# Regression Models for Description of Roasted Ground Coffee Powder Color Change during Secondary Shelf-Life as Related to Storage Conditions and Packaging Material

^{*}

## Abstract

**:**

^{2}goodness of fit. Both non-linear and linear models used in this study pointed to a significant influence of intrinsic (sample moisture content) and external (relative humidity (RH) and temperature) factors on ground roasted coffee color change. Non-linear model was the most suitable for description of color changes during storage. Based on lower moisture sorption of the sample packed in triplex bag, triplex packaging is proposed as the more suitable one.

## 1. Introduction

^{2}goodness of fit.

## 2. Materials and Methods

#### 2.1. Ground Coffee Samples

#### 2.2. Moisture Content

#### 2.3. Ambient Conditions

#### 2.4. Color Measurements

#### 2.5. Nonlinear Regression Models

^{−6}and confidence interval of 95%.

#### 2.6. Linear Regression Models

## 3. Results and Discussion

#### 3.1. Experimental Data

#### 3.2. Non-Linear Regression Models

^{2}values, it was noticed that the best agreement between experimental data and model was obtained for the a* color component with R

^{2}= 0.842. The smallest value of R

^{2}was obtained for the Hue angle R

^{2}= 0.488. Eureqa Formulize works on a concept of development of the best possible fit to describe the defined set of the experimental data. In most cases obtained models are over parameterized and applicable only on the tested data set. Due to that, in this work predefined expressions (non-linear and linear) were used to describe the color components change during storage. When using the Eureqa Formulize software it is not possible to get information about the error of the estimation of the parameters and their significance. To overcome the mentioned limitations Stataistica 10.0 was used.

_{2}parameter value was not significant. This parameter was connected to the relative air humidity in the model. Interestingly, in the case of ΔE there was only one significant parameter, b

_{1}, connected to sample moisture content. By comparing the estimated parameters values obtained using two algorithms presented in Table 2 and Table 3, it can be seen that the largest differences were obtained for the estimation of the b

_{0}parameter for all six color characteristics.

^{2}values were R

^{2}(L*) = 0.918, R

^{2}(a*) = 0.936, R

^{2}(b*) = 0.783, R

^{2}(ΔE) = 0.819, R

^{2}(Chroma) = 0.794, R

^{2}(Hue angle) = 0.843, what represented a significant improvement in comparison to those obtained using Eureqa Formulize (Table 2 and Figure 1).

^{2}value, the best agreement between experimental data and model was obtained for description of the change of the a* colour component with R

^{2}= 0.977, while the smallest value of R

^{2}was obtained for the Hue angle R

^{2}= 0.642 which was in analogy with the results obtained for the L1KMK sample (Table 2). Comparing the R

^{2}values for both packaging, it was noticed that the proposed non-linear models described colour components change in triplex packaging (V1KMK) much better. As for the tin can packaging (L1KMK), parameters of the non-linear models for description of the colour components change during storage in V1KMK were also estimated using Statistica 10.0. Results are given in Table 5.

_{1}was shown to be significant. Only for description of the Hue angle change all parameters were significant. The proposed model described the experimental data very well (Figure 4), R

^{2}(a*) = 0.990, R

^{2}(b*) = 0.974, R

^{2}(ΔE) = 0.918, R

^{2}(Chroma) = 0.978, R

^{2}(Hue angle) = 0.918. The smallest value of R

^{2}was obtained for the L* colour component with R

^{2}= 0.471. As mentioned before, the evolutionary algorithm was not able to estimate the parameters of the proposed model, so the results obtained by the Levenberg–Marquardt algorithm presented a significant improvement. The dispersion of colour components compared to model predictions (Figure 3 and Figure 4) was quite uniform, except for the L* component visible in Figure 4.

