Directory UMM :Data Elmu:jurnal:A:Agricultural Systems:Vol64.Issue3.Jun2000:
Agricultural Systems 64 (2000) 151±170
www.elsevier.com/locate/agsy
Predicting corn and soybean productivity for
Illinois soils
J.D. Garcia-Paredes, K.R. Olson *, J.M. Lang
Department of Natural Resources and Environmental Sciences, University of Illinois at Urbana-Champaign,
Urbana, IL, 61801, USA
Received 15 January 2000; received in revised form 4 March 2000; accepted 20 March 2000
Abstract
Current corn and soybean productivity data is needed in Illinois for land-use planning,
sustainable farm management, and accurate land appraisal. The out-of-date source of soil
productivity data is Circular 1156 Soil Productivity in Illinois (Fehrenbacher et al., 1978,
Soil productivity in Illinois. UIUC. College of Agriculture. COOP. EXT. SERV. Circular
1156). A new major analysis based on current Illinois farmer crop-yield data is needed to
assure the availability of reliable 10-year average corn and soybean yield estimates by soils.
The overall objective of this study was to update the corn and soybean yields which serve as a
productivity index for Illinois soils since these two crops are grown on approximately 90% of
the cropland. An approach based on multiple regression was used to evaluate the relationship
between 16 selected soil properties of 34 major soils and established 1970s (1967±1976) corn
and soybean yields as published in Circular 1156. Statistical models developed from major
soils were tested internally by calculating the 10-year average corn and soybean yields for each
of the 34 major soils. The coecients generated from multiple regression were further tested
using the soil property values for the additional 165 soils identi®ed in nine counties representing the crop reporting districts and weather districts in Illinois. The 10-year average crop
yield trends were determined for 66 counties in the northern region and for 36 counties in the
southern region for the 20-year time period between 1976 and 1995. These 20-year yield trend
increases were added to the established (Circular 1156) and model predicted 1970s crop yields
to estimate 1990s (1986±1995) corn and soybean yields for the average management level for
all 199 Illinois soil types in nine selected counties. The 1990s crop yield estimates for the
selected counties were weighted by extent of each soil type in the county and compared
against 10-year county averages for the 1990s farmer reported Illinois Agricultural Statistics
(IAS) corn and soybean yields. Predicted 1990s county crop yields were statistically similar to
* Corresponding author. Tel.: +1-217-333-9639; fax: +1-217-224-3219.
E-mail address: k- [email protected] (K.R. Olson).
0308-521X/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved.
PII: S0308-521X(00)00020-2
152
J.D. Garcia-Paredes et al. / Agricultural Systems 64 (2000) 151±170
1990s farmer reported (IAS) county crop yields. The proposed approach to updating corn and
soybean yields worked well and should be useful in surrounding states or countries. # 2000
Elsevier Science Ltd. All rights reserved.
Keywords: Crop-yield prediction; Soil property models; Illinois soils; Soil types; Yield trends
1. Introduction
Crop yields are the result of environmental factors such as soil, climate, and
management inputs. The eect of technology and management on crop yield is
determined, in part, by the type of soil. Consequently more speci®c information on
the in¯uence of soil properties on crop yields is required. Many scientists have tried
to ®nd relationships between soil properties, climate, and crop yields, and grouped
soils in order to compare them (Sarkar et al., 1966; Robles et al., 1977; Allgood and
Gray, 1978). Most of these agronomic research studies have enhanced the importance of soil depth on crop yields in a direct and indirect way (Shrader et al., 1960;
De la Rosa et al., 1981; Reith et al., 1984; Thompson et al., 1991; Craft et al., 1992).
Many of the soil properties considered as important for determining crop yields,
have been related to moisture holding capacity (Baier and Robinson, 1968; Olson,
1981; Olson and Olson, 1986; Ulmer et al., 1988).
