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In [74]:



    


library(MASS)
require(graphics)
library(Cairo)



    


















    






Error in library(Cairo): there is no package called ‘Cairo’
Traceback:

1. library(Cairo)
2. stop(txt, domain = NA)
















In [50]:



    


data <- read.table("apple.txt",
                   sep="",
                   col.names=c("Variety", "FusariumStrain", "Days", "AppleWeight",
                               "Radius", "FungalRadialAdvance", "RateOfAdvance"))
data$Variety = as.factor(data$Variety)
data$FusariumStrain = as.factor(data$FusariumStrain)



    











In [51]:



    


data



    


















    









VarietyFusariumStrainDaysAppleWeightRadiusFungalRadialAdvanceRateOfAdvance


	
1     1      70   156.2 3.66  2.04  0.0291

	
1     2      70   153.9 3.65  1.23  0.0176

	
1     3      70   137.8 3.51  1.25  0.0179

	
1     4      70   141.0 3.53  1.66  0.0237

	
1     5      70   145.8 3.58  1.74  0.0249

	
1     6      70   147.8 3.60  1.88  0.0269

	
1     7      70   174.9 3.81  2.26  0.0323

	
2     1     103    91.3 3.07  1.16  0.0113

	
2     2     103   115.5 3.05  1.26  0.0122

	
2     3     103    99.5 3.15  0.41  0.0040

	
2     4     103   101.2 3.17  2.39  0.0232

	
2     5     103   106.8 3.23  2.01  0.0195

	
2     6     103    88.1 3.03  1.98  0.0192

	
2     7     103   100.2 3.16  2.26  0.0219

	
3     1      54    66.5 2.66  2.29  0.0424

	
3     2      54    67.6 2.68  1.02  0.0189

	
3     3      54    64.8 2.64  0.27  0.0050

	
3     4      54    59.3 2.57  2.63  0.0487

	
3     5      54    70.1 2.71  2.58  0.0478

	
3     6      54    68.1 2.69  2.11  0.0391

	
3     7      54    64.0 2.63  2.73  0.0506

	
4     1     138    68.7 2.74  1.46  0.0106

	
4     2     138    66.7 2.71  0.53  0.0038

	
4     3     138    72.4 2.78  0.05  0.0004

	
4     4     138    68.6 2.74  1.69  0.0122

	
4     5     138    68.0 2.73  1.60  0.0116

	
4     6     138    62.2 2.65  2.15  0.0156

	
4     7     138    73.1 2.79  1.67  0.0121

	
5     1      89    62.7 2.46  1.33  0.0149

	
5     2      89    60.6 2.44  0.59  0.0066

	
5     3      89    67.8 2.53  0.60  0.0067

	
5     4      89    64.4 2.44  1.95  0.0219

	
5     5      89    54.5 2.35  1.76  0.0198

	
5     6      89    57.4 2.40  1.25  0.0140

	
5     7      89    60.9 2.44  2.05  0.0230





















In [52]:



    


nrow(data)



    


















    






35
















In [53]:



    


data$RateOfAdvance



    


















    







    
	
  1. 0.0291
    2. 
	
  2. 0.0176
    3. 
	
  3. 0.0179
    4. 
	
  4. 0.0237
    5. 
	
  5. 0.0249
    6. 
	
  6. 0.0269
    7. 
	
  7. 0.0323
    8. 
	
  8. 0.0113
    9. 
	
  9. 0.0122
    10. 
	
  10. 0.004
    11. 
	
  11. 0.0232
    12. 
	
  12. 0.0195
    13. 
	
  13. 0.0192
    14. 
	
  14. 0.0219
    15. 
	
  15. 0.0424
    16. 
	
  16. 0.0189
    17. 
	
  17. 0.005
    18. 
	
  18. 0.0487
    19. 
	
  19. 0.0478
    20. 
	
  20. 0.0391
    21. 
	
  21. 0.0506
    22. 
	
  22. 0.0106
    23. 
	
  23. 0.0038
    24. 
	
  24. 4e-04
    25. 
	
  25. 0.0122
    26. 
	
  26. 0.0116
    27. 
	
  27. 0.0156
    28. 
	
  28. 0.0121
    29. 
	
  29. 0.0149
    30. 
	
  30. 0.0066
    31. 
	
  31. 0.0067
    32. 
	
  32. 0.0219
    33. 
	
  33. 0.0198
    34. 
	
  34. 0.014
    35. 
	
  35. 0.023
    36. 



















