Prepare the data

dat <- fread("Output/wheat_data_prepped.csv")
#fix rotation
dat[local=="Tygerhoek", rotation := "CW"]
#drop all blank yields and biomass estimates
dat <- dat[!is.na(yld) & is.na(yldb)]
dat[, c("wind","yldb") := NULL]

# Max yield index ---------------------------------------------------------
dat[, yld_max := max(yld,na.rm = T), by = .(year,local,rotation)]

#keep original yield
dat[, yld.OR := yld]

#calculate control normalised yield
dat[, yld := yld/yld_max*100]

#remove sprayed N
dat[, N_tot := N_tot - N_spray]

Model results

Langgewens

Canola-Wheat

Langgewens Canola-Wheat results, 2018 was excluded due to wind damage.

Yield response to Nitrogen
District
Relative yield (Max trial yield = 100)
2016 2017 2019
(1) (2) (3)
Total Nitrogen Applied 0.231*** -0.073 0.085
(0.046) (0.052) (0.083)
Total Nitrogen Applied squared -0.001*** 0.0002 -0.0004
(0.0002) (0.0003) (0.0004)
Intercept 70.105*** 77.606*** 64.720***
(1.825) (2.092) (3.324)
Observations 126 128 64
R2 0.274 0.050 0.017
Adjusted R2 0.262 0.035 -0.015
Residual Std. Error 8.821 (df = 123) 10.112 (df = 125) 11.363 (df = 61)
F Statistic 23.181*** (df = 2; 123) 3.287** (df = 2; 125) 0.533 (df = 2; 61)
Note: p<0.1; p<0.05; p<0.01

It is evident that only 2016 has a good fit.

grid.arrange(p.seg.2016.Langgewens.CW,p.seg.2019.Langgewens.CW, nrow =1)

summary.segmented(m.seg.2016.Langgewens.CW)
## 
##  ***Regression Model with Segmented Relationship(s)***
## 
## Call: 
## segmented.lm(obj = model, seg.Z = ~N_tot)
## 
## Estimated Break-Point(s):
##               Est. St.Err
## psi1.N_tot 58.914  13.45
## 
## Meaningful coefficients of the linear terms:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 69.09987    2.00399  34.481  < 2e-16 ***
## N_tot        0.24690    0.06209   3.976 0.000119 ***
## U1.N_tot    -0.23488    0.06660  -3.527       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.781 on 122 degrees of freedom
## Multiple R-Squared: 0.2861,  Adjusted R-squared: 0.2686 
## 
## Convergence attained in 2 iter. (rel. change 1.9336e-16)
slope(m.seg.2016.Langgewens.CW)
## $N_tot
##            Est.  St.Err. t value CI(95%).l CI(95%).u
## slope1 0.246900 0.062091 3.97640  0.123980  0.369810
## slope2 0.012018 0.024078 0.49913 -0.035647  0.059684
summary.segmented(m.seg.2019.Langgewens.CW)
## 
##  ***Regression Model with Segmented Relationship(s)***
## 
## Call: 
## segmented.lm(obj = model, seg.Z = ~N_tot)
## 
## Estimated Break-Point(s):
##               Est. St.Err
## psi1.N_tot 50.721  23.79
## 
## Meaningful coefficients of the linear terms:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  61.8266     3.6140  17.108   <2e-16 ***
## N_tot         0.1864     0.1120   1.665    0.101    
## U1.N_tot     -0.2250     0.1200  -1.875       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 11.2 on 60 degrees of freedom
## Multiple R-Squared: 0.06126,  Adjusted R-squared: 0.01432 
## 
## Convergence attained in 4 iter. (rel. change 0)
slope(m.seg.2019.Langgewens.CW)
## $N_tot
##             Est.  St.Err.  t value CI(95%).l CI(95%).u
## slope1  0.186390 0.111980  1.66460 -0.037593   0.41038
## slope2 -0.038601 0.043144 -0.89471 -0.124900   0.04770

Medics-Wheat

Langgewens Medics-Wheat results, 2018 was excluded due to wind damage.

