Team:BFSUICC-China/Model

Model Based on Cu(II) ion Concentration to Predict Fluoresence

Original Data

After we take the In of the fluorescence

Trying to predict the fluorescence of Cu2+ under different concentration, we consider concentration of Cu2+ as independent variable x, and fluorescence(ln) as dependent variable y. We established models 1-6.

Model 1: 𝑦=𝛼+𝛽𝑥+𝜀 Model 2: 𝑦=𝛼+𝛽𝑥1/2+𝜀 Model 3; 𝑦=𝛼+𝛽𝑥1/3+𝜀 Model 4: 𝑦=𝛼+𝛽𝑥1/4+𝜀 Model 5: 𝑦=𝛼+𝛽𝑥1/5+𝜀 Model 6: 𝑦=𝛼+𝛽𝑥1/6+𝜀

Where 𝛼 is intercept term，𝜀 is residual, as 𝜀 follows white nose distribution. We did OLS regression for model 1-6, respectively. The result is shown in below

After we investigate the data, it shows that the Model 1 has least agreement, even after adjustment R2 is only 0.536, which means fluorescence(ln) has poor linear relationship with Cu2+ concentration.

As we taking more roots of Cu2+ concentration, agreement adj-R2 keep increasing. For example, Cu2+ concentration 1/2, agreement increased to 0.779; when Cu2+ concentration 1/5, agreement increased to 0.991; but when Cu2+ concentration 1/6, agreement decreased to 0.989, and F has decreased as well. Therefore, we consider that we might taken the power of 1/5.5, having

As a result, model is then for sure:y=7.972+3.385*x^(1/5.5)

For 1.d.p. :y=8+3.4*x^(1/5.5)

We will use this model to predict fluorescence under different Cu2+ concentration.