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) & spray == "F1"]
dat[, c("wind","yldb") := NULL]

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

#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 0.237*** -0.075 0.187
(0.046) (0.059) (0.144)
Total Nitrogen Applied squared -0.001*** 0.0002 -0.001
(0.0002) (0.0003) (0.001)
Intercept 72.608*** 84.932*** 76.314***
(1.848) (2.359) (5.758)
Observations 126 128 32
R2 0.282 0.043 0.064
Adjusted R2 0.270 0.028 -0.001
Residual Std. Error 8.930 (df = 123) 11.401 (df = 125) 13.917 (df = 29)
F Statistic 24.108*** (df = 2; 123) 2.831* (df = 2; 125) 0.990 (df = 2; 29)
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)
## Warning: Removed 1 rows containing missing values (geom_errorbarh).
## Warning: Removed 1 rows containing missing values (geom_vline).

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 81.394 16.069
## 
## Meaningful coefficients of the linear terms:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 72.60949    1.86678  38.896  < 2e-16 ***
## N_tot        0.19232    0.03991   4.818 4.21e-06 ***
## U1.N_tot    -0.19714    0.05202  -3.789       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.925 on 122 degrees of freedom
## Multiple R-Squared: 0.2883,  Adjusted R-squared: 0.2708 
## 
## Convergence attained in 2 iter. (rel. change 1.8718e-16)
slope(m.seg.2016.Langgewens.CW)
## $N_tot
##              Est.  St.Err.  t value CI(95%).l CI(95%).u
## slope1  0.1923200 0.039913  4.81840   0.11331  0.271330
## slope2 -0.0048227 0.033369 -0.14453  -0.07088  0.061235
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 61.716 33.336
## 
## Meaningful coefficients of the linear terms:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  73.5273     6.2959  11.679 2.82e-12 ***
## N_tot         0.2555     0.1951   1.310    0.201    
## U1.N_tot     -0.3056     0.2090  -1.462       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 13.79 on 28 degrees of freedom
## Multiple R-Squared: 0.1121,  Adjusted R-squared: 0.01697 
## 
## Convergence attained in 3 iter. (rel. change 3.4144e-16)
slope(m.seg.2019.Langgewens.CW)
## $N_tot
##             Est. St.Err.  t value CI(95%).l CI(95%).u
## slope1  0.255460 0.19507  1.30960  -0.14412   0.65505
## slope2 -0.050131 0.07516 -0.66699  -0.20409   0.10383

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 0.225*** -0.047 -0.217
(0.073) (0.136) (0.130)
Total Nitrogen Applied squared -0.001*** 0.0003 0.001
(0.0004) (0.001) (0.001)
Intercept 83.373*** 81.663*** 90.963***
(2.947) (5.441) (5.207)
Observations 32 32 32
R2 0.249 0.017 0.096
Adjusted R2 0.197 -0.051 0.034
Residual Std. Error (df = 29) 7.124 13.151 12.584
F Statistic (df = 2; 29) 4.809** 0.244 1.547
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 28.931  7.701
## 
## Meaningful coefficients of the linear terms:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  78.7553     3.2693  24.090  < 2e-16 ***
## N_tot         0.5839     0.1849   3.158  0.00379 ** 
## U1.N_tot     -0.6145     0.1870  -3.286       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.539 on 28 degrees of freedom
## Multiple R-Squared: 0.3892,  Adjusted R-squared: 0.3237 
## 
## Convergence attained in 2 iter. (rel. change 1.8993e-16)
slope(m.seg.2016.Langgewens.MW)
## $N_tot
##             Est.  St.Err. t value CI(95%).l CI(95%).u
## slope1  0.583940 0.184940  3.1575  0.205120  0.962770
## slope2 -0.030592 0.027742 -1.1027 -0.087419  0.026235

