# Application of Logistic Regression Models for the Marketability of Cucumber Cultivars

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Production and Preparation of Cucumber Fruit Samples

#### 2.2. Experimental Design

#### 2.3. Data Analysis

_{1}, X

_{2}, …, X

_{i}are the independent variables and π (x) is the probability of marketability of cucumbers. In our study, the independent variables used in the different multiple analyses were DOS, cultivar, fruit weight loss percentage (FWL %) during storage, and month of evaluation.

- Estimating the model parameters associated with cultivars and storage time as the main factors influencing the probability of marketability;
- Estimating the model parameters associated with cultivars and cucumber FWL % as the main factors influencing the probability of marketability; and
- Using multiple binary logistic regression to identify the factors capable of predicting with greater precision the probability of marketability.

## 3. Results and Discussion

#### 3.1. Influence of Storage Time on the Commercialization of Cucumber Cultivars

#### 3.2. Effect of Cultivar and Storage Time as Factors Influencing Marketability

#### 3.3. Effect of Cultivar and Fruit Weight Loss as Factors Influencing Marketability

#### 3.4. Future Lines of Research

#### 3.5. Selection of the Study Variables with the Greatest Influence on the Probability of Marketability

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Diagram of the interest in and practical application of the logistic regression model in comparative studies of cucumber cultivars to identify cultivars with the longest postharvest shelf life. In the figure, π (x) is the probability of marketability of a cucumber, “x” is the days of storage, “e” is Euler’s number, “α” is the intercept, and “β” is the slope. Source: Author’s elaboration based on Díaz-Pérez [22].

**Figure 2.**Details of noncommercial cucumber fruits identified during the study. Apical wilt caused by fruit aging and water loss (

**a**). Apical rot (

**b**). Loss of green color (i.e., chlorophyll) with yellow development (

**c**).

**Figure 3.**Timeline of the probability of marketability of the LET cucumber cultivars. The results are obtained from the simple logistic model for each cultivar as a function of the days of storage.

**Figure 4.**Timeline of the probability of marketability in mini cucumber cultivars. The results are obtained from the simple logistic model for each cultivar, as a function of the days of storage.

**Figure 5.**Timeline of the probability of marketability as a function of the days of storage (DOS) for the Levantino and Litoral cucumber cultivars.

**Figure 6.**Timeline of the probability of marketability as a function of the days of storage (DOS) for the Poniente, Galerno, and Valle cucumber cultivars.

**Figure 7.**Timeline of the probability of marketability as a function of the days of storage (DOS) for the mini-type cucumber cultivars.

**Figure 8.**Probability of marketability based on fruit loss percentage during storage for the Levantino and Litoral cultivars.

**Figure 9.**Probability of marketability based on fruit loss percentage during storage for the Galerno, Poniente, and Valle cultivars.

**Figure 10.**Probability of marketability based on fruit weight loss of the mini-type cucumber cultivars studied. The results are obtained from the simple logistic model for each cultivar and based on fruit weight loss percentage (FWL %) during storage.

**Table 1.**Sampling for each crop cycle and month of evaluation and days in which the samples of each cucumber cultivar were measured in the laboratory.

Evaluated Cycle | Month of Evaluation/Cycle | DOS ^{(a)} | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Cultivars | 14–15 | 16–17 | 17–18 | Nov. | Dec. | Jan. | Feb. | Mar. | 0 | 7 | 14 | 21 | 28 | 35 | ||

LET | ||||||||||||||||

Litoral | X | X | X | X | X | X | X | X | X | X | X | |||||

Levantino | X | X | X | X | X | X | X | X | X | X | X | |||||

Galerno | X | X | X | X | X | X | X | X | X | X | X | |||||

Poniente | X | X | X | X | X | X | X | X | X | X | X | |||||

Valle | X | X | X | X | X | X | X | X | X | X | X | |||||

Mini-type | 0 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | ||||||||

Katrina | X | X | X | X | X | X | X | X | X | X | X | X | ||||

176 | X | X | X | X | X | X | X | X | X | X | X | X | ||||

15999 | X | X | X | X | X | X | X | X | X | X | X | X | ||||

16000 | X | X | X | X | X | X | X | X | X | X | X | X | ||||

16054 | X | X | X | X | X | X | X | X | X | X | X | X |

^{(a)}Days of storage over which the fruit samples were measured during postharvest in the laboratory. X: Sampling conducted.