#### 3.3. Linear Regression Models

^{2}= 0.856. The smallest value of R

^{2}was obtained for the b* component with R

^{2}= 0.400. In the case of non-linear regression models (Table 2), the best agreement between model and experiment was also obtained for a* colour component and the smallest value of R

^{2}was obtained for the Hue angle. As mentioned before, parameters of the linear regression model were also estimated using variance minimization method implemented into Statistica 10.0. Results are given in Table 7.

_{2}(combined with relative air humidity) are significant, while in the case of Hue angle, all parameters except β

_{3}(combined with air temperature) are significant. Interestingly, p-value analysis revealed that in case of ΔE only parameter β

_{3}proved to be significant, which meant that temperature was the key factor affecting total colour difference. Cardelli and Labudza [29] also showed that storage temperature affects shelf-life of roasted and ground coffee. The best agreement between model and experimental data regarding R

^{2}value was obtained for the a* colour component with R

^{2}= 0.937, while the smallest value of R

^{2}was obtained for the ΔE component, with R

^{2}= 0.457. As in the case of non-linear model for coffee sample L1KMK packed in tin can, models developed using Statistica 10.0 described experimental data more precisely than models developed using Eureqa Formulize.

^{2}= 0.979 and the smallest R

^{2}value was obtained for Hue angle (R

^{2}= 0.786). Comparing the R

^{2}values of both non-linear and linear regression models for colour components change during storage of V1KMK sample, it can be noticed that non-linear models could be selected as more suitable for the colour change description.

_{2}(connected to relative air humidity) were significant while in the case of the L* colour component parameters β

_{0}and β

_{2}were significant. Interestingly, p-value analysis revealed that in the case of the Hue angle there were no significant parameters, while in the case on non-linear regression model for description of the Hue angle change all parameters were significant. The phenomena could be explained by the fact that model linearization was performed using logarithm values of the experimental data. By introducing logarithmic values, disruption between orders of magnitude of the measured data can occur. The best agreement between model and experimental data was obtained for the a* component (R

^{2}= 0.984) and the smallest value of R

^{2}was obtained for the L* component (R

^{2}= 0.504). Dispersion of colour components comparing to model predictions followed a linear trend (Figure 7 and Figure 8). The largest data dispersion was evident for models describing the change of the Hue angle estimated using the Eureqa Formulize and for models describing the L* component estimated using the Statistica 10.0.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Non-linear regression models for description of color component change during storage of L1KMK estimated using Eureqa Formulize: (

**a**) L*, (

**b**) a*, (

**c**) b*, (

**d**) ΔE, (

**e**) Chroma, (

**f**) Hue angle (R

^{2}= 0.737, 0.842, 0.258, 0.611, 0.519, 0.488).

**Figure 2.**Non-linear regression models for description of color component change during storage of L1KMK estimated using Statistica 10.0.: (

**a**) L*, (

**b**) a*, (

**c**) b*, (

**d**) ΔE, (

**e**) Chroma, (

**f**) Hue angle (R

^{2}= 0.918, 0.936, 0.783, 0.819, 0.794, 0.843).

**Figure 3.**Non-linear regression models for description of colour component change during storage of V1KMK estimated using Eureqa Formulize: (

**a**) L* (not determined), (

**b**) a*, (

**c**) b*, (

**d**) ΔE, (

**e**) Chroma, (

**f**) Hue angle (R

^{2}= n/m, 0.977, 0.965, 0.738, 0.973, 0.642).

**Figure 4.**Non-linear regression models for description of colour component change during storage of V1KMK estimated using Statistica 10.0.: (

**a**) L*, (

**b**) a*, (

**c**) b*, (

**d**) ΔE, (

**e**) Chroma, (

**f**) Hue angle (R

^{2}= 0.471, 0.990, 0.974, 0.918, 0.978, 0.918).

**Figure 5.**Linear regression models for description of colour component change during storage of L1KMK estimated using the Eureqa Formulize: (

**a**) L*, (

**b**) a*, (

**c**) b*, (

**d**) ΔE, (

**e**) Chroma, (

**f**) Hue angle (R

^{2}= 0.714, 0.856, 0.400, 0.724, 0.509, 0.561).