Dierences in crop yield and soil productivity may be represented by productivity
indices. Productivity ratings are a good indicator of the suitability of soils for crop
production. They are useful in determining optimum soil management and use
(Anderson et al., 1938; Fehrenbacher et al., 1970). Accurate and reliable soil productivity information is desired for crop yield estimates and productivity indices of
each soil type to complement land appraisal and use management. Most soil productivity data currently adopted were obtained from publication Circular 1016
Productivity of Illinois Soils (Odell and Oschwald, 1970). Much of the data were
developed during a period of 1933 to 1950 and updating occurred in the 1960s.
Productivity data published in 1978 in Circular 1156 Soil Productivity in Illinois
(Fehrenbacher et al., 1978) were updated by numerical adjustment emerging from
improved technology.
Crop yields increased signi®cantly in Illinois from 1945 to 1995. These incremental
increases of yield were primarily a result of improved technology (Swanson et al.,
1977) which included: (1) biological-chemical inputs such as improved varieties,
mineral fertilizers, pesticides, and higher plant populations; (2) mechanical resources
like machinery; and (3) management. Along with augmented crop yield trend, there
were annual ¯uctuations from weather eects.
Trends in crop yields are important for economic decision makers, as well as for
farm owners and operators because yield performance may in¯uence determinations
regarding agricultural inputs levels and adoption of new technologies (Outt et al.,
1987). Additionally, past, present and future crop yield data could be used as a basis
for land valuation (assessment), crop insurance, and other related farm business
(Swanson, 1957).
J.D. Garcia-Paredes et al. / Agricultural Systems 64 (2000) 151±170
153
Crop yield trends were one of the main concerns in the 1970s. Several studies
examined crop yield trend movement to determine if it was increasing or leveling o.
Many of these studies were focused at or within a state level. Herbst (1975) made a
comparison of four 5-year periods (1953±1957 to 1961±1965), (1961±1965 to 1969±
1973), for corn, soybean, wheat, and oat. Greater yield increments were identi®ed in
the previous 5-year period (1953±1957 to 1961±1965) compared to the latter period
(1961±1965 to 1969±1973).
A study with corn and soybean yields on the Allerton trust farm (Piatt County, IL)
for 27 years (1950±1976) demonstrated that yields, unadjusted and adjusted by
weather, were accelerated linearly (Swanson et al., 1977). Sonka (1978) studied corn
yield trends and variability in Illinois for the period of 1927 to 1977. There were no
indications that corn yield had reached a plateau despite yield variability increases
since 1970. Chicoine and Scott (1988) evaluated the behavior of corn and soybean
yield from 1972 to 1985 in Illinois. They found signi®cant evidence that soybean yield
trends may be leveling o. However, the results for corn were inconclusive.
Productivity data published in Circular 1156 Soil Productivity in Illinois (Fehrenbacher et al., 1978) were updated through previous number adjustment re¯ecting
technology improvements. In 1994 a supplement to Circular 1156 was released to
include new soils established between 1978 and 1994 (Olson and Lang, 1994). This
supplement used 1970s (1967±1976) management to estimate crop yields. These
published yields are very antiquated, more than 20 years old. Changes in crops yield
and crop rotation have had an eect. Yield adjustments should be modi®ed by soil
type to parallel technology innovation eects on crop production, soil productivity,
and subsequent productivity indices.
The overall objective of this study was to update the corn and soybean yields
which serve as a productivity index for Illinois soils since these crops are grown on
90% of the cropland. An approach based on multiple regression was used to evaluate the relationship between 16 selected soil properties of major soils and established
1970s (1967±1976) corn and soybean yields as published in Circular 1156. The
average crop yield trend increases from 1976 to 1995 in farmer reported yields by
Illinois Agricultural Statistics (IAS) for the northern and southern regions of Illinois
were added to the established (published in Circular 1156) and model predicted
1970s (1967±1976) crop yields to estimate 1990s (1986±1995) corn and soybean
yields for the average management level for all 199 Illinois soil types in nine selected
counties. The 1990s crop yield estimates for each soil were weighted by extent of that
soil type in the county and compared against 10-year county averages for the 1990s
farmer reported (IAS) corn and soybean yields.