In [54]:



    


round(data$FungalRadialAdvance / data$Days, 4) == data$RateOfAdvance



    


















    







    
	
  1. TRUE
    2. 
	
  2. TRUE
    3. 
	
  3. TRUE
    4. 
	
  4. TRUE
    5. 
	
  5. TRUE
    6. 
	
  6. TRUE
    7. 
	
  7. TRUE
    8. 
	
  8. TRUE
    9. 
	
  9. TRUE
    10. 
	
  10. TRUE
    11. 
	
  11. TRUE
    12. 
	
  12. TRUE
    13. 
	
  13. TRUE
    14. 
	
  14. TRUE
    15. 
	
  15. TRUE
    16. 
	
  16. TRUE
    17. 
	
  17. TRUE
    18. 
	
  18. TRUE
    19. 
	
  19. TRUE
    20. 
	
  20. TRUE
    21. 
	
  21. TRUE
    22. 
	
  22. TRUE
    23. 
	
  23. TRUE
    24. 
	
  24. TRUE
    25. 
	
  25. TRUE
    26. 
	
  26. TRUE
    27. 
	
  27. TRUE
    28. 
	
  28. TRUE
    29. 
	
  29. TRUE
    30. 
	
  30. TRUE
    31. 
	
  31. TRUE
    32. 
	
  32. TRUE
    33. 
	
  33. TRUE
    34. 
	
  34. TRUE
    35. 
	
  35. TRUE
    36.

Exploratory Analysis

Histograms for Apple Weight and Apple Radius





In [72]:



    


# 1. Open jpeg file
#jpeg("histograms.jpg", width = 750, height = 350)
svg(filename="histograms.svg", 
    width=5, 
    height=4, 
    pointsize=12)

# 2. Create the plot
par(mfrow=c(1, 2))
hist(data$AppleWeight, cex.axis=0.9, cex.lab=1.2, main="", xlab="Apple Weight (g)")
hist(data$Radius, cex.axis=0.9, cex.lab=1.2, main="", xlab="Apple Radius (cm)")

# 3. Close the file
dev.off()



    


















    






Warning message in svg(filename = "histograms.svg", width = 5, height = 4, pointsize = 12):
“unable to load shared object '/usr/local/Cellar/r/3.5.1/lib/R/library/grDevices/libs//cairo.so':
  dlopen(/usr/local/Cellar/r/3.5.1/lib/R/library/grDevices/libs//cairo.so, 6): image not found”Warning message in svg(filename = "histograms.svg", width = 5, height = 4, pointsize = 12):
“failed to load cairo DLL”









    






null device: 1









    
























In [70]:



    


# 1. Open jpeg file
jpeg("boxplots.jpg", width = 1200, height = 800)

# 2. Create the plot
par(mfrow=c(1, 3))

boxplot(AppleWeight~Variety, data=data, main="", cex.axis=0.9, cex.lab=1.2, 
   xlab="Apple Variety", ylab="Apple Weight (g)")
boxplot(RateOfAdvance~FusariumStrain, data=data, main="", cex.axis=0.9, cex.lab=1.2, 
   xlab="Fusarium Strain", ylab="Rate of Advance")
plot.design(RateOfAdvance ~ FusariumStrain + Variety, data=data, main="", cex.axis=0.9, cex.lab=1.2)

# 3. Close the file
dev.off()



    


















    






pdf: 2
















In [64]:



    


# 1. Open jpeg file
jpeg("boxplots.jpg", width = 750, height = 600)

# 2. Create the plot
with(data, interaction.plot(x.factor=Variety, trace.factor = FusariumStrain,
                            cex.axis=0.9, cex.lab=1.2, 
                            response=RateOfAdvance, fun=mean, legend=T, ylab="Rate of Advance", col=2:8))

# 3. Close the file
dev.off()



    


















    






pdf: 2

Fungal Radial Advance models

Most complex model.





In [130]:



    


model_fra <- aov(FungalRadialAdvance ~ Variety * FusariumStrain * AppleWeight * Days, data=data)



    











In [131]:



    


summary(model_fra)



    


















    








                                        Df Sum Sq Mean Sq F value  Pr(>F)   
Variety                                  1  0.778   0.778   1.537 0.23023   
FusariumStrain                           1  4.344   4.344   8.578 0.00861 **
AppleWeight                              1  0.417   0.417   0.824 0.37550   
Days                                     1  0.670   0.670   1.322 0.26442   
Variety:FusariumStrain                   1  0.028   0.028   0.054 0.81812   
Variety:AppleWeight                      1  0.039   0.039   0.076 0.78570   
FusariumStrain:AppleWeight               1  0.158   0.158   0.312 0.58274   
Variety:Days                             1  0.008   0.008   0.015 0.90355   
FusariumStrain:Days                      1  0.025   0.025   0.049 0.82714   
AppleWeight:Days                         1  0.007   0.007   0.013 0.91048   
Variety:FusariumStrain:AppleWeight       1  0.050   0.050   0.098 0.75727   
Variety:FusariumStrain:Days              1  0.000   0.000   0.000 0.99207   
Variety:AppleWeight:Days                 1  0.526   0.526   1.039 0.32076   
FusariumStrain:AppleWeight:Days          1  0.006   0.006   0.012 0.91305   
Variety:FusariumStrain:AppleWeight:Days  1  0.000   0.000   0.000 0.98994   
Residuals                               19  9.621   0.506                   
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

