**Table 2.**Estimated independent simple logistic regression parameters for each LET cucumber cultivar as a function of the days of storage (DOS), which is a factor influencing the probability of marketability.

Cultivar | Coefficients | Odds Ratio | 95% CI for (Exp(β)) | ||||
---|---|---|---|---|---|---|---|

Variable | (α, β) | Wald χ^{2} | p | (Exp(β)) | Lower | Upper | |

Period: November–January | |||||||

Levantino * | DOS | −0.330 | 193.198 | <0.000 | 0.719 | 0.687 | 0.753 |

Constant | 6.430 | 192.484 | <0.000 | 619.996 | |||

Litoral * | DOS | −0.366 | 180.054 | <0.000 | 0.694 | 0.658 | 0.732 |

Constant | 5.910 | 171.565 | <0.000 | 368.591 | |||

Period: February–March | |||||||

Galerno * | DOS | −0.585 | 15.730 | <0.000 | 0.557 | 0.417 | 0.744 |

Constant | 7.620 | 15.470 | <0.000 | 2039.480 | |||

Poniente * | DOS | −0.357 | 186.558 | <0.000 | 0.700 | 0.665 | 0.737 |

Constant | 6.033 | 179.682 | <0.000 | 417.092 | |||

Valle * | DOS | −0.514 | 66.923 | <0.000 | 0.598 | 0.529 | 0.676 |

Constant | 5.521 | 57.952 | <0.000 | 249.885 |

**Table 3.**Estimation of independent simple logistic regression parameters for each mini cucumber cultivar based on the days of storage (DOS), which is a factor influencing the probability of marketability.

Cultivar | Coefficients | Odds ratio | 95% CI for (Exp(β)) | ||||
---|---|---|---|---|---|---|---|

Variable | (α, β) | Wald χ^{2} | p | (Exp(β)) | Lower | Upper | |

176 * | DOS | −0.296 | 125.198 | <0.000 | 0.744 | 0.706 | 0.784 |

Constant | 4.724 | 114.867 | <0.000 | 112.664 | |||

15999 * | DOS | −0.348 | 30.631 | <0.000 | 0.706 | 0.624 | 0.799 |

Constant | 4.207 | 40.793 | <0.000 | 67.155 | |||

16000 * | DOS | −0.367 | 34.819 | <0.000 | 0.693 | 0.613 | 0.783 |

Constant | 5.209 | 43.385 | <0.000 | 182.856 | |||

16054 * | DOS | −0.590 | 27.759 | <0.000 | 0.554 | 0.445 | 0.690 |

Constant | 6.019 | 29.840 | <0.000 | 411.181 | |||

Katrina * | DOS | −0.345 | 214.049 | <0.000 | 0.708 | 0.676 | 0.742 |

Constant | 4.237 | 197.549 | <0.000 | 69.201 |

**Table 4.**Estimation of the multiple logistic regression parameters for cultivars (Levantino and Litoral) and DOS as factors influencing the probability of marketability.

Variables | Coefficients | Wald χ^{2} | p | Odds Ratio | 95% CI for (Exp(β)) | |
---|---|---|---|---|---|---|

(α, β) | (Exp(β)) | Lower | Upper | |||

Constant | 5.602 | 325.113 | <0.000 | 271.048 | ||

DOS | −0.346 | 373.355 | <0.000 | 0.707 | 0.683 | 0.733 |

Levantino | 1.144 | 39.917 | <0.000 | 3.140 | 2.202 | 4.477 |

Litoral | Reference |

**Table 5.**Estimation of the multiple logistic regression parameters for cultivars (Galerno, Poniente, and Valle) and days of storage (DOS) as factors influencing the probability of marketability.

Variables | Coefficients | Wald χ^{2} | p | Odds Ratio | 95% CI for (Exp(β)) | |
---|---|---|---|---|---|---|

