Comprehensive information on Nitrogen Use Efficiency for cereal crop production, N use Efficiency

 

Research Methods in Agriculture

Regression

ON THIS PAGE

1. Regression with confidence Intervals
2. Surface Response Model
3. Linear-Plateau
4. Linear-Linear
5. Difference in Slope and Intercept

Frequency Distribution in Excel
2013 Linear Plateau Program (Foster) not used



2013 Josh Pittman (Linear Plateau) not used


2013 Romulo Lollato (Oklahoma Wheat Yields, YR vs. avg Yield, Linear Plateau)

Cate-Nelson (ppt file)  Cate Nelson SSSAJ Article

Surface Response Model
linear and quadratic relationships of x and y with z and a linear interaction term. 

Z = x x2 y y2 xy

data one;
input red nir NDVI yield height;
cards;
.5 .6 .7 4000 32
.4 .7 .8 5000 39
.5 .8 .9 5500 41
.4 .5 .7 3500 30
.3 .5 .6 3400 29
.2 .4 .5 2200 25
.24 .45 .55 2400 28
.29 .46 .58 2600 29
proc rsreg data = one out = two;
  model NDVI = red nir /predict;
proc g3grid data = two out = three;
  grid red*nir=NDVI/spline;
proc g3d data = three gout=new;
  plot red*nir=NDVI;
run;

3x. Surface response scatter plot

Linear-Plateau Program (Romulo data)

data one;
input x y;

/* Avg. wheat yield data over time */
cards;
1950 604.892513
1951 638.4976526
1952 1243.390166
1953 806.5233506
1954 1008.154188
1955 537.6822338
1956 1108.969607
1957 840.1284902
1958 1747.46726
1959 1344.205584
1960 1747.46726
1961 1613.046701
1962 1276.995305
1963 1411.415864
1964 1545.836422
1965 1881.887818
1966 1411.415864
1967 1142.574747
1968 1545.836422
1969 1881.887818
1970 1747.46726
1971 1344.205584
1972 1545.836422
1973 2016.308377
1974 1411.415864
1975 1613.046701
1976 1613.046701
1977 1814.677539
1978 1814.677539
1979 2553.99061
1980 2016.308377
1981 1814.677539
1982 2217.939214
1983 2352.359773
1984 2419.570052
1985 2016.308377
1986 1949.098097
1987 1814.677539
1988 2419.570052
1989 1814.677539
1990 2217.939214
1991 1814.677539
1992 1949.098097
1993 2016.308377
1994 1814.677539
1995 1411.415864
1996 1276.995305
1997 2150.728935
1998 2553.99061
1999 2352.359773
2000 2285.149493
2001 2217.939214
2002 1881.887818
2003 2621.20089
2004 2352.359773
2005 2150.728935
2006 1613.046701
2007 1881.887818
2008 2486.780331
2009 1478.626143
2010 2083.518656
2011 1478.626143
2012 2419.570052
proc print;
proc nlin data = one best = 3;
  parms b0=500 to 1000 by 100 b1=10 to 50 by 10 njoint=1970 to 1990 by 5;
  if x<njoint then do;
  model y = b0 + b1*x;
der.b0=1;
der.b1=x;
der.njoint=0;
end;
else do;
model y=b0+b1*njoint;
der.b0=1;
der.b1=njoint;
der.njoint=b1;
end;
file print;
if _obs_ =1 and _model_ =0 then do;
  plateau = b0 + b1*njoint;
  put plateau=;
end;
  plateau=b0+b1*njoint;
id plateau;
  output out = new p = pry parms=b0 b1 njoint sse=sse;
run;
proc plot;
plot y*x='+' pry*x='*'/overlay;
run;
proc means noprint;
var y sse b0 b1 njoint plateau;
output out = new2 n = tdf
mean = y sse b0 b1 njoint plateau
css=csst;
data new3; set new2;
intercpt=b0; slope=b1; joint=njoint;
rsq=(csst-sse)/csst;
edf=tdf-3;
ssr=csst-sse;
msr=ssr/2;
mse=sse/edf;
f=msr/mse;
probf=1-(probf(f,2,edf));
keep intercpt slope joint plateau rsq f probf;
proc print;
run;