Yield response to Nitrogen
District
Relative yield (Max trial yield = 100)
2016 2017 2019
(1) (2) (3)
Total Nitrogen Applied 0.215*** 0.025 -0.132
(0.068) (0.102) (0.120)
Total Nitrogen Applied squared -0.001*** -0.0001 0.001
(0.0003) (0.001) (0.001)
Intercept 73.014*** 71.756*** 63.720***
(2.730) (4.094) (4.832)
Observations 64 64 64
R2 0.145 0.003 0.019
Adjusted R2 0.117 -0.030 -0.013
Residual Std. Error (df = 61) 9.331 13.993 16.516
F Statistic (df = 2; 61) 5.173*** 0.077 0.597
Note: p<0.1; p<0.05; p<0.01

It is evident that only 2016 has a good fit.

p.seg.2016.Langgewens.MW

summary.segmented(m.seg.2016.Langgewens.MW)
## 
##  ***Regression Model with Segmented Relationship(s)***
## 
## Call: 
## segmented.lm(obj = model, seg.Z = ~N_tot)
## 
## Estimated Break-Point(s):
##              Est. St.Err
## psi1.N_tot 58.03  17.34
## 
## Meaningful coefficients of the linear terms:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 72.48868    3.06317  23.665   <2e-16 ***
## N_tot        0.21191    0.09491   2.233   0.0293 *  
## U1.N_tot    -0.27630    0.10171  -2.717       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 9.491 on 60 degrees of freedom
## Multiple R-Squared:  0.13,  Adjusted R-squared: 0.08652 
## 
## Convergence attained in 2 iter. (rel. change 1.6828e-16)
slope(m.seg.2016.Langgewens.MW)
## $N_tot
##             Est.  St.Err. t value CI(95%).l CI(95%).u
## slope1  0.211910 0.094909  2.2328  0.022063 0.4017500
## slope2 -0.064389 0.036568 -1.7608 -0.137540 0.0087585

Darling

Canola-Wheat

Darling Canola-Wheat results

Yield response to Nitrogen
District
Relative yield (Max trial yield = 100)
2016 2017 2018
(1) (2) (3)
Total Nitrogen Applied 0.443*** -0.099 0.195**
(0.118) (0.116) (0.077)
Total Nitrogen Applied squared -0.001** -0.0001 -0.001*
(0.001) (0.001) (0.0004)
Intercept 31.112*** 71.491*** 68.823***
(4.748) (4.623) (3.084)
Observations 64 63 64
R2 0.343 0.163 0.141
Adjusted R2 0.322 0.135 0.113
Residual Std. Error 16.230 (df = 61) 15.783 (df = 60) 10.542 (df = 61)
F Statistic 15.929*** (df = 2; 61) 5.841*** (df = 2; 60) 5.006*** (df = 2; 61)
Note: p<0.1; p<0.05; p<0.01

It is evident that only 2016 has a good fit.

## Warning: Removed 1 rows containing missing values (geom_vline).
## Warning: Removed 1 rows containing missing values (geom_text).

p.seg.2018.Darling.CW

summary.segmented(m.seg.2018.Darling.CW)
## 
##  ***Regression Model with Segmented Relationship(s)***
## 
## Call: 
## segmented.lm(obj = model, seg.Z = ~N_tot)
## 
## Estimated Break-Point(s):
##             Est. St.Err
## psi1.N_tot  100 32.021
## 
## Meaningful coefficients of the linear terms:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 68.79955    2.86347  24.027   <2e-16 ***
## N_tot        0.14464    0.04676   3.093    0.003 ** 
## U1.N_tot    -0.19773    0.09889  -2.000       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 10.46 on 60 degrees of freedom
## Multiple R-Squared: 0.1688,  Adjusted R-squared: 0.1273 
## 
## Convergence attained in 4 iter. (rel. change 6.841e-07)
slope(m.seg.2018.Darling.CW)
## $N_tot
##             Est.  St.Err.  t value CI(95%).l CI(95%).u
## slope1  0.144640 0.046760  3.09320  0.051104   0.23817
## slope2 -0.053088 0.087132 -0.60928 -0.227380   0.12120

Medics-Wheat

Darling Medics-Wheat results

Yield response to Nitrogen
District
Relative yield (Max trial yield = 100)
2016 2017 2018
(1) (2) (3)
Total Nitrogen Applied 0.568*** 0.011 0.589***
(0.084) (0.138) (0.115)
Total Nitrogen Applied squared -0.002*** 0.00001 -0.002***
(0.0004) (0.001) (0.001)
Intercept 32.008*** 57.283*** 24.987***
(3.382) (5.473) (4.613)
Observations 64 63 64
R2 0.653 0.002 0.543
Adjusted R2 0.642 -0.031 0.528
Residual Std. Error 11.559 (df = 61) 18.682 (df = 60) 15.767 (df = 61)
F Statistic 57.472*** (df = 2; 61) 0.064 (df = 2; 60) 36.205*** (df = 2; 61)
Note: p<0.1; p<0.05; p<0.01

It is evident that only 2016 has a good fit.

