Team:Hong Kong JSS/Model
Achievement
- Mathematically described the effect of six condition factors on the percentage decrease of copper ion concentration
- Successfully predict the effect of the pumping on the percentage decrease of copper ion concentration by the model generated
Experimental Data
In order to better investigate the factors affecting the functionality of the device, and to predict the percentage change of copper ion after using the device; we performed two more sets of the experiments to collect more statistical data. The experiments vary the device on/off conditions and initial copper concentration system and recorded the percentage changes in these situations. (For details of the experiments, please refer to the “Experiment”and "Demonstration"sections)
The experiments results are as follow:
Data obtained in the above experiments were collected. Together with the data obtained in the main project, all data were put to multiple linear regression analysis. SPSS was used to generate statistical analysis.
A multiple linear regression was calculated to predict percentage change of copper ion concentration based on the Duration of incubation time, Initial concentration, Presence of IPTG, Device power, Presence of CgMT gene and Presence of E. coli. A significant regression equation was found (F(6,133) = 86.492, p <0.000), with an R2 of .796.
Experiments’ predicted percentage change of copper ion concentration is equals to 0.006 - 0.006 (Duration) + 0.019 (Initial Concentration) - 0.064 (Presence of IPTG) - 0.153 (Device power) - 0.008 (Presence of CgMT) - 0.033 (Presence of E. coli), where Duration is measured in hours, Initial concentration is measured by mg/L, Presence of IPTG is coded as 0 = absent, 1 = present; Device power is coded as 0 = off, 1 = on; Presence of CgMT is coded as 0 = absent, 1 = present and Presence of E. coli is coded as 0 = absent, 1 = present.
Experiment’s percentage change decrease 0.6% for each hour of duration; increase 1.9% for each mg/L of initial concentration; IPTG present decreased 6.4% more than IPTG absent; Device power on decreased 15.3% more than device power off; CgMT present decreased 0.8% more than CgMT absent and E. coli present decreased 3.3% more than E.coli absent.
In this regression model, duration, initial concentration, presence of IPTG and device power were significant predictors of percentage change; while presence of CgMT and E.coli did not show significance in prediction.
According to the multiple regression model, we would like to investigate the effect of changing the flow rate of the device on percentage change of copper ion. We adjust the flow rate of the pump of the device to 50% power. Based on the regression model, we predicted the percentage change of copper ion concentration. And after doing the experiment, we can see that the experimental result was coherent with the prediction.
Therefore the mathematical model
y = -0.006 x1 + 0.019 x2 – 0.064 x3 – 0.153 x4 – 0.008 x5 – 0.033x6 + 0.006, where y is the percentage change of copper ion concentration; x1 is the duration of incubation; x2 is the initial concentration; x3 is the presence of IPTG; x4 is the device power; x5 is the presence of CgMT and x6 is the presence of E. coli
is valid.
The experiments results are as follow:
The effectiveness of B-CAD when the pump was On/Off.
Different initial copper concentration of the aquaponic water (5, 10, 15 mg/L).
Multiple Linear Regression Analysis
Data obtained in the above experiments were collected. Together with the data obtained in the main project, all data were put to multiple linear regression analysis. SPSS was used to generate statistical analysis.
A multiple linear regression was calculated to predict percentage change of copper ion concentration based on the Duration of incubation time, Initial concentration, Presence of IPTG, Device power, Presence of CgMT gene and Presence of E. coli. A significant regression equation was found (F(6,133) = 86.492, p <0.000), with an R2 of .796.
Experiments’ predicted percentage change of copper ion concentration is equals to 0.006 - 0.006 (Duration) + 0.019 (Initial Concentration) - 0.064 (Presence of IPTG) - 0.153 (Device power) - 0.008 (Presence of CgMT) - 0.033 (Presence of E. coli), where Duration is measured in hours, Initial concentration is measured by mg/L, Presence of IPTG is coded as 0 = absent, 1 = present; Device power is coded as 0 = off, 1 = on; Presence of CgMT is coded as 0 = absent, 1 = present and Presence of E. coli is coded as 0 = absent, 1 = present.
Experiment’s percentage change decrease 0.6% for each hour of duration; increase 1.9% for each mg/L of initial concentration; IPTG present decreased 6.4% more than IPTG absent; Device power on decreased 15.3% more than device power off; CgMT present decreased 0.8% more than CgMT absent and E. coli present decreased 3.3% more than E.coli absent.
In this regression model, duration, initial concentration, presence of IPTG and device power were significant predictors of percentage change; while presence of CgMT and E.coli did not show significance in prediction.
Follow Up Experiment
According to the multiple regression model, we would like to investigate the effect of changing the flow rate of the device on percentage change of copper ion. We adjust the flow rate of the pump of the device to 50% power. Based on the regression model, we predicted the percentage change of copper ion concentration. And after doing the experiment, we can see that the experimental result was coherent with the prediction.
The mathematical model is valid.
Therefore the mathematical model
y = -0.006 x1 + 0.019 x2 – 0.064 x3 – 0.153 x4 – 0.008 x5 – 0.033x6 + 0.006, where y is the percentage change of copper ion concentration; x1 is the duration of incubation; x2 is the initial concentration; x3 is the presence of IPTG; x4 is the device power; x5 is the presence of CgMT and x6 is the presence of E. coli
is valid.
Limitation
Due to time constrain, we are only focusing our model on the most critical factors. In real-life situations, there could be more factors such as salinity, temperature, plant and fish density affecting the effeciency of the B-CAD. Besides, we had only tested our model with one of the six factors we included in the equation. Again, this is mainly due to time constrain and we are currently planing more experiments to test the other factors.
Future direction
Reference:
To improve our mathematical model, we need to:
- Verify the mathematical model by testing different conditions factors described in the equation.
- Describe more factors affecting the effectiveness of the device. Such as temperature, initial bacterial amount and culture/tank volume ratio.
Reference:
1. DeFries, J. C., & Fulker, D. W. (1985). Multiple regression analysis of twin data. Behavior genetics, 15(5), 467-473.
2. Kleinbaum, D. G., Kupper, L. L., Muller, K. E., & Nizam, A. (1988). Applied regression analysis and other multivariable methods (Vol. 601). Belmont, CA: Duxbury Press.
3. Mason, C. H., & Perreault Jr, W. D. (1991). Collinearity, power, and interpretation of multiple regression analysis. Journal of marketing research, 28(3), 268-280.