Linear-Plateau Program (Melissa, r2 peak, GDD, Yield)

data one;
input x y;
cards;
50 0.56
66 0.5
69 0.63
75 0.71
80 0.82
86 0.82
100 0.89
105 0.93
112 0.94
119 0.6
126 0.69
PROC PRINT;
data one; set one;
if exp = 'e502' then delete;
/* LINEAR PLATEAU */
PROC NLIN DATA = ONE BEST = 3;
PARMS B0=0.3 to 0.5 by 0.01 B1=0.01 to 0.03 by 0.001 NJOINT=80 to 90 by 1;
IF X<NJOINT THEN DO;
MODEL Y = B0 + B1*X;
DER.B0=1;
DER.B1=X;
DER.NJOINT=0;
END;
ELSE DO;
MODEL Y=B0+B1*NJOINT;
DER.B0=1;
DER.B1=NJOINT;
DER.NJOINT=B1;
END;
FILE PRINT;
IF _obs_ =1 AND _MODEL_ =0 THEN DO;
PLATEAU = B0 + B1*NJOINT;
PUT PLATEAU=;
END;
PLATEAU=B0+B1*NJOINT;
ID PLATEAU;
OUTPUT OUT = NEW P = PRY PARMS=B0 B1 NJOINT SSE=SSE;
RUN;
PROC PLOT;
PLOT Y*X='+' PRY*X='*'/OVERLAY;
RUN;
PROC MEANS NOPRINT;
VAR Y SSE B0 B1 NJOINT PLATEAU;
OUTPUT OUT = NEW2 N = TDF
MEAN = Y SSE B0 B1 NJOINT PLATEAU
CSS=CSST;
DATA NEW3; SET NEW2;
INTERCPT=B0; SLOPE=B1; JOINT=NJOINT;
RSQ=(CSST-SSE)/CSST;
EDF=TDF-3;
SSR=CSST-SSE;
MSR=SSR/2;
MSE=SSE/EDF;
F=MSR/MSE;
PROBF=1-(PROBF(F,2,EDF));
KEEP INTERCPT SLOPE JOINT PLATEAU RSQ F PROBF;
PROC PRINT;
RUN;

Linear-Linear Program

data one;
  input rep trt x  y;
cards;
proc nlin data = one best = 2;
parms b0=500 to 1000 by 100 b1=10 to 50 by 5 joint=1970 to 1990 by 5
    b2 = 200 to 300 by 10;
    if x<joint then do;
    model y = b0 + b1*x;
    der.b0=1;
    der.b1=x;
    der.joint=0;
    der.b2=0;
    end;
else do;
   model y=b0+(b1-b2)*joint+b2*x;
   der.b0=1;
   der.b1=joint; 
   der.joint=b1-b2;
   der.b2=x-joint; 

end;

file print;
            if _obs_ =1 and _model_ =0 then do;
            joinlev = b0 + b1*joint;
            put joinlev=;
end;

joinlev=b0+b1*joint; 
            id joinlev;
            output out = new p = pry parms=b0 b1 joint b2 sse=sse;

run;
            proc plot;
            plot y*x='+' pry*x='*'/overlay;

run;
proc means noprint;

var y sse b0 b1 joint b2 joinlev;
output out = new2 n = tdf
mean = y sse b0 b1 joint b2 joinlev
           css=csst;
data new3; set new2;
intercpt=b0; slope=b1; joint=joint; slope2=b2; jresp=joinlev;
rsq=(csst-sse)/csst;
edf=tdf-4;
ssr=csst-sse;
msrg=ssr/3;
mse=sse/edf;
f=msrg/mse;
probf=1-(probf(f,2,edf));
keep intercpt slope joint slope2 joinlev rsq msrg mse edf f probf;
proc print;
run;

2015 Linear Plateau (class project)  SOIL 5112  ***

 

Stability Analysis (treatment by environment interactions)  click to go to this page


Regression Analysis with Confidence Intervals (point and line)

data one;
input red nir NDVI yield height;
cards;
.5 .6 .7 4000 32
.4 .7 .8 5000 39
.5 .8 .9 5500 41
.4 .5 .7 3500 30
.3 .5 .6 3400 29
.2 .4 .5 2200 25
.24 .45 .55 2400 28
.29 .46 .58 2600 29
proc reg data = one;
model yield=height/p clm;
output out = dog p = pyd l95m=l95m u95m=u95m;
proc gplot; plot pyd*height yield*height='x' l95m*height u95m*height/overlay;
run;

cli 95% confidence limits for an individual predicted value
clm 95% confidence limits for the expected value of the dependent variable (mean)

(if you use cli, get rid of all the "m's" on the end of the l95 and u95 values)

Program for Determining the Significance Between Slope and Intercept Components from 2 Independent Regressions

(can match this up with the Magruder example of NPK vs NP) Magruder excel file, and examples below.