In [132]:



    


coef(model_fra)



    


















    








	
(Intercept)

		
17.305584403028

	
Variety

		
-4.27936631848325

	
FusariumStrain

		
-0.0670350290326962

	
AppleWeight

		
-0.169951280951447

	
Days

		
-0.219579225748811

	
Variety:FusariumStrain

		
-0.351116907038438

	
Variety:AppleWeight

		
0.0411890659847118

	
FusariumStrain:AppleWeight

		
0.000778843061500377

	
Variety:Days

		
0.0751461165708688

	
FusariumStrain:Days

		
0.006564010997157

	
AppleWeight:Days

		
0.00262400108229716

	
Variety:FusariumStrain:AppleWeight

		
0.0067601297530425

	
Variety:FusariumStrain:Days

		
-0.00076070823573468

	
Variety:AppleWeight:Days

		
-0.000932361630757493

	
FusariumStrain:AppleWeight:Days

		
-0.00010362096336471

	
Variety:FusariumStrain:AppleWeight:Days

		
6.37279861512619e-06




















In [133]:



    


layout(matrix(1:4,ncol=2)) 
plot(model_fra)

Basic model





In [134]:



    


model_fra_basic <- aov(FungalRadialAdvance ~ 1, data=data)



    











In [135]:



    


stepAIC(model_fra_basic, scope= ~ Variety * FusariumStrain * AppleWeight * Days)



    


















    






Start:  AIC=-23.95
FungalRadialAdvance ~ 1

                 Df Sum of Sq    RSS     AIC
+ FusariumStrain  1    4.3437 12.332 -32.511
+ Days            1    1.3410 15.334 -24.884
<none>                        16.675 -23.950
+ Variety         1    0.7781 15.897 -23.622
+ AppleWeight     1    0.2000 16.475 -22.372

Step:  AIC=-32.51
FungalRadialAdvance ~ FusariumStrain

                 Df Sum of Sq    RSS     AIC
+ Days            1    1.3410 10.991 -34.541
+ Variety         1    0.7781 11.553 -32.793
<none>                        12.332 -32.511
+ AppleWeight     1    0.1965 12.135 -31.074
- FusariumStrain  1    4.3437 16.675 -23.950

Step:  AIC=-34.54
FungalRadialAdvance ~ FusariumStrain + Days

                      Df Sum of Sq    RSS     AIC
<none>                             10.991 -34.541
+ Variety              1    0.2511 10.739 -33.350
+ FusariumStrain:Days  1    0.0309 10.960 -32.639
+ AppleWeight          1    0.0276 10.963 -32.629
- Days                 1    1.3410 12.332 -32.511
- FusariumStrain       1    4.3437 15.334 -24.884










    








Call:
   aov(formula = FungalRadialAdvance ~ FusariumStrain + Days, data = data)

Terms:
                FusariumStrain      Days Residuals
Sum of Squares        4.343683  1.341000 10.990585
Deg. of Freedom              1         1        32

Residual standard error: 0.586051
Estimated effects may be unbalanced

















In [136]:



    


best_model_fra = aov(formula = FungalRadialAdvance ~ FusariumStrain + Days, data = data)



    











In [137]:



    


summary(best_model_fra)



    


















    








               Df Sum Sq Mean Sq F value Pr(>F)   
FusariumStrain  1  4.344   4.344  12.647 0.0012 **
Days            1  1.341   1.341   3.904 0.0568 . 
Residuals      32 10.991   0.343                  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

















In [138]:



    


coef(best_model_fra)



    


















    








	
(Intercept)

		
1.5065299304708

	
FusariumStrain

		
0.176142857142857

	
Days

		
-0.00678053730852041




















In [139]:



    


layout(matrix(1:4,ncol=2)) 
plot(best_model_fra)

Rate of Advance model





In [140]:



    


model_roa <- aov(RateOfAdvance ~ Variety * FusariumStrain * AppleWeight, data=data)



    











In [141]:



    


summary(model_roa)



    


















    








                                   Df   Sum Sq   Mean Sq F value Pr(>F)  
Variety                             1 0.000443 0.0004425   3.653 0.0667 .
FusariumStrain                      1 0.000625 0.0006250   5.159 0.0313 *
AppleWeight                         1 0.000441 0.0004407   3.637 0.0672 .
Variety:FusariumStrain              1 0.000001 0.0000009   0.007 0.9332  
Variety:AppleWeight                 1 0.000911 0.0009113   7.522 0.0107 *
FusariumStrain:AppleWeight          1 0.000046 0.0000462   0.381 0.5422  
Variety:FusariumStrain:AppleWeight  1 0.000002 0.0000017   0.014 0.9059  
Residuals                          27 0.003271 0.0001211                 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

