(α, β) | (Exp(β)) | Lower | Upper | |||

Constant | 4.272 | 160.644 | <0.000 | 71.692 | ||

DOS | −0.398 | 266.725 | <0.000 | 0.671 | 0.640 | -0.398 |

Galerno | 1.007 | 5.654 | 0.017 | 2.736 | 1.193 | 1.007 |

Poniente | 2.447 | 72.483 | <0.000 | 11.558 | 6.580 | 2.447 |

Valle | Reference | |||||

Constant | 6.720 | 249.830 | <0.000 | 828.620 | ||

DOS | −0.398 | 266.725 | <0.000 | 0.671 | 0.640 | 0.704 |

Valle | −2.447 | 72.483 | <0.000 | 0.087 | 0.049 | 0.152 |

Galerno | −1.441 | 12.835 | <0.000 | 0.237 | 0.108 | 0.521 |

Poniente | Reference | |||||

Constant | 5.279 | 125.272 | <0.000 | 196.184 | ||

DOS | −0.398 | 266.725 | <0.000 | 0.671 | 0.640 | 0.704 |

Poniente | 1.441 | 12.835 | <0.000 | 4.224 | 1.920 | 9.290 |

Valle | −1.007 | 5.654 | 0.017 | 0.365 | 0.159 | 0.838 |

Galerno | Reference |

**Table 6.**Estimation of the multiple logistic regression parameters for the mini-type cultivars and days of storage (DOS) as factors influencing the probability of marketability.

Variables | Coefficients | Wald χ^{2} | p | Odds Ratio | 95% CI for (Exp(β)) | |
---|---|---|---|---|---|---|

(α, β) | (Exp(β)) | Lower | Upper | |||

Constant | 4.180 | 343.022 | <0.000 | 65.337 | ||

DOS | −0.340 | 426.987 | <0.000 | 0.712 | 0.689 | 0.735 |

176 | 1.247 | 39.387 | <0.000 | 3.480 | 2.357 | 5.136 |

15999 | −0.054 | 0.035 | 0.851 | 0.947 | 0.537 | 1.670 |

16000 | 0.701 | 6.905 | 0.009 | 2.016 | 1.195 | 3.401 |

16054 | −0.491 | 3.170 | 0.075 | 0.612 | 0.357 | 1.051 |

Katrina | Reference | |||||

Constant | 3.689 | 164.413 | <0.000 | 40.000 | ||

DOS | −0.340 | 426.987 | <0.000 | 0.712 | 0.689 | 0.735 |

Katrina | 0.491 | 3.170 | 0.075 | 1.633 | 0.952 | 2.803 |

176 | 1.738 | 31.765 | <0.000 | 5.684 | 3.106 | 10.400 |

15999 | 0.437 | 1.469 | 0.225 | 1.547 | 0.764 | 3.134 |

16000 | 1.192 | 11.771 | 0.001 | 3.293 | 1.667 | 6.506 |

16054 | Reference | |||||

Constant | 4.881 | 248.244 | <0.000 | 131.723 | ||

DOS | −0.340 | 426.987 | <0.000 | 0.712 | 0.689 | 0.735 |

16054 | −1.192 | 11.771 | 0.001 | 0.304 | 0.154 | 0.600 |

Katrina | −0.701 | 6.905 | 0.009 | 0.496 | 0.294 | 0.837 |

176 | 0.546 | 3.547 | 0.049 | 1.726 | 1.012 | 3.046 |

15999 | −0.755 | 4.444 | 0.035 | 0.470 | 0.233 | 0.948 |

16000 | Reference | |||||

Constant | 4.125 | 181.986 | <0.000 | 61.891 | ||

DOS | −0.340 | 426.987 | <0.000 | 0.712 | 0.689 | 0.735 |

16000 | 0.755 | 4.444 | 0.035 | 2.128 | 1.054 | 4.296 |

16054 | −0.437 | 1.469 | 0.225 | 0.646 | 0.319 | 1.309 |

Katrina | 0.054 | 0.035 | 0.851 | 1.056 | 0.599 | 1.861 |

176 | 1.301 | 16.643 | <0.000 | 3.673 | 1.966 | 6.863 |

15999 | Reference | |||||

Constant | 5.426 | 325.873 | <0.000 | 227.345 | ||

DOS | −0.340 | 426.987 | <0.000 | 0.712 | 0.689 | 0.735 |

15999 | −1.301 | 16.643 | <0.000 | 0.272 | 0.146 | 0.509 |

16000 | −0.546 | 3.547 | 0.060 | 0.579 | 0.328 | 1.022 |

16054 | −1.738 | 31.765 | <0.000 | 0.176 | 0.096 | 0.322 |

Katrina | −1.247 | 39.387 | <0.000 | 0.287 | 0.195 | 0.424 |

176 | Reference |

**Table 7.**Estimation of the multiple logistic regression parameters for cucumber cultivars (Levantino and Litoral) and FWL % during storage as factors influencing the probability of marketability.