2. Materials and methods
2.1. Procedures
Our approach included the following steps: (1) to develop crop yield-soil property models by stepwise multiple regression with 1970s (1967±1976) crop yields
154
J.D. Garcia-Paredes et al. / Agricultural Systems 64 (2000) 151±170
along with soil properties from 34 major (base and benchmark) soils; (2) to
internally check by calculating average corn and soybean yields using the model
generated coecients and the soil properties values for each of the 34 major soils;
(3) to test coecients generated from multiple regression using the soil property
values for an additional 165 soils identi®ed in nine counties representing the crop
reporting districts and weather districts in Illinois; (4) to identify any corn and
soybean yield outliers (greater than 2 S.D.); (5) determine the reasons for the
outliers and propose modi®cation to improve the predictive models; (6) to determine the magnitude of farmer reported (IAS) corn and soybean yield changes from
1976 to 1995 for northern (high productivity) and southern (lower productivity)
regions; (7) to use the 20-year crop regional yield increases to predict 1990s crop
yields for 199 soils in nine northern and southern Illinois counties; (8) to evaluate the model predicted plus 20-year trend increased crop yields and established
(Circular 1156) plus 20-year trend increased crop yields for nine selected
test counties (Fig. 1) by comparing with the 1990s farmer reported county crop
production (IAS).
2.2. Soil types selection
Thirty-four major soil types were chosen for a model development to determine crop yield estimates. These included nine base soils which were selected
to represent the best producing soils under basic management which were
assigned the highest basic productivity indices (PIs) in Circular 1156 (Soil
Productivity in Illinois; Fehrenbacher et al., 1978). Each of these soils have
extensive acreage in Illinois. From various soil survey and soil conservation
programs, it was determined that a list of 30 benchmark soils represented most
of the major soil conditions in the state. There are ®ve major soils on both the
base and benchmark lists. This major (base and benchmark) soils list was
the basis for developing a crop yield-soil property rating (CYSPR) model
(Table 1).
A comprehensive list of physical and chemical properties which aect or appear
to aect crop yields in Illinois were identi®ed by multiple regression and included:
(1) surface layer thickness (cm); (2) surface layer percent silt; (3) percent organic
matter in surface layer; (4) CEC of surface layer; (5) depth (cm) to redoxamorphic
(wetness) features drainage class (relates to drainage class); (6) subsoil thickness
(cm); (7) plant available water to a depth of 150 cm; (8) rooting depth as a function
of soil structure (cm); (9) depth in cm to 2nd parent material (usually thickness of
loess); (10) permeability; (11) surface layer pH; (12) subsoil pH; (13) surface layer
bulk density; (14) subsoil bulk density; (15) percent Na on the exchange; and (16)
percent clay in subsoil.
Field measured soil property data from the Illinois soil characterization data
base (2160 pedons) and the United States Department of Agriculture, Natural
Resources Conservation Service (USDA±NRCS) estimated soil properties data
base were used to compile a comprehensive list of soil property ranges for each
selected soil type.
J.D. Garcia-Paredes et al. / Agricultural Systems 64 (2000) 151±170
155
Fig. 1. Northern and southern soil productivity regions and nine test counties in Illinois.
2.3. Regression analysis of Circular 1156 crop yields
Stepwise multiple regression was implemented to establish the relationship
between 10-year crop yield estimates from Circular 1156 and selected soil property
values. The soil properties were represented with a numeric value common for each
soil property. Only one value was assigned by soil type and property for the appropriate A horizon, B horizon or soil pro®le.
156
J.D. Garcia-Paredes et al. / Agricultural Systems 64 (2000) 151±170
Table 1
Base (previous most productive) and benchmark (representing major soil conditions)
soils in Illinois
Base soils
Benchmark soils
Drummer siclab
Elburn silb
Flanagan silb
Ipava silb
Joy sil
Lisbon sil
Littleton sil
Muscatine sil
Sable siclb
Alvin fsl
Ashkum sicl
Belknap sil
Blount sil
Bluford sil
Catlin sil
Cisne sil
Denny sil
Drummer siclb
Ebbert sil
Elburn silb
Elliot sil
Flanagan silb
Grantsburg sil
Harpster sicl
Herrick sil
Hickory l
Hoopeston sl
Huey sil
Ipava silb
Karnak sicl
Milford sicl
Morley sil
Sable siclb
Sawmill sicl
Saybrook sil
Selma l
Varna sil
Virden sil
Weir sil
a
b
sicl, silty clay loam; fsl, ®ne sandy loam; sil, silt loam; l, loam; sl, sandy loam.
