Strengths and Limitations of Regression Analysis, Using Linear Programming - Coursework Example

Business Modelling The statistical analysis of the relationship between the numbers of variables is referred to as regression analysis. The individuals caring out the investigations will look forward in assessing the certainty of and effect of a single variable onto another. According to Wendorf, (2004) this can be either the impact of the price of a commodity with increase in the demand for the product. To effectively understand such issues an individual will collect data parting the question at hand and thereafter employs regression to estimate the quantitative effect of causal variable in comparison with the variable that they directly or indirectly influence their performance, (Wendorf, 2004). This method of data analysis has been in operation for an extended period especially in the economic statistics. Regression has also become popular among lawyers in the recent past, being used as evidence of liability under Title VII of the civil Rights Act 1964. Regression analysis while handling a single explanatory variable is characterized as a “simple regression.” (Fox, 1997) Regression analysis will be used when it is determined that two or more variables have a connection in a linear relationship, Hinkle, (1996). When we focus on simple regression, it means that we have only two variables in question. The variables will be denoted by X and Y. and the relationship can be determined as; y = ß0 + ß1 x + έ, this is a linear equation because it will result in a straight line when presented in a graph, (Fox, 1997). (Yang, et al. 2007) Strengths and limitations of regression analysis Data analysis is an activity we cannot escape from in our day to day activities. Data may be realized from the business activities such as their mode of supply or transport. Businesses will, therefore seek to obtain the most favorable model through analyzing the data. The kind of analysis is called “The linear regression analysis,” (Fox, 1997). Regression analysis has a number of strengths, first according to Fox (1997), regression method of data analysis is beneficial in circumstances where forecasts are promising, such as the number of intended admissions in a college. This methodology assists administrators to predict and get ready for additional demands that are likely to arise in the future Regression analysis is also a quite cheaper method as data are easily collected and usually can be gathered from other earlier source. Furthermore, independent variable data are not expensive to update as compared to acuity-quality data, (Fox, 1997). Vonon (1998) advocates for the technique by says that method, of data analysis, is particularly beneficial to administrators with inadequate resources, and who cannot meet the expense of carrying out a full dependency-activity-quality study from scratch, Linear regression data analysis has a number of predicaments in their application in data analysis of two variables to give the desired output as discussed below. As a result of the many variables that are required for data analysis, Vonon (1998) says that it would be considered complicating thus requiring the knowledge, skills and expertise of a statistician in designing and implementing for efficient and reliable regression analysis, this is a major drawback to the technique of data analysis. The existence of naturally qualitative independent variables makes it difficult of the data collection as compared to collection and analysis of others dependent variables for example the perceptions of particular population leaders where the data is being collected may, Fox, (1997) Personal judgement independent, that is, it is not influenced by other variables. Another drawback to linear regression analysis is putting in place regression statistical analysis techniques on nursing teams, for example, would lead to the feeling of alienation of some nurses. According to Fox, (1997) the primary challenge is seen to be a lack of ownership, control and understanding of nurses at the other extreme, A major assumption of linear regression analysis is in the areas of data collection. Analysts assume that the population will remain constant over the period and continue to operate efficiently and effectively Fox, (1997). Nevertheless it will not be the case in the as individuals tend to respond differently when interviewed or even give false information to the analyst, (Fox, 1997) (Ziff, 1998 vol. 12, p. 385-392.) 2. “Critically evaluate at least three disadvantages of using linear programming as a decision-solving technique in a logistics, transportation or supply chain context.” A linear programming is defined as a problem where the constraints are either maximized or minimized in a linear function. The constraints may be equalities or inequalities. Linear programming is the most regularly functional form of controlled optimization. It is used to identify the highest or lowest point of the objective function (Wilson, 2007). This may be in situations such as the transport industry where the organisation will be seeking to know the most favorable number of trips to take in transportation of goods with the limiting resource being either fuel consumption or carrying capacity of each track (Beasley, 1996). A situation where optimization is obligatory it means that there must be more than one possible way out to the problem. The process is then applied to choose the best solution from among those available. The term best is dependent upon the problem at hand, and it may be referring to the solution that yields the most profit or that consumes least of the limiting resources, Beasley, (1996). The main elements of the constraint optimization problem are; Variables, the objective function, constraints, and variable bounds. Modeling Linear