Variables | Coefficients | Wald χ^{2} | p | Odds Ratio | 95% CI for (Exp(β)) | |
---|---|---|---|---|---|---|

(α, β) | (Exp(β)) | Lower | Upper | |||

Constant | 7.718 | 227.008 | <0.000 | 2248.731 | ||

FWL % | −1.395 | 236.828 | <0.000 | 0.248 | 0.207 | 0.296 |

Litoral | 1.941 | 79.759 | <0.000 | 6.965 | 4.549 | 10.663 |

Levantino | Reference |

**Table 8.**Estimation of multiple logistic regression parameters for cucumber cultivars (Galerno, Poniente, and Valle) and fruit weight loss percentage during storage as factors influencing the probability of marketability.

Variables | Coefficients | Wald χ^{2} | p | Odds Ratio | 95% CI for (Exp(β)) | |
---|---|---|---|---|---|---|

(α, β) | (Exp(β)) | Lower | Upper | |||

Constant | 5.091 | 198.615 | <0.000 | 162.540 | ||

FWL % | −1.069 | 273.219 | <0.000 | 0.343 | 0.302 | 0.390 |

Galerno | −0.155 | 0.147 | 0.702 | 0.857 | 0.388 | 1.891 |

Poniente | 1.351 | 29.928 | <0.000 | 3.861 | 2.380 | 6.265 |

Valle | Reference | |||||

Constant | 6.442 | 251.470 | <0.000 | 627.610 | ||

FWL % | −1.069 | 273.219 | <0.000 | 0.343 | 0.302 | 0.390 |

Valle | −1.351 | 29.928 | <0.000 | 0.259 | 0.160 | 0.420 |

Galerno | −1.506 | 14.408 | <0.000 | 0.222 | 0.102 | 0.483 |

Poniente | Reference | |||||

Constant | 4.936 | 125.463 | <0.000 | 139.224 | ||

FWL % | −1.069 | 273.219 | <0.000 | 0.343 | 0.302 | 0.390 |

Poniente | 1.506 | 14.408 | <0.000 | 4.508 | 2.072 | 9.810 |

Valle | 0.155 | 0.147 | 0.702 | 1.167 | 0.529 | 2.577 |

Galerno | Reference |

**Table 9.**Estimation of the independent simple logistic regression parameters for each mini-type cucumber cultivar as a function of postharvest FWL % as a factor influencing the probability of marketability.

cv. | Variable | Coefficients | Wald χ^{2} | p | Odds Ratio | 95% CI for (Exp(β)) | |
---|---|---|---|---|---|---|---|

(α, β) | (Exp(β)) | Lower | Upper | ||||

176 * | DOS | −0.507 | 116.197 | <0.000 | 0.603 | 0.550 | 0.661 |

Constant | 3.983 | 116.870 | <0.000 | 53.696 | |||

15999 * | DOS | −0.434 | 30.836 | <0.000 | 0.648 | 0.556 | 0.755 |

Constant | 3.829 | 44.146 | <0.000 | 46.005 | |||

16000 * | DOS | −0.387 | 35.562 | <0.000 | 0.679 | 0.598 | 0.771 |

Constant | 3.385 | 63.741 | <0.000 | 29.505 | |||

16054 * | DOS | −0.603 | 27.788 | <0.000 | 0.547 | 0.437 | 0.685 |

Constant | 4.089 | 33.558 | <0.000 | 59.709 | |||

Katrina * | DOS | −0.446 | 207.820 | <0.000 | 0.640 | 0.603 | 0.680 |

Constant | 3.230 | 197.323 | <0.000 | 25.277 |

**Table 10.**Estimation of the multiple logistic regression parameters for the Levantino and Litoral cucumber cultivars.

Variables | Coefficients | Wald χ^{2} | p | Odds Ratio | 95% CI for (Exp(β)) | |
---|---|---|---|---|---|---|

(α, β) | (Exp(β)) | Lower | Upper | |||

Constant | 10.561 | 262.608 | <0.000 | 38,613.016 | ||

DOS | −0.259 | 108.555 | <0.000 | 0.772 | 0.735 | 0.810 |

FWL % | −0.627 | 58.702 | <0.000 | 0.534 | 0.455 | 0.627 |

Month | ||||||

November | −2.809 | 79.297 | <0.000 | 0.060 | 0.032 | 0.112 |

December | −2.246 | 60.086 | <0.000 | 0.106 | 0.060 | 0.187 |

January | Reference |

**Table 11.**Estimation of the multiple logistic regression parameters for the Levantino and Litoral cucumber cultivars.

Variables | Coefficients | Wald χ^{2} | p | Odds Ratio | 95% CI for (Exp(β)) | |
---|---|---|---|---|---|---|