## Warning: Removed 1 rows containing missing values (geom_vline).
## Warning: Removed 1 rows containing missing values (geom_text).

grid.arrange(p.seg.2016.Darling.MW,p.seg.2018.Darling.MW, nrow =1)

summary.segmented(m.seg.2016.Darling.MW)
## 
##  ***Regression Model with Segmented Relationship(s)***
## 
## Call: 
## segmented.lm(obj = model, seg.Z = ~N_tot)
## 
## Estimated Break-Point(s):
##               Est. St.Err
## psi1.N_tot 55.891 10.961
## 
## Meaningful coefficients of the linear terms:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  29.6280     3.6763   8.059 3.88e-11 ***
## N_tot         0.6217     0.1139   5.458 9.67e-07 ***
## U1.N_tot     -0.5153     0.1221  -4.221       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 11.39 on 60 degrees of freedom
## Multiple R-Squared: 0.6688,  Adjusted R-squared: 0.6523 
## 
## Convergence attained in 2 iter. (rel. change 0)
slope(m.seg.2016.Darling.MW)
## $N_tot
##           Est.  St.Err. t value CI(95%).l CI(95%).u
## slope1 0.62168 0.113910  5.4578  0.393830   0.84952
## slope2 0.10640 0.043888  2.4245  0.018617   0.19419
summary.segmented(m.seg.2018.Darling.MW)
## 
##  ***Regression Model with Segmented Relationship(s)***
## 
## Call: 
## segmented.lm(obj = model, seg.Z = ~N_tot)
## 
## Estimated Break-Point(s):
##               Est. St.Err
## psi1.N_tot 76.147 15.768
## 
## Meaningful coefficients of the linear terms:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 22.95802    4.50830   5.092 3.77e-06 ***
## N_tot        0.55856    0.09639   5.795 2.70e-07 ***
## U1.N_tot    -0.48707    0.12547  -3.882       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 15.24 on 60 degrees of freedom
## Multiple R-Squared: 0.5798,  Adjusted R-squared: 0.5587 
## 
## Convergence attained in 3 iter. (rel. change 0)
slope(m.seg.2018.Darling.MW)
## $N_tot
##           Est.  St.Err. t value CI(95%).l CI(95%).u
## slope1 0.55856 0.096391 5.79470  0.365750   0.75137
## slope2 0.07149 0.080326 0.88999 -0.089187   0.23217

Porterville

Canola-Wheat

Porterville Canola-Wheat results

Yield response to Nitrogen
District
Relative yield (Max trial yield = 100)
2016 2017 2018 2019
(1) (2) (3) (4)
Total Nitrogen Applied 0.475*** -0.123 0.285*** 0.332***
(0.140) (0.123) (0.066) (0.098)
Total Nitrogen Applied squared -0.002** 0.0005 -0.001* -0.001**
(0.001) (0.001) (0.0003) (0.0005)
Intercept 19.926*** 61.254*** 58.953*** 54.368***
(5.599) (4.950) (2.631) (3.922)
Observations 64 64 64 64
R2 0.284 0.024 0.572 0.232
Adjusted R2 0.261 -0.008 0.558 0.207
Residual Std. Error (df = 61) 19.138 16.919 8.995 13.405
F Statistic (df = 2; 61) 12.098*** 0.736 40.691*** 9.222***
Note: p<0.1; p<0.05; p<0.01

It is evident that only 2016 has a good fit.

