Business Statistics - Term Paper Example

Business Statistics The paper says that business statistics plays an important role in the decision making process of the business mangers. It allows them to convert raw data into more presentable and understandable form. The paper also says that linear regression, descriptive statistics and correlation coefficient are important tools for all managers to make the best possible decisions in this global world including investments, quality maintenance, cash flow management, forecasting and controls. Introduction The paper will talk about the business statistics as a discipline that helps the managers to make relevant quick decisions in the uncertain business environment. It will also talk about the importance of these statistical tools in every functional department of the organizations. This will be followed by a discussion on the three most important statistical tools of the business statistics used by the managers in the current scenario. The discussion will describe these tools- linear regression, descriptive statistics and coefficient of correlation, with some relevant examples from the business environment which will signify the importance of the theory. Business statistics is a field that makes use of the statistical tools and allows the business managers to make the best possible decisions at the time of uncertainty. These tools allow the managers to covert the raw data into useful information which plays a significant role in the decision making process (Keller, pp. 6). Business statistics is used in all the functional departments of an organization – finance, human resource, marketing, operations and management and accounting. In the finance function, it is normally used to make decisions relating to measuring risk using variances, investments in stock markets using means, acquisition of assets and valuations (Keller, pp. 7). In marketing, it allows the managers to make decisions on the four Ps based on the identified consumer patterns and buying behavior using histograms, means and inferences (Keller, pp. 8). It also plays a vital in the company’s operations and management. It allows the managers to decide on the reorder points using histograms, waiting lines using Poisson distribution, location analysis using regression and quality using variance (Keller, pp.10). Linear Regression Linear Regression is an important statistical technique that compares the change in one variable with respect to another variable(s). It is most commonly used tool in the business environment for various purposes including decision making. This is considered the best method for the estimation of the line of best fit which minimizes the chances of error (Victor, pp. 1). Linear regression is be used in a wide variety of business functions across the organizations (Victor, pp. 1). In the accounting function, it is used to project the costs based on the level of activity as well as separate the fixed and the variable costs (Victor, pp. 1). It allows the analysts to develop a linear relationship – a line of best fit of cost against the level of activity based on the historical data. It then allows them to project the costs for future years based on a certain level of activity and decide on the best budgeted figures (Victor, pp. 1). In another scenario, it allows the analysts to separate the fixed and variable costs from the total costs. This leads to the effective control of the costs and indirectly reduction in the long run (Victor, pp. 1). On the other hand, it can be used to understand the price elasticity of a particular company’s products. This allows the managers to better understand the change in the sales with a change in price and decide on the best price that will maximize the revenue. At the same time, a finance manager can use linear regression to predict the trend in the prices of a particular stock. Based on the historical data in chronological order, a time series plot can be prepared for several years (Keller, pp. 7). Based on it, the pattern can be predicted and best decisions can be made to for effective investments (Keller, pp. 7). At the same time, sales projections can be made based on historical values. Figure 1 shows the situation. Figure 1: Sales Projections on monthly basis1 In business environment, managers come across various complex situations where relationships are not precise and clear (Victor, pp. 1). In these complex situations, linear regression can be used to develop relationships and identify the necessary patterns and hence, allow the managers to reach good decisions in a limited amount of time (Victor, pp. 1). An example of this situation could be the effect of the advertising on the sales figures for a specific product (Victor, pp. 1). The equation for linear regression is y = β0 + β1x where β1 = slope = change in mean value of Y for a unit change in x. In this case β1 = cov(x,y) / var (x). Descriptive Statistics Descriptive statistics summarizes a group of data into more presentable and understandable manner. It is used to describe the collection of data and clearly identify the trends and patterns in them. The measures of central tendency and dispersion describe that data with the use of numbers whereas the graphic representations provide a clear picture (Keller, pp. 93, 101, 102, 