Statistics is a branch of mathematics that focuses solely on the process of collecting, analyzing, interpreting, and presentation of data. Statistics can be considered from two fronts, which are basic and advanced statistics while considering the main types of statistics, which data analysis and descriptive statistics. Data analysis focuses more on the idea of analyzing a wide array of data with the sole intention being towards predicting a specific outcome. When dealing with basic statistics, one of the key aspects to note is that it allows for predictions using previous data, which can be analyzed in a manner that justifies the predictions. On the other hand, the use of descriptive statistics allows for easier categorization of data that has been collected, which presents a rather advanced expectation when compared to data analysis. The focus for this report is to embark on an in-depth analysis of statistics from multiple perspectives with the focus being towards evaluating their application.
Question One: Completely and thoroughly explain how Basic Statistics could be used by a large electrical utility company to predict how much electricity their customers will be using during the different seasons of the year.
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The main use of basic statistics is prediction using data sets provided, which would allow for easier planning. That can be seen in companies that seek to provide specific products, which creates the need for them to predict the consumption rate from their customers in a bid to maximizing on efficiency in delivery. Electrical utility companies take advantage of basic statistics for purposes of having to predict the overall levels of consumption by their customers within different seasons in a year. The following is an analysis of how a large electrical utility company would be able to position itself in the use of basic statistics to achieve the expected outcome in predicting consumption.
Computing Basic Data
For a company to be in a position allowing it to predict an outcome effectively, one of the key aspects of consideration is the amount of data that it is able to gather within a given period that would determine knowledge capacity. The use of basic statistics helps in computing of basic consumption data, which is important for the company, as it would help in the prediction of electrical consumption levels within different levels. Bickel & Doksum (2015) argue that basic statistics does not only focus on data collection but also focuses on the effectiveness of the data computation process, as this would serve towards justifying overall capacities to meet set out objectives. In this case, the company would be expected to gather as much data as possible relating to the consumption levels for consumptions during different seasons, which would then be compounded to create a single dataset.
The computation of the datasets is expectation to take a period of one year during which the computer would focus much of its attention towards gathering information relating to the consumption levels for their customers. What much be noted is that the company considered in this framework is fairly large; thus, meaning that the amount of data that it is expected to gather would be significant. That means that the company would be expected to use much of its human resources to aid in the computation of such data before it is able to proceed in the next step as part of its approach to predicting consumption.
Variance
After the data has been computed, the next use of basic statistics is to help in the calculation of variance in the dataset, which would focus on the mean from the data that has been gathered and computed. Rust, Krawchuk, & Monseur (2017) argue that variance calculation is important, as it aids in the overall process of calculating how far each of the data sets is from the mean, which is important towards predicting more data sets. The use of statistics allows for easier identification of the expected variance calculation that would help in meeting the set out goal while taking into account the overall amount of data gathered and presented within the datasets. The calculation used would help in ensuring that the electrical utility company is able to determine how each of the data sets can be compared to the mean.
The next process would involve having to apply the difference and summation of the entire dataset based on the outcome from the variance calculations undertaken. The application of the difference and summation helps in the identification of a pattern within the data sets, which is important in predicting some of the other sets. The company would then be expected to generate a statement of projection from the pattern created, which allows for easier determination of the expected consumption levels within a given period. As has been noted earlier, the company is using computed data from a one year period thereby meaning that this would aid in the generation of a statement that provides projections focusing on electricity consumption within a one year period.
Time-Series Aggregation
Time-series aggregation allows for computation of data within fixed time intervals with the sole intention being towards ensuring that the data is considered as being more useful in prediction from a short and long-term perspective (Bahl, Kümpel, Seele, Lampe, & Bardow, 2017). In this case, the company would be expected to focus on time-series that are defined based on the differing seasons within a given year with the intention being to determine exact consumption expectations. Using the data the projection statement that has been generated based on the data collected, the company would be in a rather effective position of having to create specific time intervals that would determine the expected periods to define consumption. Specifically, the company may focus on a technique that is described as masking, which allows for elimination of data sets that are not within a given time interval for easier computation.
The use of masking would enhance the validity and reliability of the data projected within given time series, as it becomes much easier to predict data within a shorter time interval. In this case, the time interval would be approximately 3 months years considering that the year would be separated based on the seasons. The company would be expected to engage in masking for all the four seasons occurring within a given year, as this would serve as a key determinant of the expected time series to aid in determining electricity consumption at different periods. Consequently, that means that the company would be expected to generate four different statements representing summer, winter, autumn, and spring seasons. The four statements will seek to provide an accurate projection of electricity consumption while taking into account the dataset that has been computed.
Question Two: Completely and thoroughly explain how any type of Advanced Statistics could be used by a large bank to manage any aspect of their business.
Banks and other financial institutions apply advanced statistics in different areas of their businesses with the sole intention being towards enhancing overall efficiency in their capacity to maximize on their businesses. In most cases, the use of statistics creates a rather positive approach through which to build on their capacities to achieve some of their set out goals while taking into account their business expectations. One of the key types of advanced statistics that is applied in a large bank is logistic regression, which a bank may use as part of credit risk analysis, as it aids in the generation of a credit score.