## Warning: Removed 1 rows containing missing values (geom_vline).
## Warning: Removed 1 rows containing missing values (geom_text).

grid.arrange(p.seg.2016.Porterville.CW, p.seg.2018.Porterville.CW,p.seg.2019.Porterville.CW, nrow =2)

summary.segmented(m.seg.2016.Porterville.CW)
## 
##  ***Regression Model with Segmented Relationship(s)***
## 
## Call: 
## segmented.lm(obj = model, seg.Z = ~N_tot)
## 
## Estimated Break-Point(s):
##                Est. St.Err
## psi1.N_tot 129.999 19.711
## 
## Meaningful coefficients of the linear terms:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 22.18100    5.19341   4.271 7.05e-05 ***
## N_tot        0.29476    0.08481   3.476 0.000953 ***
## U1.N_tot    -0.48789    0.17935  -2.720       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 18.96 on 60 degrees of freedom
## Multiple R-Squared: 0.3085,  Adjusted R-squared: 0.2739 
## 
## Convergence attained in 7 iter. (rel. change 3.8817e-06)
slope(m.seg.2016.Porterville.CW)
## $N_tot
##            Est.  St.Err. t value CI(95%).l CI(95%).u
## slope1  0.29476 0.084808  3.4756   0.12512   0.46440
## slope2 -0.19313 0.158030 -1.2221  -0.50924   0.12297
summary.segmented(m.seg.2018.Porterville.CW)
## 
##  ***Regression Model with Segmented Relationship(s)***
## 
## Call: 
## segmented.lm(obj = model, seg.Z = ~N_tot)
## 
## Estimated Break-Point(s):
##               Est. St.Err
## psi1.N_tot 28.062 10.061
## 
## Meaningful coefficients of the linear terms:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  55.3706     3.0962  17.883  < 2e-16 ***
## N_tot         0.5574     0.1751   3.183  0.00231 ** 
## U1.N_tot     -0.4371     0.1771  -2.468       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.757 on 60 degrees of freedom
## Multiple R-Squared: 0.6005,  Adjusted R-squared: 0.5806 
## 
## Convergence attained in 3 iter. (rel. change 0)
slope(m.seg.2018.Porterville.CW)
## $N_tot
##           Est.  St.Err. t value CI(95%).l CI(95%).u
## slope1 0.55744 0.175150  3.1827  0.207100   0.90779
## slope2 0.12031 0.026273  4.5791  0.067755   0.17286
summary.segmented(m.seg.2019.Porterville.CW)
## 
##  ***Regression Model with Segmented Relationship(s)***
## 
## Call: 
## segmented.lm(obj = model, seg.Z = ~N_tot)
## 
## Estimated Break-Point(s):
##               Est. St.Err
## psi1.N_tot 61.727 20.327
## 
## Meaningful coefficients of the linear terms:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  53.0590     4.3279  12.260   <2e-16 ***
## N_tot         0.3423     0.1341   2.553   0.0132 *  
## U1.N_tot     -0.3446     0.1437  -2.398       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 13.41 on 60 degrees of freedom
## Multiple R-Squared: 0.2442,  Adjusted R-squared: 0.2064 
## 
## Convergence attained in 3 iter. (rel. change 0)
slope(m.seg.2019.Porterville.CW)
## $N_tot
##              Est.  St.Err.   t value CI(95%).l CI(95%).u
## slope1  0.3423400 0.134090  2.552900  0.074107   0.61057
## slope2 -0.0022218 0.051667 -0.043003 -0.105570   0.10113

Medics-Wheat

Porterville Medics-Wheat results

Yield response to Nitrogen
District
Relative yield (Max trial yield = 100)
2016 2017 2018 2019
(1) (2) (3) (4)
Total Nitrogen Applied 0.223*** -0.084 0.135 -0.116
(0.081) (0.111) (0.096) (0.082)
Total Nitrogen Applied squared -0.001** 0.0003 -0.001 0.001
(0.0004) (0.001) (0.0005) (0.0004)
Intercept 65.884*** 68.226*** 72.553*** 73.865***
(3.236) (4.469) (3.854) (3.307)
Observations 64 64 64 64
R2 0.125 0.023 0.050 0.034
Adjusted R2 0.096 -0.009 0.019 0.003
Residual Std. Error (df = 61) 11.062 15.276 13.172 11.302
F Statistic (df = 2; 61) 4.362** 0.725 1.612 1.082
Note: p<0.1; p<0.05; p<0.01

It is evident that only 2016 has a good fit.

