# MATH 601 INTRODUCTIONS TO ANALYTICS

## 2.1 Executive summary on surgical unit managers

Task 4 is divided into five parts which describe if a patient has crucial difficulty after surgery it will increase the budgeted cost related to those surgery difficulties and finding the probabilities. The first part of task four shows the unit has no crucial surgery in any particular given month in figure 14 with one probability distribution. Figure 15 shows the unit has a minimum of two critical surgery in a given month and figure 16 shows the unit has no critical surgery in a particular given quarter. Figure 17 shows the unit has at least two critical surgery in a given quarter. The patient will spare the budgeted amount which is related to major complications throughout the particular year in figure 18. Task 5 has two parts which represent the perfection of unit managers with 90% assured intervals for each and every six variables in the particular data set, in the first part of task five it is showing that if the sample size is equal for each and every variable why margin error is different (Pluye et al. 2018). The second part of the task describes if the budgeted cost for the research increase and the quarterly sample size is double then how much accuracy will increase after doing this. Figures 19 and figure 20 show the confidence variable and dataset of the Q-Q plot. Figure 21, 22, 25, 28, 31, and figure 35 show T-test statistics for variable one and two, three, four, five, and six. Figure 23, 26, 29, 33, and figure 36 shows the interval of confidence for variable two, three, four, five, and six. Figure 24, 27, 30, and figure 34 shows variable two, three, four, and five for the Q-Q plot. Task 6 shows the previous quarter’s mean considers one variable and shows all detailed steps of the statistical process and also considers the p-value for each and every single variable with the appropriate conclusion. In the addition of which variables are responsible for 90% confidence that represents a significant increase in the quarter’s average (Steen et al. 2018).  Figure 37 and figure 38 show one variable’s frequency table and statistical analysis. All the technical reports are presented carefully in this entire work using the SAS platform elaborately in detail.

## 2.2 Important three points after analyzing module 2

• By using a histogram of qualitative variables data visualization was analyzed.
• Box plots help to show the all details in the graphical representation in a detailed manner for quantitative variables.
• Bubble plot representation shows the overall satisfaction of a particular patient with respect to medical knowledge.
• The principle of the quantitative variables is mainly to represent the accurate quantity of data in binary format means 0 and 1 based on this report.
• A bar plot represents whether a particular patient needs a surgical unit or not.
• Bar line chart which elaborately represents a patient suggests a surgical unit with no complications.
• Technical report, Series plot represents overall satisfaction of a patient with respect to the recommendation of a surgical unit.
• The line chart is used to represent not to recommend a particular patient to any surgical unit that was unsatisfied.
• By using the probability distribution it can understand that a unit either has more than one critical surgery in a given particular month or no major surgery in the given particular quarter.
• By using statistical analysis the final result of each and every task of six variables is formed.
• Entire technical task based on SAS platform which is used to help statistical calculation.

## 2.3 Weaknesses of methods

In this section, various methods have been implemented in the SAS studio environment to carry out the project. Different calculations and map plotting according to the data set have been generated to visualize the forecast values of risk assessment. The data has been analyzed from the given data set regarding the health risks associated with the longevity of dolphins. The methods are implemented on the data set and various visualizations like bar plots, histograms, and many more have been generated as the result. The attributes or the variable of the data set have been analyzed and the plotting has been generated as per the requirements. The data set can be accessed to visualize the statistics alongside the calculations of each variable to summarize the outcomes of risk factors. The data visualization can be more effective by implementing the methods. The implementations of T-testes for each variable have been generated and can be accessed more accurately by importing the data set. The methods needed to be more adequate to accrue the visualizations as per the requirements. The confidence interval can be generated more accurately with the use of superior data set of dolphins’ health. The predictive models can be generated by analyzing the variables and other attributes of the data set including confidence interval and Q-Q plot accordingly. The variables have been accessed and the plotting criteria have been met by implementing methods for each variable as per the requirements of the project.

# Module 3

## 3.1 Major Findings of Final model

In this section, the final model has been developed based on the data set that is the information on dolphin’s health. The data set has been analyzed and the attributes of the data set can be accessed in order to visualize and analyze the longevity of dolphins. The data set has been accessed in order to implement models of the analysis to track the longevity of dolphins’ health as per the requirements. The implementation of R studio has resulted in various visualization aspects of the project and the health risks regarding the model have been implemented. All the tasks according to module 3 have been performed regarding the health risk analysis based on the longevity aspects. All the visualization has been performed in order to meet the decision-making criteria and the future study related to the same concern.

All the correlation plotting according to the data set of dolphin’s health have been implemented in order to visualize the longevity of life of dolphins (Bou-Cabo et al., 2022). According to the dataset, various graphs and plotting have been generated by implementing various models of regression algorithms. The distribution plot has been generated for count vs. longevity to visualize the lifespan of dolphins. On the other hand, the plotting of longevity vs. close relation has been generated by accessing the data set to provide a clear understanding of the health risks of dolphins. All the graphical representations including box plot, bar plot, and many more have been generated related to the IQ range, longevity, social integrity, and more. The data visualizations have been performed in the R studio software environment to carry out the project requirements. The data distribution according to the attributes of the data set has been measured and all the distribution plotting has been generated as per the requirements of this particular module.

In this section, the linear model has been performed in order to produce the summary statistics of the data set and the predictive analysis of the health risks of dolphins (Schwacke et al., 2022). The data set has been accessed and the distribution of the attributes has been measured to implement the linear model as per the requirements. All the aspects of the linear model including summary, standardized residuals, and so on have been described in this section. The linear model has been applied and according to the summary of it, RMSE and R2 values have been derived alongside coefficient values. According to the summary, residual values are from -13.5571 to 15.28344 and an R2 value of 008539. On the other hand, the residuals from min to max have been generated accordingly. The linear regression model has been developed in order to generate the visualizations of it. The model has been implemented and the graph of longevity extent vs. close relationship has been generated to measure the health risk statistics. On the other hand, all the models including the cubic model and quadratic model have been implemented and the summary statistics alongside the visualization of each model have been generated. The visualizations of longevity vs. close relationships have been generated for each model.