Credit risk reflects on three specific terminals associated with the provision of credit, which are default, bankruptcy, and prepayment. A large bank often considers these three terminals as competing risk. The use of the logistic regression model, as a key statistical approach, allows for easier computation of both static and time-varying covariates relating to credit performance. That means that the model is able to create an avenue through which to determine probabilities of a customer defaulting on a loan or even facing bankruptcy while servicing a loan. The model creates a standard regression that would seek to highlight how the bank would expect to gain from the interest rate set out while quantifying the bank’s capacity to achieve profitability. That allows for easier determination of the bank’s credit exposure, which would help in determining whether indeed a customer is credit worthy.
The logistic regression model considers all key variables that are likely to impact on overall performance capacities when dealing with the issue of credit, which include unemployment and inflation. Harrell Jr (2015) argues that the logistic regression model is effective in banking, as it accounts for credit exposure within a ‘stressed’ environment while considering the overall possibility that the conditions that a bank is likely to face may not be favorable. The need for having to consider the stress or strain that the bank would experience is important, as it allows for easier determination of whether the bank would gain overall capacities from the credit it offers. From that perspective, what becomes clear is that the development of the credit score is able to consider all ‘stress’ factors that are likely to impact on the bank’s ability to gain expected profits. The ultimate result is that this would help create a rather proactive position in which the bank would be able to make its decision focusing on risk prediction focusing on the economic conditions.
The application of the logistic regression model may occur at both the individual and the aggregated pool levels depending on the nature of data that is available for the credit managers to use in making their decision. At the individual level, the credit manager is expected to focus on data from a customer’s account with the sole focus being towards ensuring that indeed the manager is able to make effective decisions based on the customer’s financial capabilities. Depending on the type of credit that a customer may seek, the loan manager would be able to apply the model in the regression of data to aid in determining financial trends for the customer to allow for easier decision making.
On the other hand, credit managers may also focus on the aggregated pool level as part of the overall structure of decision making, as the manager is likely to expect data that relates to the economic conditions. The evaluation of the economic conditions is important, as it seeks to create an avenue through which to determine the most likely outcome in terms of set performance standards. An example can be seen from the application of the model in the area of inflation, which will help in predicting the expected rates of inflation over a given period. The credit manager would then be in a better position of having to determine whether the interest rate charged would be effective to cushion the bank from inflation.
The logistic regression model focuses on two main dimensions when dealing with credit risk analysis, which are age of the loan and calendar time to serve as a key determinant of whether the credit is worth the risk (Chen et al., 2017). The credit manager may consider these two variables as they relate to each other with the sole intention being towards creating an effective front through which to justify the originating interest rates. When dealing with a customer that has a low credit score, the credit manager may focus on reducing the age of the load while extending the calendar time. That would mean that it would much easier for the manager to actually be in a position that would justify overall outcomes in terms of maximizing on the interest rates to achieve the banks overall expectations.
The use of the logistic regression model creates a general avenue through which to advance prediction of the possible outcomes with regard to financial capacity for the customer during the entire period of servicing the loan. That is important as it ensures that the credit manager is in a rather effective position allowing for easier determination of set out factors that are likely to affect customer’s ability to pay his or her loan. However, the regression model serves more like a predictive model with the aim being towards predicting the expected outcomes in terms of financial performance. The general expectation from this is that it creates a positive framework through which credit managers are able to make decisions on whether to give credit to a customer or not. The ultimate outcome of using the model is that it provides the bank with an easier understanding of the customer’s financial behavior while maximizing on the overall process through which to determine whether indeed the bank would give out credit to specific customers.
Conclusion
In summary, statistics is a branch of mathematics that focuses solely on the process of collecting, analyzing, interpreting, and presentation of data. The main use of basic statistics is prediction using data sets provided, which would allow for easier planning. Electrical utility companies take advantage of basic statistics for purposes of having to predict the overall levels of consumption by their customers within different seasons in a year. Banks and other financial institutions apply advanced statistics in different areas of their businesses with the sole intention being towards enhancing overall efficiency in their capacity to maximize on their businesses. One of the key types of advanced statistics that is applied in a large bank is logistic regression as part of credit risk analysis.
References
Bahl, B., Kümpel, A., Seele, H., Lampe, M., & Bardow, A. (2017). Time-series aggregation for synthesis problems by bounding error in the objective function. Energy , 135 , 900-912.
Bickel, P. J., & Doksum, K. A. (2015). Mathematical Statistics: Basic Ideas and Selected Topics, Volumes I-II Package . Chapman and Hall/CRC.
Chen, W., Xie, X., Wang, J., Pradhan, B., Hong, H., Bui, D. T., ... & Ma, J. (2017). A comparative study of logistic model tree, random forest, and classification and regression tree models for spatial prediction of landslide susceptibility. Catena , 151 , 147-160.
Harrell Jr, F. E. (2015). Regression modeling strategies: with applications to linear models, logistic and ordinal regression, and survival analysis . Springer.
Rust, K. F., Krawchuk, S., & Monseur, C. (2017). Sample Design, Weighting, and Calculation of Sampling Variance. Implementation of Large‐Scale Education Assessments , 137-167.
