There are those that say, ‘If it ain’t broke, don’t fix it.’ but there is always improvement to be made to increase a business’s profits. While some co-workers may think that you can tell the future, you know that it is simply a program that everyone has on his or her computers at home or at the office. Using just one forward-looking program; probability, distribution, uncertainty, sampling, statistical inference, regression analysis, time series, forecasting methods, optimization, and/or decision tree modeling, can take a business that is experiencing a loss and turn them around, so they will see a profit later in their fiscal year, if not sooner.
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All businesses need to be able to see what is coming before it hits so that they can prepare for whatever the future has in store for them. By using any of the listed models; probability, distribution, uncertainty, sampling, statistical inference, regression analysis, time series, forecasting methods, optimization, and/or decision tree modeling, a company will be in a better position to avert or take advantage of the coming issue.
Using probabilities is something that everybody does every day. There is a chance that someone will slip and fall in the shower or burn themselves with coffee on the way to work, or work out to heavily at the gym and tear a tendon, or any number of other events. Probability helps the owners of a business to predict if an event will, or will not happen (Test Prep Toolkit, n.d.). If an event as a zero probability, that event cannot happen; if the event has anything greater than a zero, there is a chance for that event to happen. (Albright & Winston, 2017). It is like playing 21in a casino at the one deck table. The player’s odds of hitting a 21 are slim, but if they continue to play with the same deck, and the player knows how to count cards, his odds increase as he plays. The odds for the player may be something like twenty percent at the beginning of the game but will improve closer to ninety percent the closer to the end of the deck they get.
There are many types of distributions that can be used for many things. The text discusses only four, and only two in-depth, normal and binomial. The normal distribution, or the bell curve as it is commonly known, can be used for anything from comparing the height of people to where someones I.Q. is compared to others in a group. For example, distributions can be used in a manufacturing plant to determine if the parts that a machine produces fall within the parameters of the blueprints for that part. “Once you know how your data is distributed, you can plan the appropriate type of analysis going forward (SAS Institute Inc., 2018, para. 2). The Quality Assurance worker will pull the specified number of samples off the line and takes them back to their lab. The worker measures each one of the samples carefully and enters the data into a computer. If the computer determines that the parts are too far out of specification, the worker will see that. Once they see that, they can stop the machine making the part to determine what the problem is and what needs to be completed to correct the issue and get the parts back to specifications.
The binomial distribution is a distribution that can be used “when sampling from a population that only has two types of members, and when performing a sequence of identical experiments, each of which has only two possible outcomes (Albright & Winston, 2017, p. 190). An example of this is throwing two multi-colored darts at a dartboard. Both the darts and the colored darts have an equal chance to be used and the same chance to not be used.
“Uncertainty is the measurement of the goodness of a result (NIST/SEMATECH, 2013, Section 2.5). There are four basic steps in using uncertainty. The first step is to “specify the target parameter of interest and an equation for its estimator” (Jurek, Maldonado, Greenland, & Church, 2007, para. 1). Next, it is necessary for someone to “specify the equation for random and bias effects on the estimator” (Jurek, Maldonado, Greenland, & Church, 2007, para. 1). For the third step, one must “specify prior probability distributions for the bias parameters” (Jurek, Maldonado, Greenland, & Church, 2007, para. 1). The final step is to use the “Monte-Carlo or another analytic technique to propagate the uncertainty about the bias parameters through the equation, to obtain an approximate posterior probability distribution for the parameter of interest (Jurek, Maldonado, Greenland, & Church, 2007, para. 1). If there was not something that could check the results, we could not judge the results for making the decisions relating to scientific excellence (NIST/SEMATECH, 2013). An example of this would be checking to make sure that the results of a prior, like a probability, test are a good fit. There can be more than one answer to uncertainty, depending on the prior test that was completed.
The easiest to understand and simplest sampling methodology is simple random sampling. A simple random sample is a subset of a population where each object has the same chance as any other object in that population to be picked (“Simple Random Sample,” 2018). A disadvantage to using simple random sampling is that the examiner may create a sampling error. One example of a sampling error is when an analyst does not pick a sample that represents the entire population (“Sampling error,” 2018).
An example of this would be playing Bingo. There is a population of numbered balls in a spinner. The caller stops the spinner and withdraws one of the balls. The spinner is the original population, and the balls that the caller pulls out is the sample. Each member of the original population has the same chance as the other members of the population to be picked.
There are “three forms of statistical inference …each one representing a different way of using the information obtained in the sample to draw conclusions about the population” (“Unit 4A: Introduction to statistical inference,” 2018, para. 15), but here we will only discuss statistical inference in general.
“The general idea that underlies statistical inference is the comparison of particular statistics from on observational dataset (i.e., the mean, the standard deviation, the differences among the means of subsets of the data), with an appropriate reference distribution in order to judge the significance of those statistics.” (Bartlein, 2018, para. 1).
An example of this would be people taking exit polls during an election. The poll takers ask certain questions to attempt to determine how the election will turn out. Sometimes they are wrong and sometimes they are right.