Secondly, the models have been implemented and the visualizations have been generated accordingly to produce the risk associated with the dolphin’s life. The t- steps of two samples have been generated in order to proceed with the implementations of the models as per the requirements of the project. According to the t-test, the mean of x and y has been produced and the values are 0.16 and 0.12 respectively. The test splitting has been performed in order to implement the models accordingly that has been mentioned earlier. According to the summary of the quadratic model, the residuals have been generated and the values are from min -19.6050 to max 14.3625 and the r2 value of 0.8713. The graph of leverage vs. standardized residuals has been generated based on the summary statistics that have been generated. On the other hand, the cubic model has been implemented in the data set. According to the summary of the model implementation, residual values have been generated and the values are from a min of -24.5564 to a max of 15.3395 alongside the R2 value of 0.8633. Based on the summary statistics, the graph for close relationship vs. longevity extent has been generated.

## 3.2 IQ

In this section, the predictions can be generated based on the models that have been developed in the software implementations. All the attributes of the data set have been accessed and the prediction for each criterion has been generated based on the attributes as per the requirements of the project. The key factors like close relationships, social integration, IQ, and more have been generated alongside the graphical implementations of each attribute. According to the prediction analysis, the upper value based on the lm model is 111.41, and the graph of longevity vs. close relationships has been generated as per the requirements. On the other hand, the prediction for IQ has been generated based on the implementation of the lm model that has been mentioned previously. Based on the prediction, the upper value of consecutive prediction based on the model fit is 61.93. The IQ prediction has been generated and the graphical representations have been generated too. The graph for IQ vs. longevity has been generated and that can be measured in forecasting values for future reference regarding the risk associated with dolphin health. The IQ predictor has been generated and based on that longevity can be predicted as per the requirements and the models can be implemented based on the IQ predictor.

## 3.3 GPS data

In this section, the justification for predictions based on the GPS data can be accessed. The model implementations have been done by accessing the data set and the GPS tracking can be helpful in these cases to predict the analytical discussion of the longevity of dolphins (Murphy et al., 2021). The health risk has been reviewed in the software implementation by accessing the attributes of the data set.

On the other hand, the final model according to the linear regression of the multivariate model has been generated, and the summary statistics have been generated based on that. The distribution plotting of the multivariate LR with social integration and the close relationship has been generated accordingly. According to the summary, the residuals are from the value of -15.5504 to 16.6110 and the adjusted R2 values have been generated as a value of 0.876.

## 3.4 Implication

In this section, various regression models can be implemented alongside multivariate regression and more. The multivariate regression model has been implemented in order to measure the attributes of the data set regarding the health risks of dolphins. The data visualizations can be generated based on the model. According to the model implementation, the summary has been generated, and according to the summary, residuals have been generated from a max value of 18.791 to a min value of -15.483 alongside an R2 value of 0.8766. Based on the regression model that has been implemented, the graph for longevity vs. multi-variables of the data set has been generated as per the requirements of the project. The data set has been analyzed in order to provide the forecasting values for future reference. The attributes of the data set have been analyzed and based on the model implementations; the predictions have been generated on the attributes to learn the future outcomes of the health risk prediction according to the project requirements.

## References

Bernerth, J.B., Cole, M.S., Taylor, E.C. and Walker, H.J., 2018. Control variables in leadership research: A qualitative and quantitative review. Journal of Management, 44(1), pp.131-160.

Bou-Cabo, M., Lara, G., Gutiérrez-Muñoz, P., Saavedra, C., Miralles, R. and Espinosa, V., 2022. A Risk-Based Model Using Communication Distance Reduction for the Assessment of Underwater Continuous Noise: An Application to the Bottlenose Dolphin (Tursiops truncatus) Inhabiting the Spanish North Atlantic Marine Demarcation. Journal of Marine Science and Engineering10(5), p.605.

Kuckartz, U. and Rädiker, S., 2019. Analyzing qualitative data with MAXQDA (pp. 1-290). Basel, Switzerland:: Springer International Publishing.

Murphy, S., Evans, P.G., Pinn, E. and Pierce, G.J., 2021. Conservation management of common dolphins: Lessons learned from the North‐East Atlantic. Aquatic Conservation: Marine and Freshwater Ecosystems31, pp.137-166.

Neuendorf, K.A., 2018. Content analysis and thematic analysis. In Advanced research methods for applied psychology (pp. 211-223). Routledge.

Pluye, P., Bengoechea, E.G., Granikov, V., Kaur, N. and Tang, D.L., 2018. A world of possibilities in mixed methods: review of the combinations of strategies used to integrate the phases, results, and qualitative and quantitative data. International Journal, 10(1), pp.1-16.

Schwacke, L.H., Marques, T.A., Thomas, L., Booth, C.G., Balmer, B.C., Barratclough, A., Colegrove, K., De Guise, S., Garrison, L.P., Gomez, F.M. and Morey, J.S., 2022. Modeling population effects of the Deepwater Horizon oil spill on a long‐lived species. Conservation Biology, p.e13878.

Steen, J., DeFillippi, R., Sydow, J., Pryke, S. and Michelfelder, I., 2018. Projects and networks: Understanding resource flows and governance of temporary organizations with quantitative and qualitative research methods. Project management journal, 49(2), pp.3-17.