**Figure 6.**Linear regression models for description of colour components change during storage of L1KMK estimated using Statistica 10.0.: (

**a**) L*, (

**b**) a*, (

**c**) b*, (

**d**) ΔE, (

**e**) Chroma, (

**f**) Hue angle (R

^{2}= 0.825, 0.937, 0.774, 0.457, 0.622, 0.696).

**Figure 7.**Linear regression models for description of colour components change during storage of V1KMK estimated using the Eureqa Formulize: (

**a**) L*, (

**b**) a*, (

**c**) b*, (

**d**) ΔE, (

**e**) Chroma, (

**f**) Hue angle (R

^{2}= 0.714, 0.856, 0.400, 0.724, 0.509, 0.561).

**Figure 8.**Linear regression models for description of colour components change during storage of V1KMK estimated using Statistica 10.0.: (

**a**) L*, (

**b**) a*, (

**c**) b*, (

**d**) ΔE, (

**e**) Chroma, (

**f**) Hue angle (R

^{2}= 0.504, 0.984, 0.975, 0.993, 0.981, 0.842).

**Table 1.**Color components of roasted ground coffee samples during 6 months of storage. Results are shown as average ± SD.

Sample | Parameter | Storage Time (Days) | |||||
---|---|---|---|---|---|---|---|

30 | 60 | 90 | 120 | 150 | 180 | ||

V1KMK | L* | 24.74 ± 0.03 | 25.62 ± 0.09 | 25.73 ± 0.00 | 21.45 ± 0.24 | 24.19 ± 0.01 | 26.13 ± 0.07 |

a* | 12.48 ± 0.02 | 12.62 ± 0.01 | 12.37 ± 0.01 | 11.93 ± 0.03 | 11.54 ± 0.01 | 11.00 ± 0.02 | |

b* | 19.18 ± 0.02 | 19.01 ± 0.03 | 18.40 ± 0.02 | 17.39 ± 0.11 | 17.51 ± 0.01 | 16.29 ± 0.03 | |

ΔE | / | 0.91 ± 0.08 | 1.27 ± 0.01 | 3.78 ± 0.21 | 1.99 ± 0.01 | 3.52 ± 0.05 | |

Chroma | 22.88 ± 0.03 | 22.82 ± 0.02 | 22.17 ± 0.02 | 21.09 ± 0.09 | 20.97 ± 0.01 | 19.66 ± 0.03 | |

Hue | 0.99 ± 0.01 | 0.98 ± 0.00 | 0.98 ± 0.00 | 0.97 ± 0.00 | 0.99 ± 0.00 | 0.98 ± 0.00 | |

Moisture content | 1.28 ± 0.01 | 1.46 ± 0.01 | 1.68 ± 0.02 | 1.82 ± 0.01 | 1.87 ± 0.01 | 1.97 ± 0.02 | |

RH | 64 ± 1.00 | 32 ± 1.00 | 58 ± 1.00 | 45 ± 1.00 | 32 ± 1.00 | 20 ± 1.00 | |

T | 18 ± 0.20 | 18 ± 0.20 | 17 ± 0.10 | 17 ± 0.20 | 15 ± 0.00 | 14 ± 0.00 | |

L1KMK | L* | 28.23 ± 0.04 | 24.17 ± 0.85 | 25.46 ± 0.01 | 23.78 ± 0.00 | 24.48 ± 0.01 | 23.81 ± 0.02 |

a* | 11.25 ± 0.04 | 11.94 ± 0.19 | 12.07 ± 0.00 | 12.20 ± 0.01 | 12.46 ± 0.01 | 12.08 ± 0.01 | |

b* | 19.29 ± 0.01 | 17.55 ± 0.50 | 17.63 ± 0.02 | 18.23 ± 0.01 | 18.87 ± 0.01 | 17.70 ± 0.03 | |