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 0.527** -0.058 0.382***
(0.223) (0.157) (0.100)
Total Nitrogen Applied squared -0.002 -0.001 -0.002***
(0.001) (0.001) (0.001)
Intercept 41.342*** 86.689*** 68.546***
(8.961) (6.193) (4.002)
Observations 32 31 32
R2 0.333 0.347 0.370
Adjusted R2 0.287 0.300 0.326
Residual Std. Error 21.658 (df = 29) 14.928 (df = 28) 9.672 (df = 29)
F Statistic 7.241*** (df = 2; 29) 7.439*** (df = 2; 28) 8.506*** (df = 2; 29)
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 97.695 18.135
## 
## Meaningful coefficients of the linear terms:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 69.33299    3.97737  17.432  < 2e-16 ***
## N_tot        0.25378    0.08504   2.984  0.00584 ** 
## U1.N_tot    -0.38498    0.11070  -3.478       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 9.508 on 28 degrees of freedom
## Multiple R-Squared: 0.4119,  Adjusted R-squared: 0.3489 
## 
## Convergence attained in 3 iter. (rel. change 0)
slope(m.seg.2018.Darling.CW)
## $N_tot
##            Est.  St.Err. t value CI(95%).l CI(95%).u
## slope1  0.25378 0.085040  2.9842  0.079582  0.427970
## slope2 -0.13120 0.070866 -1.8514 -0.276370  0.013959

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 0.722*** -0.085 0.705***
(0.120) (0.233) (0.176)
Total Nitrogen Applied squared -0.002*** 0.001 -0.002**
(0.001) (0.001) (0.001)
Intercept 31.381*** 71.952*** 26.670***
(4.832) (9.190) (7.063)
Observations 32 31 32
R2 0.778 0.023 0.603
Adjusted R2 0.763 -0.046 0.576
Residual Std. Error 11.680 (df = 29) 22.153 (df = 28) 17.070 (df = 29)
F Statistic 50.927*** (df = 2; 29) 0.336 (df = 2; 28) 22.018*** (df = 2; 29)
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.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 56.116 13.077
## 
## Meaningful coefficients of the linear terms:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  28.5918     5.2525   5.443 8.26e-06 ***
## N_tot         0.7837     0.1627   4.816 4.59e-05 ***
## U1.N_tot     -0.6182     0.1744  -3.544       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 11.51 on 28 degrees of freedom
## Multiple R-Squared: 0.7923,  Adjusted R-squared:  0.77 
## 
## 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 0.78372 0.162740  4.8157  0.450350   1.11710
## slope2 0.16556 0.062705  2.6403  0.037116   0.29401
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 93.505 21.957
## 
## Meaningful coefficients of the linear terms:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  26.3426     6.9776   3.775 0.000765 ***
## N_tot         0.5799     0.1492   3.887 0.000568 ***
## U1.N_tot     -0.5495     0.1942  -2.830       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 16.68 on 28 degrees of freedom
## Multiple R-Squared: 0.6339,  Adjusted R-squared: 0.5947 
## 
## 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 0.579890 0.14919 3.88700   0.27429   0.88549
## slope2 0.030384 0.12432 0.24439  -0.22428   0.28505

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 0.650** -0.376** 0.270** 0.406**
(0.267) (0.178) (0.119) (0.165)
Total Nitrogen Applied squared -0.002 0.001 -0.001 -0.001*
(0.001) (0.001) (0.001) (0.001)
Intercept 23.121** 91.660*** 63.519*** 56.091***
(10.690) (7.125) (4.769) (6.628)
Observations 32 32 32 32
R2 0.296 0.209 0.493 0.271
Adjusted R2 0.247 0.155 0.458 0.221
Residual Std. Error (df = 29) 25.838 17.221 11.526 16.019
F Statistic (df = 2; 29) 6.090*** 3.836** 14.086*** 5.392**
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.2019.Porterville.CW, nrow =1)
## Warning: Removed 1 rows containing missing values (geom_text).
## Warning: Removed 1 rows containing missing values (geom_errorbarh).
## Warning: Removed 1 rows containing missing values (geom_vline).