On both lists.
2.4. Preliminary statistical analysis
A correlation analysis was used to provide information about the nature of the
variables used in the multiple regression models, and to identify which variables
were more highly correlated. Simple statistical data analyses were evaluated (stemleaf diagrams, box plot, and normal probability plot) in order to check the usual
assumption in regression analysis. The diagrams for most of the predictor variables
were acceptable bell-shaped curves. The variable exchangeable sodium was not a
bell-shaped curve, since all but one of the soils had values of zero. The Statistical
Analysis System (SAS) was applied to analyze the soil and yield data. The R-square
option was utilized with emphasis on maximizing R for regression.
J.D. Garcia-Paredes et al. / Agricultural Systems 64 (2000) 151±170
157
Multiple regression analysis was used to provide estimates of the relationships
between crop yield and soil variables. All computations were carried out with
respect to the following model:
Yi 0 1 X1 2 X2 ::: i Xi ; i
1
where Yi is the response or dependent variable, which represents the predicted crop
yields. The explanatory factors X1, X2, . . . Xi are assumed to be independent. i is the
error due to the fact that the postulated independent variables do not completely
account for the variation in Y. The parameter b0, b1 . . . bi are the population
regression coecients for the soil eects.
There are several methods to select an optimum set of independent variables. A
criteria for determining how many variables to consider in the model is to use Mallows' Cp statistic (Freund and Littel, 1991). The Cp values are calculated with the
following formula:
Cp SSE p=MSE ÿ N ÿ 2p 1
2
where MSE, the error mean square for the model; SSE(p), the error sum of squares
for the subset model with p independent variables; N, the total sample size.
If Cp>(p+1) then the model is not completely speci®ed. On the contrary, if
Cp
www.elsevier.com/locate/agsy
Predicting corn and soybean productivity for
Illinois soils
J.D. Garcia-Paredes, K.R. Olson *, J.M. Lang
Department of Natural Resources and Environmental Sciences, University of Illinois at Urbana-Champaign,
Urbana, IL, 61801, USA
Received 15 January 2000; received in revised form 4 March 2000; accepted 20 March 2000
Abstract
Current corn and soybean productivity data is needed in Illinois for land-use planning,
sustainable farm management, and accurate land appraisal. The out-of-date source of soil
productivity data is Circular 1156 Soil Productivity in Illinois (Fehrenbacher et al., 1978,
Soil productivity in Illinois. UIUC. College of Agriculture. COOP. EXT. SERV. Circular
1156). A new major analysis based on current Illinois farmer crop-yield data is needed to
assure the availability of reliable 10-year average corn and soybean yield estimates by soils.
The overall objective of this study was to update the corn and soybean yields which serve as a
productivity index for Illinois soils since these two crops are grown on approximately 90% of
the cropland. An approach based on multiple regression was used to evaluate the relationship
between 16 selected soil properties of 34 major soils and established 1970s (1967±1976) corn
and soybean yields as published in Circular 1156. Statistical models developed from major
soils were tested internally by calculating the 10-year average corn and soybean yields for each
of the 34 major soils. The coecients generated from multiple regression were further tested
using the soil property values for the additional 165 soils identi®ed in nine counties representing the crop reporting districts and weather districts in Illinois. The 10-year average crop
yield trends were determined for 66 counties in the northern region and for 36 counties in the
southern region for the 20-year time period between 1976 and 1995. These 20-year yield trend
increases were added to the established (Circular 1156) and model predicted 1970s crop yields
to estimate 1990s (1986±1995) corn and soybean yields for the average management level for
all 199 Illinois soil types in nine selected counties. The 1990s crop yield estimates for the
selected counties were weighted by extent of each soil type in the county and compared
against 10-year county averages for the 1990s farmer reported Illinois Agricultural Statistics
(IAS) corn and soybean yields. Predicted 1990s county crop yields were statistically similar to
* Corresponding author. Tel.: +1-217-333-9639; fax: +1-217-224-3219.