ΔE | / | 1.81 ± 0.68 | 1.76 ± 0.01 | 1.37 ± 0.00 | 0.40 ± 0.01 | 1.79 ± 0.01 | |

Chroma | 22.33 ± 0.03 | 21.22 ± 0.51 | 21.36 ± 0.02 | 21.94 ± 0.00 | 22.61 ± 0.01 | 21.43 ± 0.02 | |

Hue | 1.04 ± 0.00 | 0.97 ± 0.01 | 0.97 ± 0.00 | 0.98 ± 0.00 | 0.99 ± 0.00 | 0.97 ± 0.00 | |

Moisture content | 1.01 ± 0.01 | 1.41 ± 0.01 | 1.66 ± 0.01 | 2.25 ± 0.01 | 2.21 ± 0.10 | 2.27 ± 0.02 | |

RH | 58 ± 1.00 | 64 ± 1.00 | 53 ± 1.00 | 44 ± 1.00 | 28 ± 1.00 | 20 ± 1.00 | |

T | 18 ± 0.00 | 18 ± 0.00 | 16 ± 0.20 | 16 ± 0.10 | 14 ± 0.10 | 20 ± 0.10 |

**Table 2.**Non-linear regression models coefficients for description of color component change during storage for L1KMK (α = 95%) estimated using Eureqa Formulize software.

Parameter | Coefficient | R^{2} | Correlation Coefficient | Maximum Error | Mean Squared Error | Mean Absolute Error | |
---|---|---|---|---|---|---|---|

L* | b_{0} b _{1} b _{2} b _{3} | 40.590 −0.236 −0.028 −0.085 | 0.737 | 0.883 | 2.810 | 0.658 | 0.326 |

a* | b_{0} b _{1} b _{2} b _{3} | 12.82 0.134 0.022 −0.075 | 0.842 | 0.934 | 0.360 | 0.022 | 0.084 |

b* | b_{0} b _{1} b _{2} b _{3} | 64.140 −0.213 −0.107 −0.265 | 0.528 | 0.770 | 0.957 | 0.221 | 0.296 |

ΔE | b_{0} b _{1} b _{2} b _{3} | 0.225 1.208 0.147 0.5442 | 0.611 | 0.817 | 2.325 | 1.115 | 0.596 |

Chroma | b_{0} b _{1} b _{2} b _{3} | 43.780 −0.076 −0.038 −0.179 | 0.519 | 0.759 | 1.007 | 0.144 | 0.237 |

Hue angle | b_{0} b _{1} b _{2} b _{3} | 1.925 −0.175 −0.780 −0.102 | 0.488 | 0.836 | 0.044 | 0.0003 | 0.009 |

**Table 3.**Non-linear regression models coefficients for description of color component change during storage for tin can packaging (L1KMK) (α = 95%) estimated using Statistica 10.0.

^{†}marked values are significant at p < 0.05.

L* | a* | b* | ||||

Parameter | Value | p-Value | Value | p-Value | Value | p-Value |

b_{0} | 68.793 ± 18.421 ^{†} | 0.002 | 13.259 ± 1.541 ^{†} | 0 | 53.819 ± 13.173 ^{†} | 0.001 |

b_{1} | −0.284 ± 0.038 ^{†} | 0 | 0.098 ± 0.017 ^{†} | 0 | −0.156 ± 0.036 ^{†} | 0 |

b_{2} | −0.085 ± 0.027 ^{†} | 0.007 | 0.012 ± 0.012 | 0.305 | −0.084 ± 0.025 ^{†} | 0.004 |

b_{3} | −0.192 ± 0.069 ^{†} | 0.015 | −0.071 ± 0.029 ^{†} | 0.031 | −0.242 ± 0.063 ^{†} | 0.002 |