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 128.809 26.414
## 
## Meaningful coefficients of the linear terms:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  25.6924     9.9325   2.587   0.0152 *
## N_tot         0.4135     0.1622   2.549   0.0166 *
## U1.N_tot     -0.6980     0.3430  -2.035       NA  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 25.65 on 28 degrees of freedom
## Multiple R-Squared: 0.3301,  Adjusted R-squared: 0.2584 
## 
## Convergence attained in 2 iter. (rel. change 0)
slope(m.seg.2016.Porterville.CW)
## $N_tot
##            Est. St.Err.  t value CI(95%).l CI(95%).u
## slope1  0.41352 0.16220  2.54950  0.081273   0.74576
## slope2 -0.28451 0.30224 -0.94136 -0.903620   0.33459
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 37.532 25.568
## 
## Meaningful coefficients of the linear terms:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  53.1633     8.1244   6.544 4.29e-07 ***
## N_tot         0.6113     0.4596   1.330    0.194    
## U1.N_tot     -0.5624     0.4647  -1.210       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 16.25 on 28 degrees of freedom
## Multiple R-Squared: 0.2758,  Adjusted R-squared: 0.1982 
## 
## Convergence attained in 2 iter. (rel. change 2.2708e-06)
slope(m.seg.2019.Porterville.CW)
## $N_tot
##            Est.  St.Err. t value CI(95%).l CI(95%).u
## slope1 0.611310 0.459590 1.33010 -0.330110   1.55270
## slope2 0.048936 0.068941 0.70982 -0.092284   0.19016

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 0.294** -0.159 0.216 -0.071
(0.124) (0.174) (0.144) (0.128)
Total Nitrogen Applied squared -0.001* 0.001 -0.001 0.0003
(0.001) (0.001) (0.001) (0.001)
Intercept 68.592*** 81.182*** 74.432*** 83.563***
(4.954) (6.974) (5.793) (5.135)
Observations 32 32 32 32
R2 0.204 0.031 0.095 0.018
Adjusted R2 0.149 -0.036 0.032 -0.049
Residual Std. Error (df = 29) 11.974 16.855 14.001 12.411
F Statistic (df = 2; 29) 3.714** 0.463 1.518 0.271
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 146.834 20.949
## 
## Meaningful coefficients of the linear terms:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  70.6933     4.2476   16.64 4.72e-16 ***
## N_tot         0.1488     0.0551    2.70   0.0116 *  
## U1.N_tot     -0.4929     0.2849   -1.73       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 11.86 on 28 degrees of freedom
## Multiple R-Squared: 0.2457,  Adjusted R-squared: 0.1649 
## 
## Convergence attained in 2 iter. (rel. change 0)
slope(m.seg.2016.Porterville.MW)
## $N_tot
##            Est.  St.Err. t value CI(95%).l CI(95%).u
## slope1  0.14877 0.055104  2.6997   0.03589   0.26164
## slope2 -0.34414 0.279570 -1.2310  -0.91683   0.22854

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 -0.015 0.065 0.078
(0.132) (0.084) (0.118)
Total Nitrogen Applied squared -0.00000 -0.0005 -0.0002
(0.001) (0.0004) (0.001)
Intercept 82.267*** 88.119*** 81.368***
(5.300) (3.363) (4.736)
Observations 32 32 32
R2 0.006 0.074 0.037
Adjusted R2 -0.063 0.010 -0.029
Residual Std. Error (df = 29) 12.810 8.128 11.446
F Statistic (df = 2; 29) 0.084 1.155 0.559
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).

