326389E-O3
SUM
F SQUARES,
... CU$ES,
!a
FOURTH POWERS.
1,022744?824E*11
9.3499195597E-02
4.0572958229E'03
8.3067637354E.04
BF7A,RETA2,KAPPA,W1W2
1.04?25651E 00
4,94105232E 00
1,34160933E 00
3.18995962E 00
3.4625!33E 00
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