p.seg.2016.Porterville.MW

summary.segmented(m.seg.2016.Porterville.MW)
## 
##  ***Regression Model with Segmented Relationship(s)***
## 
## Call: 
## segmented.lm(obj = model, seg.Z = ~N_tot)
## 
## Estimated Break-Point(s):
##             Est. St.Err
## psi1.N_tot  130 20.533
## 
## Meaningful coefficients of the linear terms:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 67.47751    3.02386  22.315   <2e-16 ***
## N_tot        0.11003    0.04938   2.228   0.0296 *  
## U1.N_tot    -0.27270    0.10443  -2.611       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 11.04 on 60 degrees of freedom
## Multiple R-Squared: 0.1427,  Adjusted R-squared: 0.09979 
## 
## Convergence attained in 1 iter. (rel. change 8.1727e-08)
slope(m.seg.2016.Porterville.MW)
## $N_tot
##            Est.  St.Err. t value CI(95%).l CI(95%).u
## slope1  0.11003 0.049379  2.2283  0.011259  0.208810
## slope2 -0.16266 0.092013 -1.7678 -0.346720  0.021389

Caledon

Not one of the models has a good fit, there is no response to fertiliser.

Yield response to Nitrogen
District
Relative yield (Max trial yield = 100)
2016 2017 2018
(1) (2) (3)
Total Nitrogen Applied 0.0002 0.056 0.020
(0.097) (0.070) (0.087)
Total Nitrogen Applied squared -0.0001 -0.0002 -0.0001
(0.0005) (0.0004) (0.0004)
Intercept 77.424*** 74.715*** 69.491***
(3.903) (2.802) (3.538)
Observations 64 64 63
R2 0.003 0.011 0.002
Adjusted R2 -0.030 -0.021 -0.031
Residual Std. Error 13.341 (df = 61) 9.579 (df = 61) 11.565 (df = 60)
F Statistic 0.081 (df = 2; 61) 0.350 (df = 2; 61) 0.059 (df = 2; 60)
Note: p<0.1; p<0.05; p<0.01

Tygerhoek

All years show a good fit except for 2017

Yield response to Nitrogen
District
Relative yield (Max trial yield = 100)
2016 2017 2018 2019
(1) (2) (3) (4)
Total Nitrogen Applied 0.449*** 0.014 0.443*** 0.268**
(0.095) (0.061) (0.090) (0.108)
Total Nitrogen Applied squared -0.002*** 0.00002 -0.002*** -0.001**
(0.0005) (0.0003) (0.0005) (0.001)
Intercept 54.178*** 80.765*** 55.883*** 63.365***
(3.807) (2.455) (3.614) (4.340)
Observations 64 64 63 64
R2 0.362 0.018 0.325 0.092
Adjusted R2 0.341 -0.014 0.302 0.063
Residual Std. Error 13.011 (df = 61) 8.390 (df = 61) 12.330 (df = 60) 14.834 (df = 61)
F Statistic 17.283*** (df = 2; 61) 0.567 (df = 2; 61) 14.438*** (df = 2; 60) 3.101* (df = 2; 61)
Note: p<0.1; p<0.05; p<0.01 
## Warning: Removed 1 rows containing missing values (geom_vline).
## Warning: Removed 1 rows containing missing values (geom_text).

grid.arrange(p.seg.2016.Tygerhoek.CW, p.seg.2018.Tygerhoek.CW,p.seg.2019.Tygerhoek.CW, nrow =2)