E-mail address: k- [email protected] (K.R. Olson).
0308-521X/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved.
PII: S0308-521X(00)00020-2
152
J.D. Garcia-Paredes et al. / Agricultural Systems 64 (2000) 151±170
1990s farmer reported (IAS) county crop yields. The proposed approach to updating corn and
soybean yields worked well and should be useful in surrounding states or countries. # 2000
Elsevier Science Ltd. All rights reserved.
Keywords: Crop-yield prediction; Soil property models; Illinois soils; Soil types; Yield trends
1. Introduction
Crop yields are the result of environmental factors such as soil, climate, and
management inputs. The eect of technology and management on crop yield is
determined, in part, by the type of soil. Consequently more speci®c information on
the in¯uence of soil properties on crop yields is required. Many scientists have tried
to ®nd relationships between soil properties, climate, and crop yields, and grouped
soils in order to compare them (Sarkar et al., 1966; Robles et al., 1977; Allgood and
Gray, 1978). Most of these agronomic research studies have enhanced the importance of soil depth on crop yields in a direct and indirect way (Shrader et al., 1960;
De la Rosa et al., 1981; Reith et al., 1984; Thompson et al., 1991; Craft et al., 1992).
Many of the soil properties considered as important for determining crop yields,
have been related to moisture holding capacity (Baier and Robinson, 1968; Olson,
1981; Olson and Olson, 1986; Ulmer et al., 1988).
Dierences in crop yield and soil productivity may be represented by productivity
indices. Productivity ratings are a good indicator of the suitability of soils for crop
production. They are useful in determining optimum soil management and use
(Anderson et al., 1938; Fehrenbacher et al., 1970). Accurate and reliable soil productivity information is desired for crop yield estimates and productivity indices of
each soil type to complement land appraisal and use management. Most soil productivity data currently adopted were obtained from publication Circular 1016
Productivity of Illinois Soils (Odell and Oschwald, 1970). Much of the data were
developed during a period of 1933 to 1950 and updating occurred in the 1960s.
Productivity data published in 1978 in Circular 1156 Soil Productivity in Illinois
(Fehrenbacher et al., 1978) were updated by numerical adjustment emerging from
improved technology.
Crop yields increased signi®cantly in Illinois from 1945 to 1995. These incremental
increases of yield were primarily a result of improved technology (Swanson et al.,
1977) which included: (1) biological-chemical inputs such as improved varieties,
mineral fertilizers, pesticides, and higher plant populations; (2) mechanical resources
like machinery; and (3) management. Along with augmented crop yield trend, there
were annual ¯uctuations from weather eects.
Trends in crop yields are important for economic decision makers, as well as for
farm owners and operators because yield performance may in¯uence determinations
regarding agricultural inputs levels and adoption of new technologies (Outt et al.,
1987). Additionally, past, present and future crop yield data could be used as a basis
for land valuation (assessment), crop insurance, and other related farm business
(Swanson, 1957).
J.D. Garcia-Paredes et al. / Agricultural Systems 64 (2000) 151±170
153
Crop yield trends were one of the main concerns in the 1970s. Several studies
examined crop yield trend movement to determine if it was increasing or leveling o.
Many of these studies were focused at or within a state level. Herbst (1975) made a
comparison of four 5-year periods (1953±1957 to 1961±1965), (1961±1965 to 1969±
1973), for corn, soybean, wheat, and oat. Greater yield increments were identi®ed in
the previous 5-year period (1953±1957 to 1961±1965) compared to the latter period
(1961±1965 to 1969±1973).