data one;
input trt $ envmean yld;
if trt ='np' then intc_dif=0;
if trt ='npk' then intc_dif=1;
slop_dif=intc_dif*envmean;
cards;
np 8.7 6.5
np 28.15 28.4
np 25.36666667 28.6
np 22.25 22.9
np 16.06666667 18
np 24.48333333 26.1
np 19.7 20.2
np 29.01666667 30.3
np 10.58333333 11.7
np 24.23333333 24.4
np 28.31666667 30.6
np 6.8 8.7
np 9.566666667 10.9
np 9.983333333 11.9
np 22.51666667 24.1
np 8 6.1
np 16.85 20.9
np 21.2 22.8
np 29.75 34.4
np 17.35 17.4
np 23.75 26.4
np 21.25 21.4
np 16.55 17.1
np 26.41666667 32
np 14.63333333 12.5
np 5.583333333 5.4
np 16.2 15.1
np 16.05 15.8
np 33.41666667 36.9
np 36.91666667 39.5
np 27.7 34
np 24.1 26.1
np 23.95 28.5
np 34.35 41.5
np 16.58333333 20.7
np 31.83333333 30.7
np 35.65 49.3
np 9.35 10.1
np 19.38333333 23.5
np 21.46666667 25.4
np 24.93333333 23.5
np 30.95 36.2
np 30.3 38.9
np 34.78333333 44.1
np 29.78333333 38.8
np 38.48333333 51.4
np 36.21666667 45.6
np 21.86 32.3
np 26.78333333 32.2
np 44.88333333 52.6
np 35.68333333 43
np 31.26666667 38.3
np 36.75 32.2
np 24.38333333 27.9
np 33.15 31.8
np 21.6 22.2
np 17.23333333 13.2
np 12.38333333 11.7
np 25.76666667 25
np 20.11166667 16.3
np 28.53333333 31.9
np 28.06666667 23.7
np 21.90483333 24.0368
np 30.59855 29.1516
np 22.15076667 31.946
np 5.911566667 9.258
np 21.42166667 22.19
np 46.43333333 60.8
np 28.97 33.81
np 38.34555598 52.06795346
np 31.45561744 33.1039001
np 26.78102444 24.87453073
np 32.81616667 41.665
np 41.4 51.6
np 45.7383689 54.67134146
np 32.16666667 31
np 35.33551989 43.63420513
np 3.909166667 6.068
np 42.8735 45.706
np 4.661666667 2.61
np 31.6285833 35.67635604
np 17.65385104 23.14757086
np 34.99166667 44.37
np 39.20333333 52.08
np 28.09405289 32.9500485
npk 8.7 5.5
npk 28.15 32.3
npk 25.36666667 22.7
npk 22.25 25.1
npk 16.06666667 21.9
npk 24.48333333 27
npk 19.7 20.6
npk 29.01666667 32.2
npk 10.58333333 12.4
npk 24.23333333 26.7
npk 28.31666667 33.6
npk 6.8 8.2
npk 9.566666667 9.9
npk 9.983333333 10.9
npk 22.51666667 23.1
npk 8 9.9
npk 16.85 15.1
npk 21.2 24.1
npk 29.75 34.4
npk 17.35 19.7
npk 23.75 21.4
npk 21.25 24.2
npk 16.55 16.7
npk 26.41666667 32.1
npk 14.63333333 15.3
npk 5.583333333 2.5
npk 16.2 15.6
npk 16.05 17
npk 33.41666667 35.7
npk 36.91666667 39.4
npk 27.7 35.2
npk 24.1 27.6
npk 23.95 27
npk 34.35 32.3
npk 16.58333333 22.2
npk 31.83333333 29.9
npk 35.65 34.5
npk 9.35 9.9
npk 19.38333333 23.8
npk 21.46666667 27.1
npk 24.93333333 31
npk 30.95 29.6
npk 30.3 37.1
npk 34.78333333 43.3
npk 29.78333333 30.4
npk 38.48333333 47.8
npk 36.21666667 45.3
npk 21.86 23.8
npk 26.78333333 33.7
npk 44.88333333 50.3
npk 35.68333333 37
npk 31.26666667 32.6
npk 36.75 40.3
npk 24.38333333 25.4
npk 33.15 32.6
npk 21.6 23.4
npk 17.23333333 21.3
npk 12.38333333 12.3
npk 25.76666667 29.7
npk 20.11166667 25.07
npk 28.53333333 32.2
npk 28.06666667 42.1
npk 21.90483333 31.5786
npk 30.59855 36.9428
npk 22.15076667 31.6512
npk 5.911566667 8.5061
npk 21.42166667 24.05
npk 46.43333333 62.6
npk 28.97 37.34
npk 38.34555598 52.84454497
npk 31.45561744 38.11772693
npk 26.78102444 28.03528683
npk 32.81616667 40.716
npk 41.4 59.5
npk 45.7383689 55.55670732
npk 32.16666667 38
npk 35.33551989 45.08231665
npk 3.909166667 4.789
npk 42.8735 45.857
npk 4.661666667 8.27
npk 31.6285833 37.01767818
npk 17.65385104 23.81803027
npk 34.99166667 46.67
npk 39.20333333 49.43
npk 28.09405289 31.94973331
data two; set one;
proc sort; by trt;
proc reg;
model yld = envmean intc_dif slop_dif;
run;
proc reg;
by trt;
model yld=envmean;
run;