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 0.595*** 0.047 0.630*** 0.412**
(0.135) (0.099) (0.111) (0.168)
Total Nitrogen Applied squared -0.002*** -0.0001 -0.003*** -0.002**
(0.001) (0.0005) (0.001) (0.001)
Intercept 56.393*** 84.106*** 57.501*** 69.452***
(5.428) (3.952) (4.455) (6.728)
Observations 32 32 31 32
R2 0.500 0.055 0.549 0.173
Adjusted R2 0.466 -0.011 0.517 0.115
Residual Std. Error 13.120 (df = 29) 9.551 (df = 29) 10.724 (df = 28) 16.260 (df = 29)
F Statistic 14.520*** (df = 2; 29) 0.838 (df = 2; 29) 17.064*** (df = 2; 28) 3.024* (df = 2; 29)
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 60.985 16.403
## 
## Meaningful coefficients of the linear terms:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  54.8005     6.0825   9.009 9.14e-10 ***
## N_tot         0.5906     0.1885   3.134  0.00402 ** 
## U1.N_tot     -0.5958     0.2020  -2.950       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 13.33 on 28 degrees of freedom
## Multiple R-Squared: 0.5023,  Adjusted R-squared: 0.449 
## 
## 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  0.5906400 0.188460  3.134000   0.20460   0.97669
## slope2 -0.0051866 0.072614 -0.071427  -0.15393   0.14356
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 35.971  7.462
## 
## Meaningful coefficients of the linear terms:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  50.9976     5.1463   9.910 1.72e-10 ***
## N_tot         1.1227     0.2911   3.857 0.000646 ***
## U1.N_tot     -1.1942     0.2947  -4.053       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 10.29 on 27 degrees of freedom
## Multiple R-Squared: 0.5997,  Adjusted R-squared: 0.5552 
## 
## Convergence attained in 2 iter. (rel. change 3.1796e-16)
slope(m.seg.2018.Tygerhoek.CW)
## $N_tot
##             Est.  St.Err. t value CI(95%).l CI(95%).u
## slope1  1.122700 0.291120  3.8566   0.52541  1.720100
## slope2 -0.071493 0.045668 -1.5655  -0.16520  0.022209
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 99.131 27.897
## 
## Meaningful coefficients of the linear terms:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  71.1512     6.8984  10.314 4.84e-11 ***
## N_tot         0.2364     0.1475   1.603     0.12    
## U1.N_tot     -0.4367     0.1920  -2.274       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 16.49 on 28 degrees of freedom
## Multiple R-Squared: 0.1784,  Adjusted R-squared: 0.09032 
## 
## Convergence attained in 3 iter. (rel. change 0)
slope(m.seg.2019.Tygerhoek.CW)
## $N_tot
##            Est. St.Err. t value CI(95%).l CI(95%).u
## slope1  0.23645 0.14749  1.6031  -0.06568  0.538570
## slope2 -0.20023 0.12291 -1.6291  -0.45201  0.051537

Riversdale

Yield response to Nitrogen
District
Relative yield (Max trial yield = 100)
2016 2017 2018 2019
(1) (2) (3) (4)
Total Nitrogen Applied 0.780*** 0.315 -0.210 0.133
(0.160) (0.231) (0.506) (0.189)
Total Nitrogen Applied squared -0.002** -0.002 0.002 -0.001
(0.001) (0.001) (0.003) (0.001)
Intercept 35.977*** 71.477*** 60.888** 81.328***
(6.428) (9.281) (20.301) (7.824)
Observations 8 8 8 23
R2 0.921 0.270 0.267 0.211
Adjusted R2 0.889 -0.021 -0.027 0.133
Residual Std. Error 7.768 (df = 5) 11.216 (df = 5) 24.533 (df = 5) 15.778 (df = 20)
F Statistic 29.165*** (df = 2; 5) 0.927 (df = 2; 5) 0.908 (df = 2; 5) 2.682* (df = 2; 20)
Note: p<0.1; p<0.05; p<0.01 

p.seg.2017.Riversdale.CW
## Warning: Removed 1 rows containing missing values (geom_text).
## Warning: Removed 1 rows containing missing values (geom_errorbarh).
## Warning: Removed 1 rows containing missing values (geom_vline).

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 84.176 35.766
## 
## Meaningful coefficients of the linear terms:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  69.8149     9.2469   7.550  0.00165 **
## N_tot         0.2748     0.1977   1.390  0.23695   
## U1.N_tot     -0.4391     0.2574  -1.706       NA   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 11.05 on 4 degrees of freedom
## Multiple R-Squared: 0.4332,  Adjusted R-squared: 0.00815 
## 
## 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  0.27477 0.19771  1.38980  -0.27416   0.82369
## slope2 -0.16435 0.16476 -0.99752  -0.62178   0.29309