ΔE | Chroma | Hue Angle | ||||

Parameter | Value | p-Value | Value | p-Value | Value | p-Value |

b_{0} | 0.006 ± 0.017 | 0.741 | 47.904 ± 7.659 ^{†} | 0 | 1.567 ± 0.231 ^{†} | 0 |

b_{1} | 1.865 ± 0.501 ^{†} | 0.002 | −0.080 ± 0.024 ^{†} | 0.004 | −0.117 ± 0.021 ^{†} | 0 |

b_{2} | 0.519 ± 0.269 | 0.075 | −0.055 ± 0.016 ^{†} | 0.004 | −0.045 ± 0.015 ^{†} | 0.008 |

b_{3} | 1.214 ± 0.713 | 0.111 | −0.190 ± 0.041 ^{†} | 0 | −0.081 ± 0.038 ^{†} | 0.048 |

**Table 4.**Non-linear regression models coefficients for description of color component change during storage for triplex packing (V1KMK) (α = 95%) estimated using Eureqa Formulize.

Parameter | Coefficient | R^{2} | Correlation Coefficient | Maximum Error | Mean Squared Error | Mean Absolute Error | |
---|---|---|---|---|---|---|---|

L* | b_{0}b _{1}b _{2}b _{3} | n/m n/m n/m n/m | n/m | n/m | n/m | n/m | n/m |

a* | b_{0}b _{1}b _{2}b _{3} | 9.605 −0.016 0.123 −0.085 | 0.977 | 0.990 | 0.204 | 0.007 | 0.053 |

b* | b_{0}b _{1}b _{2}b _{3} | 32.220 −0.181 0.157 −0.390 | 0.965 | 0.987 | 0.400 | 0.036 | 0.1257 |

ΔE | b_{0}b _{1}b _{2}b _{3} | 0.011 4.580 −0.530 1.597 | 0.738 | 0.869 | 1.781 | 0.478 | 0.447 |

Chroma | b_{0}b _{1}b _{2}b _{3} | 29.760 −0.128 0.145 −0.288 | 0.973 | 0.989 | 0.431 | 0.035 | 0.122 |

Hue angle | b_{0}b _{1}b _{2}b _{3} | 2.301 −0.072 0.071 −0.386 | 0.642 | 0.856 | 0.011 | 0.000 | 0.003 |

**Table 5.**Non-linear regression models coefficients for description of colour component change during storage for V1KMK (α = 95%) estimated using Statistica 10.0.

^{†}marked values are significant at p < 0.05.

L* | a* | b* | ||||

Parameter | Value | p-Value | Value | p-Value | Value | p-Value |

b_{0} | 47.873 ± 72.388 | 0.519 | 6.274 ± 1.151 ^{†} | 0 | 13.940 ± 4.795 ^{†} | 0.011 |

b_{1} | −0.262 ± 0.178 | 0.163 | −0.009 ± 0.020 | 0.671 | −0.142 ± 0.039 ^{†} | 0.003 |

b_{2} | −0.066 ± 0.170 | 0.704 | 0.087 ± 0.019 ^{†} | 0 | 0.088 ± 0.038 ^{†} | 0.035 |

b_{3} | −0.102 ± 0.786 | 0.898 | 0.114 ± 0.091 | 0.223 | −0.004 ± 0.174 | 0.983 |

ΔE | Chroma | Hue Angle | ||||

Parameter | Value | p-Value | Value | p-Value | Value | p-Value |

b_{0} | 0.002 ± 0.002 | 0.889 | 13.165 ± 3.935 ^{†} | 0.005 | 1.676 ± 0.158 ^{†} | 0 |

b_{1} | 7.818 ± 2.474 ^{†} | 0.007 | −0.096 ± 0.034 ^{†} | 0.013 | −0.077 ± 0.010 ^{†} | 0 |

b_{2} | 0.342 ± 0.837 | 0.689 | 0.078 ± 0.033 ^{†} | 0.033 | 0.031 ± 0.009 ^{†} | 0.006 |

b_{3} | 1.217 ± 3.081 | 0.699 | 0.089 ± 0.151 | 0.567 | −0.219 ± 0.045 ^{†} | 0 |

**Table 6.**Linear regression models coefficients for description of colour components change during storage of L1KMK (α = 95%) estimated using the Eureqa Formulize software.