A study with corn and soybean yields on the Allerton trust farm (Piatt County, IL)
for 27 years (1950±1976) demonstrated that yields, unadjusted and adjusted by
weather, were accelerated linearly (Swanson et al., 1977). Sonka (1978) studied corn
yield trends and variability in Illinois for the period of 1927 to 1977. There were no
indications that corn yield had reached a plateau despite yield variability increases
since 1970. Chicoine and Scott (1988) evaluated the behavior of corn and soybean
yield from 1972 to 1985 in Illinois. They found signi®cant evidence that soybean yield
trends may be leveling o. However, the results for corn were inconclusive.
Productivity data published in Circular 1156 Soil Productivity in Illinois (Fehrenbacher et al., 1978) were updated through previous number adjustment re¯ecting
technology improvements. In 1994 a supplement to Circular 1156 was released to
include new soils established between 1978 and 1994 (Olson and Lang, 1994). This
supplement used 1970s (1967±1976) management to estimate crop yields. These
published yields are very antiquated, more than 20 years old. Changes in crops yield
and crop rotation have had an eect. Yield adjustments should be modi®ed by soil
type to parallel technology innovation eects on crop production, soil productivity,
and subsequent productivity indices.
The overall objective of this study was to update the corn and soybean yields
which serve as a productivity index for Illinois soils since these crops are grown on
90% of the cropland. An approach based on multiple regression was used to evaluate the relationship between 16 selected soil properties of major soils and established
1970s (1967±1976) corn and soybean yields as published in Circular 1156. The
average crop yield trend increases from 1976 to 1995 in farmer reported yields by
Illinois Agricultural Statistics (IAS) for the northern and southern regions of Illinois
were added to the established (published in Circular 1156) and model predicted
1970s (1967±1976) crop yields to estimate 1990s (1986±1995) corn and soybean
yields for the average management level for all 199 Illinois soil types in nine selected
counties. The 1990s crop yield estimates for each soil were weighted by extent of that
soil type in the county and compared against 10-year county averages for the 1990s
farmer reported (IAS) corn and soybean yields.
2. Materials and methods
2.1. Procedures
Our approach included the following steps: (1) to develop crop yield-soil property models by stepwise multiple regression with 1970s (1967±1976) crop yields
154
J.D. Garcia-Paredes et al. / Agricultural Systems 64 (2000) 151±170
along with soil properties from 34 major (base and benchmark) soils; (2) to
internally check by calculating average corn and soybean yields using the model
generated coecients and the soil properties values for each of the 34 major soils;
(3) to test coecients generated from multiple regression using the soil property
values for an additional 165 soils identi®ed in nine counties representing the crop
reporting districts and weather districts in Illinois; (4) to identify any corn and
soybean yield outliers (greater than 2 S.D.); (5) determine the reasons for the
outliers and propose modi®cation to improve the predictive models; (6) to determine the magnitude of farmer reported (IAS) corn and soybean yield changes from
1976 to 1995 for northern (high productivity) and southern (lower productivity)
regions; (7) to use the 20-year crop regional yield increases to predict 1990s crop
yields for 199 soils in nine northern and southern Illinois counties; (8) to evaluate the model predicted plus 20-year trend increased crop yields and established
(Circular 1156) plus 20-year trend increased crop yields for nine selected
test counties (Fig. 1) by comparing with the 1990s farmer reported county crop
production (IAS).
2.2. Soil types selection
Thirty-four major soil types were chosen for a model development to determine crop yield estimates. These included nine base soils which were selected
to represent the best producing soils under basic management which were
assigned the highest basic productivity indices (PIs) in Circular 1156 (Soil
Productivity in Illinois; Fehrenbacher et al., 1978). Each of these soils have
extensive acreage in Illinois. From various soil survey and soil conservation
programs, it was determined that a list of 30 benchmark soils represented most
of the major soil conditions in the state. There are ®ve major soils on both the
base and benchmark lists. This major (base and benchmark) soils list was
the basis for developing a crop yield-soil property rating (CYSPR) model
(Table 1).