data one;
input gdd ndvi yld;
if gdd = 87 then intc_dif=0;
if gdd = 106 then intc_dif=1;
slop_dif=intc_dif*ndvi;
cards;

87 0.363 2142.42
87 0.217 772.01
87 0.439 3285.61
87 0.448 2850.91
87 0.515 4684.25
87 0.510 4641.91
87 0.543 5315.12
87 0.368 2646.27
87 0.481 4358.23
87 0.492 4259.44
87 0.500 5277.02
87 0.515 5247.38
87 0.562 5384.28
87 0.499 4307.42
87 0.334 1589.17
87 0.378 1563.77
87 0.416 2745.06
87 0.527 2431.75
87 0.489 3240.45
87 0.417 5521.18
87 0.471 5483.07
87 0.393 3322.30
87 0.457 5233.26
87 0.495 5202.21
87 0.471 4966.52
87 0.499 5260.08
87 0.604 5629.85
87 0.434 5569.16
87 0.380 2273.68
87 0.444 2721.07
87 0.469 3908.01
87 0.486 4409.04
87 0.551 4811.27
87 0.533 5039.91
87 0.547 5387.10
87 0.416 4486.66
87 0.531 4980.63
87 0.507 4852.20
87 0.530 5346.17
87 0.550 5000.39
87 0.574 5325.00
87 0.529 4898.78
87 0.386 2248.27
87 0.421 2695.67
87 0.427 2852.33
87 0.515 3549.53
87 0.494 4948.17
87 0.562 5272.78
87 0.590 5267.14
87 0.433 4126.77
87 0.458 4698.36
87 0.536 5175.40
87 0.508 4222.74
87 0.489 5381.45
87 0.640 5377.22
87 0.483 5007.45
106 0.390 2142.42
106 0.232 772.01
106 0.509 3285.61
106 0.505 2850.91
106 0.653 4684.25
106 0.697 4641.91
106 0.731 5315.12
106 0.439 2646.27
106 0.613 4358.23
106 0.641 4259.44
106 0.681 5277.02
106 0.721 5247.38
106 0.772 5384.28
106 0.651 4307.42
106 0.341 1589.17
106 0.449 1563.77
106 0.396 2745.06
106 0.523 2431.75
106 0.665 3240.45
106 0.712 5521.18
106 0.779 5483.07
106 0.505 3322.30
106 0.712 5233.26
106 0.703 5202.21
106 0.653 4966.52
106 0.712 5260.08
106 0.777 5629.85
106 0.662 5569.16
106 0.417 2273.68
106 0.447 2721.07
106 0.531 3908.01
106 0.647 4409.04
106 0.729 4811.27
106 0.717 5039.91
106 0.752 5387.10
106 0.557 4486.66
106 0.700 4980.63
106 0.751 4852.20
106 0.751 5346.17
106 0.705 5000.39
106 0.714 5325.00
106 0.652 4898.78
106 0.364 2248.27
106 0.389 2695.67
106 0.407 2852.33
106 0.573 3549.53
106 0.665 4948.17
106 0.765 5272.78
106 0.785 5267.14
106 0.574 4126.77
106 0.648 4698.36
106 0.717 5175.40
106 0.689 4222.74
106 0.723 5381.45
106 0.811 5377.22
106 0.713 5007.45

data two; set one;
proc sort; by gdd;
proc reg;
model yld = ndvi intc_dif slop_dif;
run;
proc reg;
by gdd;
model yld=ndvi;
run;

EXTRA

Keeping a SUBSET of the ENTIRE DATA SET (keeps data for only the varieties entered)

data awnless;
set gpyt;
if cv = 'DELIVER' or cv = 'WM135' or cv = 'TAM401' or cv = 'LONGHORN' ;

run;
proc print; run;