Parameter | Coefficient | R^{2} | Correlation Coefficient | Maximum Error | Mean Squared Error | Mean Absolute Error | |
---|---|---|---|---|---|---|---|

L* | β_{0}β _{1}β _{2}β _{3} | 3.710 −0.237 −0.028 −0.087 | 0.714 | 0.874 | 0.114 | 0.001 | 0.013 |

a* | β_{0}β _{1}β _{2}β _{3} | 2.590 0.119 0.018 −0.079 | 0.856 | 0.937 | 0.032 | 0.000 | 0.007 |

b* | β_{0}β _{1}β _{2}β _{3} | 2.631 0.022 0.039 0.033 | 0.400 | 0.636 | 0.029 | 0.000 | 0.009 |

ΔE | β_{0}β _{1}β _{2}β _{3} | 4.865 −0.606 −0.119 −0.978 | 0.724 | 0.859 | 0.212 | 0.008 | 0.051 |

Chroma | β_{0}β _{1}β _{2}β _{3} | 3.791 −0.077 −0.039 −0.182 | 0.509 | 0.750 | 0.047 | 0.000 | 0.011 |

Hue angle | β_{0}β _{1}β _{2}β _{3} | 0.100 0.020 −0.001 −0.047 | 0.561 | 0.806 | 0.012 | 0.000 | 0.002 |

**Table 7.**Linear regression models coefficients for description of colour component change during the storage of L1KMK (α = 95%) estimated using Statistica 10.0.

^{†}significant at p < 0.05.

L* | a* | b* | ||||

Parameter | Value | p-value | Value | p-Value | Value | p-Value |

β_{0} | 4.202 ± 0.272 ^{†} | 0 | 2.568 ± 0.119 ^{†} | 0 | 3.980 ± 0.253 ^{†} | 0 |

β_{1} | −0.275 ± 0.039 ^{†} | 0 | 0.102 ± 0.017 ^{†} | 0 | −0.152 ± 0.036 ^{†} | 0.001 |

β_{2} | −0.081 ± 0.027 ^{†} | 0.009 | 0.014 ± 0.012 | 0.246 | −0.083 ± 0.025 ^{†} | 0.005 |

β_{3} | −0.188 ± 0.069 ^{†} | 0.017 | −0.068 ± 0.030 ^{†} | 0.041 | −0.243 ± 0.063 ^{†} | 0.002 |

ΔE | Chroma | Hue Angle | ||||

Parameter | Value | p-Value | Value | p-Value | Value | p-Value |

β_{0} | −1.784 ± 1.356 | 0.224 | 3.871 ± 0.164 ^{†} | 0 | 0.439 ± 0.148 ^{†} | 0.010 |

β_{1} | 0.579 ± 0.319 | 0.097 | −0.079 ± 0.024 ^{†} | 0.005 | −0.116 ± 0.021 ^{†} | 0 |

β_{2} | 0.153 ± 0.147 | 0.319 | −0.055 ± 0.016 ^{†} | 0.0045 | −0.044 ± 0.015 ^{†} | 0.011 |

β_{3} | 0.816 ± 0.307 ^{†} | 0.022 | −0.191 ± 0.042 ^{†} | 0 | −0.081 ± 0.038 | 0.051 |

**Table 8.**Linear regression models coefficients for description of colour component change during storage of V1KMK (α = 95%) estimated using the Eureqa Formulize.