A comprehensive list of physical and chemical properties which aect or appear
to aect crop yields in Illinois were identi®ed by multiple regression and included:
(1) surface layer thickness (cm); (2) surface layer percent silt; (3) percent organic
matter in surface layer; (4) CEC of surface layer; (5) depth (cm) to redoxamorphic
(wetness) features drainage class (relates to drainage class); (6) subsoil thickness
(cm); (7) plant available water to a depth of 150 cm; (8) rooting depth as a function
of soil structure (cm); (9) depth in cm to 2nd parent material (usually thickness of
loess); (10) permeability; (11) surface layer pH; (12) subsoil pH; (13) surface layer
bulk density; (14) subsoil bulk density; (15) percent Na on the exchange; and (16)
percent clay in subsoil.
Field measured soil property data from the Illinois soil characterization data
base (2160 pedons) and the United States Department of Agriculture, Natural
Resources Conservation Service (USDA±NRCS) estimated soil properties data
base were used to compile a comprehensive list of soil property ranges for each
selected soil type.
J.D. Garcia-Paredes et al. / Agricultural Systems 64 (2000) 151±170
155
Fig. 1. Northern and southern soil productivity regions and nine test counties in Illinois.
2.3. Regression analysis of Circular 1156 crop yields
Stepwise multiple regression was implemented to establish the relationship
between 10-year crop yield estimates from Circular 1156 and selected soil property
values. The soil properties were represented with a numeric value common for each
soil property. Only one value was assigned by soil type and property for the appropriate A horizon, B horizon or soil pro®le.
156
J.D. Garcia-Paredes et al. / Agricultural Systems 64 (2000) 151±170
Table 1
Base (previous most productive) and benchmark (representing major soil conditions)
soils in Illinois
Base soils
Benchmark soils
Drummer siclab
Elburn silb
Flanagan silb
Ipava silb
Joy sil
Lisbon sil
Littleton sil
Muscatine sil
Sable siclb
Alvin fsl
Ashkum sicl
Belknap sil
Blount sil
Bluford sil
Catlin sil
Cisne sil
Denny sil
Drummer siclb
Ebbert sil
Elburn silb
Elliot sil
Flanagan silb
Grantsburg sil
Harpster sicl
Herrick sil
Hickory l
Hoopeston sl
Huey sil
Ipava silb
Karnak sicl
Milford sicl
Morley sil
Sable siclb
Sawmill sicl
Saybrook sil
Selma l
Varna sil
Virden sil
Weir sil
a
b
sicl, silty clay loam; fsl, ®ne sandy loam; sil, silt loam; l, loam; sl, sandy loam.
On both lists.
2.4. Preliminary statistical analysis
A correlation analysis was used to provide information about the nature of the
variables used in the multiple regression models, and to identify which variables
were more highly correlated. Simple statistical data analyses were evaluated (stemleaf diagrams, box plot, and normal probability plot) in order to check the usual
assumption in regression analysis. The diagrams for most of the predictor variables
were acceptable bell-shaped curves. The variable exchangeable sodium was not a
bell-shaped curve, since all but one of the soils had values of zero. The Statistical
Analysis System (SAS) was applied to analyze the soil and yield data. The R-square
option was utilized with emphasis on maximizing R for regression.
J.D. Garcia-Paredes et al. / Agricultural Systems 64 (2000) 151±170
157
Multiple regression analysis was used to provide estimates of the relationships
between crop yield and soil variables. All computations were carried out with
respect to the following model:
Yi 0 1 X1 2 X2 ::: i Xi ; i
1
where Yi is the response or dependent variable, which represents the predicted crop
yields. The explanatory factors X1, X2, . . . Xi are assumed to be independent. i is the
error due to the fact that the postulated independent variables do not completely
account for the variation in Y. The parameter b0, b1 . . . bi are the population
regression coecients for the soil eects.
There are several methods to select an optimum set of independent variables. A
criteria for determining how many variables to consider in the model is to use Mallows' Cp statistic (Freund and Littel, 1991). The Cp values are calculated with the
following formula:
Cp SSE p=MSE ÿ N ÿ 2p 1
2
where MSE, the error mean square for the model; SSE(p), the error sum of squares
for the subset model with p independent variables; N, the total sample size.
If Cp>(p+1) then the model is not completely speci®ed. On the contrary, if
Cp