(α, β) | (Exp(β)) | Lower | Upper | |||

Constant | 12.585 | 223.694 | <0.000 | 29,2001.831 | ||

FWL % | −1.572 | 230.198 | <0.000 | 0.208 | 0.169 | 0.254 |

Phenotype | ||||||

Litoral | −2.239 | 88.104 | <0.000 | 0.107 | 0.067 | 0.170 |

Levantino | Reference | |||||

Month | ||||||

November | −2.227 | 58.624 | <0.000 | 0.108 | 0.061 | 0.191 |

December | −1.927 | 50.642 | <0.000 | 0.146 | 0.086 | 0.248 |

January | Reference |

**Table 12.**Estimation of the multiple logistic regression parameters for the Galerno, Poniente, and Valle cucumber cultivars.

Variables | Coefficients | Wald χ^{2} | p | Odds Ratio | 95% CI for (Exp(β)) | |
---|---|---|---|---|---|---|

(α, β) | (Exp(β)) | Lower | Upper | |||

Constant | 6.964 | 251.516 | <0.000 | 1058.172 | ||

Phenotype | ||||||

Valle | −2.120 | 52.380 | <0.000 | 0.120 | 0.068 | 0.213 |

Galerno | −1.581 | 15.203 | <0.000 | 0.206 | 0.093 | 0.456 |

Poniente | Reference | |||||

DOS | −0.248 | 38.792 | <0.000 | 0.781 | 0.722 | 0.844 |

FWL % | −0.459 | 19.048 | <0.000 | 0.632 | 0.515 | 0.777 |

**Table 13.**Estimation of multiple logistic regression parameters for the 176, 15999, 16000, 16054, and Katrina cucumber cultivars.

Variables | Coefficients | Wald χ^{2} | p | Odds ratio | 95% CI for (Exp(β)) | |
---|---|---|---|---|---|---|

(α, β) | (Exp(β)) | Lower | Upper | |||

Constant | 5.563 | 259.041 | <0.000 | 260.574 | ||

Phenotypes | ||||||

15999 | −1.515 | 20.334 | <0.000 | 0.220 | 0.114 | 0.425 |

16000 | −0.620 | 4.195 | 0.041 | 0.538 | 0.297 | 0.974 |

16054 | −1.852 | 31.323 | <0.000 | 0.157 | 0.082 | 0.300 |

Katrina | −1.332 | 39.393 | <0.000 | 0.264 | 0.174 | 0.400 |

176 | Reference | |||||

DOS | −0.303 | 179.599 | <0.000 | 0.738 | 0.706 | 0.772 |

FWL % | −0.104 | 10.467 | 0.001 | 0.901 | 0.846 | 0.960 |

Months | ||||||

November | 1.162 | 30.793 | <0.000 | 3.197 | 2.121 | 4.819 |

December | −0.389 | 3.939 | 0.047 | 0.678 | 0.462 | 0.995 |

January | Reference |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Díaz-Pérez, M.; Carreño-Ortega, Á.; Salinas-Andújar, J.-A.; Callejón-Ferre, Á.-J.
Application of Logistic Regression Models for the Marketability of Cucumber Cultivars. *Agronomy* **2019**, *9*, 17.
https://doi.org/10.3390/agronomy9010017

**AMA Style**

Díaz-Pérez M, Carreño-Ortega Á, Salinas-Andújar J-A, Callejón-Ferre Á-J.
Application of Logistic Regression Models for the Marketability of Cucumber Cultivars. *Agronomy*. 2019; 9(1):17.
https://doi.org/10.3390/agronomy9010017

**Chicago/Turabian Style**

Díaz-Pérez, Manuel, Ángel Carreño-Ortega, José-Antonio Salinas-Andújar, and Ángel-Jesús Callejón-Ferre.
2019. "Application of Logistic Regression Models for the Marketability of Cucumber Cultivars" *Agronomy* 9, no. 1: 17.
https://doi.org/10.3390/agronomy9010017