programming requires the knowledge of mathematics; this is because an individual will have to convert the problem into a mathematical function. One is also required to have definite objectives such as profit maximization or losses minimization, (Beasley, 1996). Decision variables are essential in linear programming as that affect the objectives, and constraints limit the level of activity of the problem. Consider a situation where, there is a limited carrying capacity of tracks and the individual is concerned bulk transportation of goods and reduce the number of trips in order to maximize profit, you need to identify such variables to adequately analyze the situation, (Beasley, 1996). Variable identification is a challenge to the management thus making it difficult to apply linear regression analysis. Linearity Linear programming depend on, rationally sufficient, on linear equations: for example when an individual increases on the level of sales, with everything else held constant, then the equation will automatically reveal an increase in revenue amount. Some decision variables fail to have a linear effect, an increase of one variable fail to have effect on the other variables. For example, an increase in the number of trips in transport of goods doesn't mean that profits will increase as well. This is because increase in the number of trips will lead to rise in fuel consumption thus increase expenses. This makes the method of analysis ineffective in such cases, (Beasley, 1996) (Thijssen, 2007). Reality Thapa, (2003) say that this model of linear programming can only be useful for real life problems that are encountered in daily business activities, the model depends on convinced expectations and the assumption, Consider an example where you assume that increasing supply units will lead to increased sales, but in actuality the increased units saturate the market, thus reducing the actual sales and the general profits, (Thapa, 2003). There are substitute approaches to solving transportation complications that are much easier and efficient than the standard simplex algorithm. This is because real-world transportation problems have vast numbers of variables that complicate the use of linear programming, (Thapa, 2003). Secondly, as a result of a distinct structure, it is conceivable to resolve the transportation linear problems in whole numbers. That is if the data of the problem that may be supplies, demands, and costs are all in full figures, (Thapa, 2003). Then there is a whole number answer. The importance property is that one does not need to execute the difficulty of using integer constraints to obtain a solution that contents the limitations. 3 Monte Carlo simulation According to David Gale, (2000), Monte Carlo simulation is also referred to probability simulation. It is a mathematical technique used to establish an understanding of the impact of the occurrence risk and uncertainty in financial, project management, cost, and other forecasting models. David Gale, (2000) says that when one develops a forecasting business model, he makes a lot of assumptions. This is because the future is not known to the investor. The assumptions made may be about the rates of investment returns, the projected cost of a construction project, or the period it would take to complete a certain task or project These being projections into the forthcoming time, the most favorable estimates done are the expected value of the project or the money (Bernd 2004). Actual value of the project is not known with certainty, but based on historical data or expertise in the field, or experience, investors can draw an estimate for the future. This view will usually contain some inherent uncertainty and risk. A Monte Carlo simulation, the random values are selected for each of the tasks expected to execute in project development, based on the range of estimates. The resulting project planning from the estimates of the model are recorded, and the process is done again and again. An emblematic Monte Carlo simulation calculates the model over a thousand of times, with each time using different randomly-selected values. On completion of the simulation, the vast numbers of results, each established on random input values are identified. These findings are used to describe the likelihood or probability, of reaching various effects in the model David Gale, (2000). Subsequently supply chain management is one of the most vital management duties to ensure positive financial results of companies, it is prudent to optimize and analyze the performance of supply chains. Simulation is responsible for getting plans closer to reality for complex situations. This technique uses fewer simplifications and assumptions as those needed in analytical solutions. Supply chain management is a major constituent of the competitive approach to advance competitiveness and profitability of a firm. Operational supply chain management encompasses the following central functions: Objectives setting, weighing performance, and Defining prospect progressive actions, David Gale, (2000) According to Chopra, (2001), predetermined goals and creation of predictive strategic tools that create alternative course of actions, help’s managers in realizing the success of any individual institute, The use of Monte Carlo simulation enables effective strategy formulation, and operational planning and control (Casco, 1998). Among supply chain management predicaments the modeling and simulation of inventory management systems are the supreme difficulty in organisation management. Through the use of Monte Carlo simulation managers can improve operation of supply chains, through effective planning of organisations inventory. This can save the society billions of dollars Casco, (1998) Risk analysis employing Monte Carlo simulation helps corporations that depend