Difference between revisions of "Team:BIT-China/FluorescentProbesModel"
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With the criteria of the least square, we construct following linear model | With the criteria of the least square, we construct following linear model | ||
</p> | </p> | ||
| − | <p class="MD- | + | <p class="MD-formula">$$FOD_{i}=\beta_{0}+\beta_{1}\ H_{2}O_{2_{i}}+\epsilon_{i},\epsilon_{i} \sim |
N(0,\sigma^2)$$</p> | N(0,\sigma^2)$$</p> | ||
Revision as of 01:04, 17 October 2018
It can be seen from the reaction pathway that when the probe is excessive, the fluorescence intensity should be linear with the hydrogen peroxide content at a specific time. The model validates this linear relationship through experimental data and predicts future possible outcomes by constructing a linear regression model. Linear regression analysis
H2O2: The concentration of H2O2, units in mM.
FOD: Florescence intensity / OD.
The Scatter Plot of data are demonstrated below.
From the chart, it is clear that the FOD is in proportion to the H2O2, only when H2O2 is between 0-2.5 mM. The data in the points that H2O2 is 5 are obviously not obeying linear model. Thus, we consider to building a linear model between 0 and 2.5mM of H2O2. The new Scatter Plot of this part of data is showed below.
The scatter plot witnessed a significant linearity of between FOD and H2O2, so we tend to use a linear model to predict and explain the results.
With the criteria of the least square, we construct following linear model
$$FOD_{i}=\beta_{0}+\beta_{1}\ H_{2}O_{2_{i}}+\epsilon_{i},\epsilon_{i} \sim N(0,\sigma^2)$$
The property of the model are demonstrated below
It is obvious that the data fits linear model well and the parameters are following
$$FOD_{i}=4752+1214.48\ H_{2}O_{2_{i}}+\epsilon_{i},\epsilon_{i} \sim N(0,425.9)$$
The data along with the fitted values of the model and the confidence interval are pictured below.
We also run a residuals analysis to ensure this linear model is proper to fit the data. First, we draw histogram and QQ-plot of standard residuals.
From the histogram, the standard residuals equally drop in the two sides of zero, which means that the residuals are possibly independent. Also, the QQ-plot implies the significant normality of residuals.
The linear model we constructed validates the linearity between the concentration of H2O2 and the fluorescence intensity divided by the OD value, which the H2O2 is in the interval from 0 to 2.5mM. And we also analyzed the residuals of the model to ensure it works well. With this model, we can properly predict the output when the concentration of H2O2 is in certain interval.