Parameter | Coefficient | R^{2} | Correlation Coefficient | Maximum Error | Mean Squared Error | Mean Absolute Error | |
---|---|---|---|---|---|---|---|

L* | β_{0}β _{1}β _{2}β _{3} | n/m n/m n/m n/m | n/m | n/m | n/m | n/m | n/m |

a* | β_{0}β _{1}β _{2}β _{3} | 2.272 −0.015 0.125 −0.090 | 0.979 | 0.991 | 0.016 | 0.000 | 0.004 |

b* | β_{0}β _{1}β _{2}β _{3} | 3.471 −0.181 0.157 −0.389 | 0.967 | 0.987 | 0.021 | 0.000 | 0.007 |

ΔE | β_{0}β _{1}β _{2}β _{3} | −28.13 2.801 −3.502 13.890 | 0.843 | 0.933 | 0.634 | 0.049 | 0.104 |

Chroma | β_{0}β _{1}β _{2}β _{3} | 3.530 −0.124 0.157 −0.352 | 0.974 | 0.990 | 0.020 | 0.000 | 0.006 |

Hue angle | β_{0}β _{1}β _{2}β _{3} | 0.340 −0.072 0.017 −0.138 | 0.786 | 0.892 | 0.009 | 0.000 | 0.002 |

**Table 9.**Linear regression models coefficients for description of colour components change during storage of V1KMK (α = 95%) estimated using Statistica 10.0.

^{†}marked values are significant at p < 0.05.

L* | a* | b* | ||||

Parameter | Value | p-Value | Value | p-Value | Value | p-Value |

β_{0} | 7.591 ± 1.343 ^{†} | 0 | 2.077 ± 0.174 ^{†} | 0 | 3.608 ± 0.257 ^{†} | 0 |

β_{1} | −0.443 ± 0.148 ^{†} | 0.009 | −0.021 ± 0.019 | 0.287 | −0.185 ± 0.028 ^{†} | 0 |

β_{2} | 0.254 ± 0.139 | 0.089 | 0.107 ± 0.018 ^{†} | 0 | 0.173 ± 0.027 ^{†} | 0 |

β_{3} | −1.829 ± 0.639 ^{†} | 0.012 | 0.004 ± 0.083 | 0.958 | −0.457 ± 0.122 ^{†} | 0.002 |

ΔE | Chroma | Hue Angle | ||||

Parameter | Value | p-Value | Value | p-Value | Value | p-Value |

β_{0} | −29.087 ± 1.412 ^{†} | 0 | 3.441 ± 0.215 ^{†} | 0 | 0.516 ± 0.094 | 0 |

β_{1} | 6.174 ± 0.267 ^{†} | 0 | −0.135 ± 0.024 ^{†} | 0 | −0.077 ± 0.010 | 0 |

β_{2} | −2.291 ± 0.143 ^{†} | 0 | 0.152 ± 0.022 ^{†} | 0 | 0.031 ± 0.009 | 0.006 |

β_{3} | 12.501 ± 0.648 ^{†} | 0.022 | −0.313 ± 0.102 ^{†} | 0.008 | −0.219 ± 0.045 | 0 |

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## Share and Cite

**MDPI and ACS Style**

Benković, M.; Tušek, A.J.
Regression Models for Description of Roasted Ground Coffee Powder Color Change during Secondary Shelf-Life as Related to Storage Conditions and Packaging Material. *Beverages* **2018**, *4*, 16.
https://doi.org/10.3390/beverages4010016

**AMA Style**

Benković M, Tušek AJ.
Regression Models for Description of Roasted Ground Coffee Powder Color Change during Secondary Shelf-Life as Related to Storage Conditions and Packaging Material. *Beverages*. 2018; 4(1):16.
https://doi.org/10.3390/beverages4010016

**Chicago/Turabian Style**

Benković, Maja, and Ana Jurinjak Tušek.
2018. "Regression Models for Description of Roasted Ground Coffee Powder Color Change during Secondary Shelf-Life as Related to Storage Conditions and Packaging Material" *Beverages* 4, no. 1: 16.
https://doi.org/10.3390/beverages4010016