comprehensively on supply chain competence to predict on the number of possible obstacles that could hinder an efficient distribution and continuity Petrovic, (2001). Moreover, the knowledge of the probability that occurrence of the risks is precedent further empowers decision-makers to articulate contingency plans, to meet customer ultimatum on time, and ultimately increase bottom line, that is increase of shareholders wealth (Landau & Binder, 2009). Similar to any other project estimating model, the Monte Carlo simulation will only give results that are as perfect and reliable as the estimates the management makes (Berg, & Bernd 2004). It's crucial to remember that the Monte Carlo simulation is embodied in probabilities and not future facts about actions taken. Nonetheless, Monte Carlo simulation can be considered a treasured tool when forecasting an unfamiliar future projection, (Fishman, 1996) This approach of analysis on the other hand has a number of disadvantages. According to Fishman, (1996), first, the method might be challenging in evaluating and identifying the most stable or otherwise in each case scenarios for each input variable. Secondly, all the contribution variables possibly will not be at their paramount or worst levels at a particular given time. Managers may face decision-making challenges since when using this strategy they tend to consider more than one situation. Correspondingly, JUNG (2004), Has the opinion that with increases in experimenter the amount of cases to deliberate, model versioning and storing becomes difficult. Monte Carlo simulation can be of abundant assistance to managers to systematically scrutinize the complete range of risk that are present and associated with each risk input variable or intended project of execution JUNG,(2004). This method of data analysis has a number of advantages they may include; the results from use of the method tend to not only show what could happen, but how likely each outcome is. It is thus vital for communicating the findings to stakeholders. Using Monte Carlo simulation, management analysts can model interdependent relationships between input variables (Fishman, 1996) 3 b Disadvantages of using Microsoft Excel for performing Monte Carlo simulation Monte Carlo is usually used in business in risk and decision-making analysis, to assist them in making business decision given the prevailing uncertainties in the market. Monte Carlo is a scientific approach of data analysis, the use of excels may not be the most appropriate methodology of performing Monte Carlo simulation because of the following reasons (Hartmann, 2009). A large number of companies or organisations make use of Monte Carlo simulation as a vital tool in their decision-making process with the organisation. An example may include. The Financial planners who use Monte Carlo simulation to determine optimal investment policies for their clients’ retirement and the benefit accrued (Glasserman, 2003). Using Microsoft excel for performing Monte Carlo simulation is the most common methodology used by for estimating the unknown parameters of the distribution data this is according to Berg, (2004). Estimators can be more considerable with the use of Microsoft excels due to the reduced error by the utilization of the computer. The level of bias tends to zero as the number of samples tend to move to infinity, (Andreasson, 2005). According to Andreasson, (2005), Microsoft Excel is thus considered a superior method for approximating variable constraints of distributions, this is as a result of excel estimates being much higher probabilities and being close to the amounts to be determined. Nevertheless, in certain cases, the likelihood of equations may be questionable, even with computers, whereas the maximum estimation, can rather be faster and easily calculated by hand than the use of Microsoft excel, (Andreasson 2005). References Andreasson, A et al. 2005, An Introduction to Optimization: Foundations and Fundamental Algorithms, Chalmers University of Technology Press. Berg, A 2004, Markov Chain Monte Carlo Simulations and Their Statistical Analysis (With Web-Based FORTRAN Code). Hackensack, NJ: World Scientific. Casco, D et al. Wasil, 1998, ‘Vehicle routing with backhauls: models, algorithms and case studies,’ Vehicle Routing: Methods and Studies, edition: Golden and Assad, North Holland, Amsterdam. Fishman, G. S 1996, Monte Carlo: Concepts, Algorithms, and Applications. New York: Springer-Verlag. Fox, J 1997, Applied Regression Analysis, Linear Models, and Related Methods. Sage Publications. Gale, D 2000, The Theory of Linear Economic Models, McGraw-Hill. Glasserman, P 2003, Monte Carlo methods in financial engineering N.Y., USA: Springer. Handy, T 2002, Operations Research- An Introduction (Sixth Edition). Pearson Education. Hartmann, A 2009, Practical Guide to Computer Simulations. World Scientific. Hinkle, D et al. 1996, Regression analysis with dummy variables: Use and interpretation. Journal of Vocational Education Research. Landau, D and Binder, A 2009, Guide to Monte Carlo Simulations in Statistical Physics, 3rd Edition (Cambridge University Press, Cambridge). Thijssen, M 2007, ‘Computer Simulations in Statistical Physics,’ Computational Physics, 2nd Edition (Cambridge University Press, Cambridge. Wendorf, C 2004, ‘Primer on multiple regression coding: Common forms and the additional case of repeated contrasts.’ Understanding Statistics. Vonon, E and Schuster, C 1998, Regression Analysis for the Social Sciences, Academic Press. Wilson, M 2007, Extended STL, Addison-Wesley Longman, Amsterdam. Yang, W et al. 2007, ‘Quantitative Computer Simulations of Biomolecules: A Snapshot,’ Journal of Computational Chemistry. Ziff, R. M 1998, Four-tap Shift-register-sequence Random-number Generators,’ Computers in Physics, Vol. 12, p. 385-392. Read More