Regression analysis is a way of using math to sort out which variable, the independent or the dependent variable, does have an impact (Gallo, 2015). For example, you are the manager of a fast food restaurant, and you want to know if it is better to stay open all night or to close the restaurant at 10:00 p.m. You gather the data about two years’ worth of paychecks for the workers along with the paychecks of the workers that have worked the overnight shift. After that it is a simple matter of inputting the right numbers into the regression analysis table and you will find your answer.
Inputting the numbers and coming out with a table of information, and then adding the chart and trendline, the line equation, and the R^2 value is the simple part of the problem, the confusing part is the numbers that are created when you add your raw data to the regression chart and try to make sense of them.
Time series is a way to look at two variables, the dependent and the independent variable, over some amount of time that has elapsed at regular intervals and make predictions. It can be used with one variable or two. There is one caveat to using time series, and that is one of your variables has to be taken at uniform time intervals. It is like being a lawyer. One day you are told that there is an inmate that would like to see you. When you see them you already know the case, everybody already knows the basics of the case. The lawyer has two things they can do, take the case pro bono and lose the money they would have made taking other cases or take the case and use the publicity to improve their business reputation in the hopes that it will draw in more and better clients. To do this, they decide to use a time series analysis. He uses information from the time they started taking pro bono cases and their income, as it was reported on their tax returns. If the time series proves that they can take on the case without losing money, then they can defend their client; if it shows that they will lose money by taking the case, then they do not have to take the case.
Forecasting is about predicting the future as accurately as possible, given all the information available, including historical data and knowledge of any future events that might impact the forecasts” (Hyndman & Athanasopoulos, 2018, Section 1.2). To forecast you need to start with five simple steps: define the problem, gather the needed information, do an exploratory analysis, choose and fit models, and finally using and evaluating the forecasting model (Hyndman & Athanasopoulos, 2018).
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An example of this would be a call center wanting to know how many employees they need for the next week. They pull up information consisting of how many calls they had received during the last four years as well as the number of employees they had staffed during the same time period. Once they have all the information they use one of several models for both the number of calls over the past four days and the number of employees that they had staffed for the same four years, run the numbers through one of several models and get the answers that they want to get, if everything is correct in the data that has been input.
Optimization means that you methodically choose numbers from the decision variable to make the objective as large or as small as possible and contain all the constraints to be satisfied (Albright & Winston, 2017). Once this is completed, you move into the model development step. It is here that you decide what the decision variables will be, what your objective will be, which constraints you will use and how everything comes together (Albright & Winston, 2017).
Joe is a farmer getting ready to plant the hay that he needs to get his cattle through the summer if needed, and through the winter. So, he takes the amount of hay that he has produced over the last ten years, how many cattle he has over the winter and uses the optimizing software that he bought but never used to find out that for the last four years he has had to purchase 40 more large rolls of hay to make it until next spring. That means that he has to plant an additional ten acres for sixty-four large round bales to make sure his livestock makes it through the summer, fall, and winter. Now he needs to find out which of his other fields he can short and not lose a lot of money or shorting the farm somewhere down the road. He uses the optimization software, finds two fields that will have little or no effect on his income.
Decision Tree Modeling
A decision tree is a graphical representation of a decision, and every outcome of that decision has been grafted to the decision tree, and everything comes to a natural end, your decision tree has found the solution to the problem. They give everyone who uses them an easy way to understand the options of their decision and all of the possible outcomes.
In a business, there is a manager that has a dilemma. He needs to be present when a new project comes through so he can make sure that everyone knows what to do and how to do it, but his boss wants to take him to lunch today, and it has been scheduled for a month, and he needs to discuss some things with the boss before they get out of hand. He decides to use a decision tree on his problem, something that was just taught to them yesterday. After running through the decision tree twice his path was clear. He would go to his boss’s office to tell him that he needs to reschedule the lunch appointment for today because his crew is starting a new project and he wants to be there to make sure that things go well, and if they do not go well then he is there to take the brunt of the ridicule that will happen.
This paper has discussed ten different approaches to use so that you can find significant information buried in data. While there are ten of them, with a little practice you will have no trouble deciding which to use to get the information that you need at that time. Any business that uses these methodologies will be preparing for the future, good or bad, and taking advantage of them. These ten models: probability, distribution, uncertainty, sampling, statistical inference, regression analysis, time series, forecasting methods, optimization, and/or decision tree modeling, assist a company to increase its profits or avoid an issue in the new product or any other decisions that need to be made.
- Albright, S. C., & Winston, W. L. (2017). Business analytics: Data analysis and decision making (6th ed.). Retrieved from https://platform.virdocs.com/app/v5/doc/351675/pg/1/toc
- Bartlein, P. (2018). Statistical inference. Retrieved November 15, 2018, from http://geog.uoregon.edu/bartlein/courses/geog495/lec10.html
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- Jurek, A. M., Maldonado, G., Greenland, S., & Church, T. R. (2007). Uncertainty analysis: an example of its application to estimating a survey proportion. Retrieved from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2465740/
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