In [142]:



    


coef(model_roa)



    


















    








	
(Intercept)

		
0.0288955951930812

	
Variety

		
0.0118605135436346

	
FusariumStrain

		
0.00760161796203462

	
AppleWeight

		
0.000118635005557201

	
Variety:FusariumStrain

		
-0.000576301760925512

	
Variety:AppleWeight

		
-0.00027634843293764

	
FusariumStrain:AppleWeight

		
-2.50949505328662e-05

	
Variety:FusariumStrain:AppleWeight

		
-7.6892897620657e-06




















In [143]:



    


layout(matrix(1:4,ncol=2)) 
plot(model_roa)

AIC for models





In [126]:



    


model_roa_basic <- aov(RateOfAdvance ~ 1, data=data)



    











In [132]:



    


stepAIC(model_roa_basic, scope= ~Variety * FusariumStrain * AppleWeight)



    


















    






Start:  AIC=-308.73
RateOfAdvance ~ Variety * FusariumStrain * AppleWeight

                                     Df  Sum of Sq       RSS     AIC
- Variety:FusariumStrain:AppleWeight  1 1.7247e-06 0.0032728 -310.71
<none>                                             0.0032710 -308.73

Step:  AIC=-310.71
RateOfAdvance ~ Variety + FusariumStrain + AppleWeight + Variety:FusariumStrain + 
    Variety:AppleWeight + FusariumStrain:AppleWeight

                                     Df  Sum of Sq       RSS     AIC
- FusariumStrain:AppleWeight          1 0.00004616 0.0033189 -312.22
- Variety:FusariumStrain              1 0.00006937 0.0033421 -311.98
<none>                                             0.0032728 -310.71
+ Variety:FusariumStrain:AppleWeight  1 0.00000172 0.0032710 -308.73
- Variety:AppleWeight                 1 0.00093324 0.0042060 -303.93

Step:  AIC=-312.22
RateOfAdvance ~ Variety + FusariumStrain + AppleWeight + Variety:FusariumStrain + 
    Variety:AppleWeight

                             Df  Sum of Sq       RSS     AIC
- Variety:FusariumStrain      1 0.00002363 0.0033426 -313.97
<none>                                     0.0033189 -312.22
+ FusariumStrain:AppleWeight  1 0.00004616 0.0032728 -310.71
- Variety:AppleWeight         1 0.00091127 0.0042302 -305.73

Step:  AIC=-313.97
RateOfAdvance ~ Variety + FusariumStrain + AppleWeight + Variety:AppleWeight

                             Df  Sum of Sq       RSS     AIC
<none>                                     0.0033426 -313.97
+ Variety:FusariumStrain      1 0.00002363 0.0033189 -312.22
+ FusariumStrain:AppleWeight  1 0.00000042 0.0033421 -311.98
- FusariumStrain              1 0.00047839 0.0038209 -311.29
- Variety:AppleWeight         1 0.00088851 0.0042311 -307.72










    








Call:
   aov(formula = RateOfAdvance ~ Variety + FusariumStrain + AppleWeight + 
    Variety:AppleWeight, data = data)

Terms:
                    Variety FusariumStrain AppleWeight Variety:AppleWeight
Sum of Squares  0.000442514    0.000624983 0.000440673         0.000888508
Deg. of Freedom           1              1           1                   1
                  Residuals
Sum of Squares  0.003342556
Deg. of Freedom          30

Residual standard error: 0.0105555
Estimated effects may be unbalanced

















In [128]:



    


best_model_roa <- aov(formula = RateOfAdvance ~ FusariumStrain + Variety + AppleWeight + 
    Variety:AppleWeight, data = data)



    











In [129]:



    


summary(best_model_roa)



    


















    








                    Df   Sum Sq   Mean Sq F value  Pr(>F)   
FusariumStrain       1 0.000625 0.0006250   5.609 0.02450 * 
Variety              1 0.000443 0.0004425   3.972 0.05544 . 
AppleWeight          1 0.000441 0.0004407   3.955 0.05592 . 
Variety:AppleWeight  1 0.000889 0.0008885   7.975 0.00835 **
Residuals           30 0.003343 0.0001114                   
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

















In [130]:



    


coef(best_model_roa)



    


















    








	
(Intercept)

		
0.0522105607927795

	
FusariumStrain

		
0.00185845754319811

	
Variety

		
0.00904381319086793

	
AppleWeight

		
7.58216427951966e-06

	
Variety:AppleWeight

		
-0.000297500551810858




















In [131]:



    


layout(matrix(1:4,ncol=2)) 
plot(best_model_roa)



    


















    
























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