105). The mean is considered the single most well-accepted and important measure in the business world. It finds immense applications in the field of finance (Keller, pp.6). The relevant managers make regular decisions based on the mean returns of the portfolio investment. Therefore, this mean allows it to predict the average growth rate and mean rate of returns (Keller, pp.7). At the same time, the dispersion measures predict the variability in the mean return of the investments. The greater the variation, the higher the risk associated with the investments (Keller, pp.7). Hence, managers constantly use these measures to make good decisions in the business environment. Some of the important formulas are: Mean = Sum of elements / number of observations. (Keller, pp. 94) Variation = Sum of (obervation – Mean)2 / Number of Obervations (Keller, pp. 102) Standard deviation = sq root of variance (Keller, pp. 105) On the other hand, a histogram could give a clear picture of the mean return and the risk of the investments (Keller, pp. 31). For example: Figure 2 shows the mean yearly returns over a particular span of time. It gives the manager a clear idea of the average returns. Figure 2: DOW Yearly Return Frequency2 Comparison between different investments and stock portfolios becomes an easy job. Another example could be developing a price structure for a telephone company (Keller, pp.31). Building of graphical representations based on the data collected on consumer behaviors and number and durations of the long calls made will allow the managers to develop the best possible price structure for the product (Keller, pp.31). Coefficient of Correlation The correlation describes the strength of the relationship between the two variables (Keller, pp.118). A positive value denotes a movement of the variables in the same direction and a negative correlation signifies a movement of the variable in the opposite directions (Keller, pp.118). The coefficient of correlation can be between -1 and +1. A value of -1 tells that the two variables have a perfect negative correlation, +1 signifies a perfect positive relation whereas a value of zero signifies no relationship between the two variables (Keller, pp. 118). The formula for correlation coefficient is: (Keller, pp. 118) Coefficient of correlation = cov (x.\, y) / {std dev (x) * std dev (y)} It allows the business managers to develop strength of the relationships between the variables. For example: Using the correlation coefficient of the past figures, a marketing manager may find that the sales of the new product launched in the January 2009 are heavily dependent on its low pricing policy (Creative Research Systems, pp1). Therefore, the manager will be very reluctant to allow the business counterparts to increase the price because it will strongly impact the sales in the coming years (Creative Research Systems, pp1). Conclusion The importance of the business statistics cannot be underestimated in management functions of any organization. These statistical tools are very useful and provide the business managers with the relevant information for the decision making. The paper concludes that managers use the output of these tools at every stage of decision making and at every level of organization. The linear regression is extremely useful in planning and accounting functions. The descriptive statistics provide a clear picture of the cluster of data showing the average and the dispersions. At the same time, the accuracy of the projections and forecasting depends on the strength of the correlation. Business Statistics for contemporary decision making by Ken Black could be used for further research on the above mentioned topics. The book provides for the explanation of the concepts in detail and in a more understandable form. At the same time, it gives insights into situations leading to best decision making in the organizations. Linear regression on curvefit. com3 provides for excellent understanding of the concept of linear regression. It provides a clear picture on the concept with diagrams and formulas. Example Below are provided the IBM stock prices for the last month. Date Stock Price 12/1/2009 126.72 12/2/2009 126 12/3/2009 126.33 12/4/2009 126.04 12/7/2009 125.83 12/8/2009 125.59 12/9/2009 127.17 12/10/2009 128.11 12/11/2009 128.44 12/14/2009 128.69 12/15/2009 127.27 12/16/2009 127.48 12/17/2009 126.19 12/18/2009 126.69 12/21/2009 127.42 12/22/2009 128.69 12/23/2009 128.76 12/24/2009 129.33 12/28/2009 131.05 12/29/2009 130.59 12/30/2009 131.31 12/31/2009 129.65 Mean = 2813.35 / 22 = 128 Variance = 62.8003/22 = 2.85 Std Dev = sq rt (2.85) = 1.69 Using the Excel Regression equation: y = 0.216x + 125.3 R2 = 0.663 Works Cited Keller, G. Warrack, B. Statistics for Management and Economics. Thomson Brooks. (2003) pp. 1-16, pp. 25-68, pp. 6, 7, 8, 10, 31, 94, 102, 105, 118 Weiss, N. A. Introductory Statistics. Addison Wesley Publishing Company. (1998) pp. 38, 40 Creative Research Systems. “Correlation” Creative Research Systems. Accessed on April 15th 2010 from http://www.surveysystem.com/correlation.htm pp. 1-2 Victor, D. “The Role of Linear Regression Analysis in Costing” Ezine Articles. Accessed on April 15th 2010 from http://ezinearticles.com/?The-Role-of-Linear-Regression-Analysis-in-Costing&id=3878932 pp. 1 Read More