summary.segmented(m.seg.2016.Tygerhoek.CW)
## 
##  ***Regression Model with Segmented Relationship(s)***
## 
## Call: 
## segmented.lm(obj = model, seg.Z = ~N_tot)
## 
## Estimated Break-Point(s):
##               Est. St.Err
## psi1.N_tot 92.706 18.514
## 
## Meaningful coefficients of the linear terms:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 55.54595    3.90963  14.207  < 2e-16 ***
## N_tot        0.30880    0.08359   3.694 0.000479 ***
## U1.N_tot    -0.36428    0.10881  -3.348       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 13.22 on 60 degrees of freedom
## Multiple R-Squared: 0.3521,  Adjusted R-squared: 0.3197 
## 
## Convergence attained in 2 iter. (rel. change 0)
slope(m.seg.2016.Tygerhoek.CW)
## $N_tot
##             Est.  St.Err.  t value CI(95%).l CI(95%).u
## slope1  0.308800 0.083591  3.69420   0.14159  0.476010
## slope2 -0.055475 0.069660 -0.79638  -0.19481  0.083865
summary.segmented(m.seg.2018.Tygerhoek.CW)
## 
##  ***Regression Model with Segmented Relationship(s)***
## 
## Call: 
## segmented.lm(obj = model, seg.Z = ~N_tot)
## 
## Estimated Break-Point(s):
##               Est. St.Err
## psi1.N_tot 32.724  6.786
## 
## Meaningful coefficients of the linear terms:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  49.1526     4.0911  12.014  < 2e-16 ***
## N_tot         0.9354     0.2314   4.042 0.000156 ***
## U1.N_tot     -0.9603     0.2341  -4.102       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 11.57 on 59 degrees of freedom
## Multiple R-Squared: 0.4153,  Adjusted R-squared: 0.3856 
## 
## Convergence attained in 2 iter. (rel. change 0)
slope(m.seg.2018.Tygerhoek.CW)
## $N_tot
##            Est.  St.Err. t value CI(95%).l CI(95%).u
## slope1  0.93544 0.231430  4.0420  0.472350  1.398500
## slope2 -0.02488 0.035467 -0.7015 -0.095849  0.046089
summary.segmented(m.seg.2019.Tygerhoek.CW)
## 
##  ***Regression Model with Segmented Relationship(s)***
## 
## Call: 
## segmented.lm(obj = model, seg.Z = ~N_tot)
## 
## Estimated Break-Point(s):
##               Est. St.Err
## psi1.N_tot 83.389 24.733
## 
## Meaningful coefficients of the linear terms:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 63.63471    4.41827  14.403   <2e-16 ***
## N_tot        0.18853    0.09447   1.996   0.0505 .  
## U1.N_tot    -0.30326    0.12297  -2.466       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 14.94 on 60 degrees of freedom
## Multiple R-Squared: 0.09484,  Adjusted R-squared: 0.04958 
## 
## Convergence attained in 2 iter. (rel. change 0)
slope(m.seg.2019.Tygerhoek.CW)
## $N_tot
##            Est.  St.Err. t value   CI(95%).l CI(95%).u
## slope1  0.18853 0.094467  1.9957 -0.00043451  0.377490
## slope2 -0.11473 0.078722 -1.4574 -0.27220000  0.042736

Riversdale

Yield response to Nitrogen
District
Relative yield (Max trial yield = 100)
2016 2017 2018 2019
(1) (2) (3) (4)
Total Nitrogen Applied 0.698*** 0.252 -0.363 0.083
(0.117) (0.157) (0.323) (0.154)
Total Nitrogen Applied squared -0.002*** -0.001 0.003 -0.001
(0.001) (0.001) (0.002) (0.001)
Intercept 41.359*** 79.200*** 66.404*** 72.504***
(4.710) (6.298) (12.946) (6.205)
Observations 16 16 16 46
R2 0.858 0.197 0.275 0.050
Adjusted R2 0.836 0.073 0.163 0.005
Residual Std. Error 8.049 (df = 13) 10.764 (df = 13) 22.124 (df = 13) 18.004 (df = 43)
F Statistic 39.118*** (df = 2; 13) 1.594 (df = 2; 13) 2.460 (df = 2; 13) 1.123 (df = 2; 43)
Note: p<0.1; p<0.05; p<0.01 

p.seg.2017.Riversdale.CW

summary.segmented(m.seg.2017.Riversdale.CW)
## 
##  ***Regression Model with Segmented Relationship(s)***
## 
## Call: 
## segmented.lm(obj = model, seg.Z = ~N_tot)
## 
## Estimated Break-Point(s):
##               Est. St.Err
## psi1.N_tot 87.853 28.752
## 
## Meaningful coefficients of the linear terms:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  78.4850     6.2719  12.514 3.03e-08 ***
## N_tot         0.1899     0.1341   1.416    0.182    
## U1.N_tot     -0.3721     0.1746  -2.132       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 10.6 on 12 degrees of freedom
## Multiple R-Squared: 0.281,  Adjusted R-squared: 0.1012 
## 
## Convergence attained in 2 iter. (rel. change 0)
slope(m.seg.2017.Riversdale.CW)
## $N_tot
##            Est. St.Err. t value CI(95%).l CI(95%).u
## slope1  0.18994 0.13410  1.4164  -0.10224  0.482110
## slope2 -0.18218 0.11175 -1.6302  -0.42566  0.061302