# Modernization Data Analysis and Visualization for Food Safety Research Outcomes
## 4 Type of Food Safety Experiments
### Shelf Life Studies
Predicting when this threshold value will be reached will allow to determine the shelf life of a certain product by a certain factor. Multiple linear regression analysis is a more complex type of statistical analysis that uses several explanatory variables to predict the outcome of a response variable, unlike simple linear regression, in which only one independent variable is used to model the response of a dependent variable. In shelf life studies, it is normal that several factors with multiple levels are evaluated to describe their effect on the shelf life of a certain product, reason why multiple linear regression is an interesting alternative for this type of experiment. When conducting analysis of variance (ANOVA), a comparison between the means of each of the groups is evaluated with results highly linked with the levels of the factors established at the beginning of the trial. As an example, imagine that you evaluated the growth of a specific microorganism at different temperatures. The results of the analysis of variance will conclude in differences between the mean groups for each specific temperature evaluated. A more efficient conclusion would be to understand how much the growth is affected when a unit of temperature is changed. This brings up the concept of marginal effect which measures the impact that a unit of change in a variable has on the outcome variable while other variables are held constant. In simple linear regression, the slope of the model measures the marginal effect of the independent variable on the dependent variable, as only one variable is modeled. However, if multiple variables are used in the regression, the marginal effect needs to be calculated with more advanced mathematical methods. Figure 8B shows the use of multiple linear regression analysis to evaluate shelf life studies. Microbial counts were established as the dependent variable, treatment as a qualitative variable with three levels (Control, Treatment A [TrtA], and Treatment B [TrtB]), and display time as a continuous variable. The control group was used as the base level for  
Figure 8: Alternative graphical representation and statistical analysis approaches to evaluate shelf life studies. (**A**) Principal component (PC) analysis for indicator microorganisms for all treatments (Treatment A and Control) \(\times\) display time (0 h, 48 h, and 96 h) combinations (\(n=50\) observations per intervention and display time). (**B**) Average (\(\pm\) 95% confidence intervals) growth rates (Log CFU/mL \(\times\) Day) for each microorganism (Bacteria A and Bacteria B) and treatment (control, Treatment A, and Treatment B) combination. The dot represents the average growth rate and the horizontal lines represent the 95% confidence interval (\(n=50\) observations per intervention and retail display time). the qualitative variable, and 95% confidence intervals were created for each slope. As an example, the model for Bacteria A is described in Equation (8). \[Counts=\beta_{0}+\beta_{1}TrtA+\beta_{2}TrB+\beta_{3}Time+\beta_{4}TrtA\times Time +\beta_{5}TrtB\times Time+\varepsilon) \tag{8}\]  
in which, \(\beta_{i}\) are parameters, and \(\varepsilon\) is the error term. As an example, the slope of the control group for Bacteria A is 0.70 Log CFU/mL \(\times\) Day, suggesting that for every one-day increase in display time, there is an increase of 0.70 Log CFU/mL of Bacteria A. The same interpretation can be translated to each of the different treatments (control, Treatment A, and Treatment B) and type of bacteria (Bacteria A and Bacteria B). Then, a 95% confidence interval can be used for statistical comparison. For instance, Treatment A is different from Treatment B and the control group for both microorganisms. Additionally, the intercept of the regression models denotes the value of the dependent variable when the independent variables are equal to zero. For our example, the intercept represents the initial microbial load of the sample before even starting the display time.