Introduction
The scenario at hand involves data modeling through the regression. The purpose of the regression model is to project the number of transformers that would be required by A-Cat Corporation for a given level of sales of refrigerators. A-Cat Corporation is committed to the use statistical evidence in its operations. In the recent past, the company has had problems with predicting the number of transformers that it requires for the production of refrigerators. The company has been using the averages to determine the number of transformers that it requires in its inventory. However, this has resulted in shortages during certain periods while in other periods A-Cat Corporation was finding itself with excess inventory. From a business perspective, having shortages may result in a myriad of problems, including the stoppage of production and even lawsuits due to failure in the delivery of orders resulting in the breaching of contracts. On the other hand, holding excess inventory is also not good for the company considering the fact that the holding costs for the inventory may be extremely high, some inventory may become obsolete while still in storage, and it also results to negative implications for the company's working capital (Slack, Chambers, & Johnston, 2010).
The operations manager at A-Cat Corporation had managed to collect data on the number of transformers required for a given level of sales over the years between 2006 and 2010. The data is provided in the exhibit below and from the data there will be developed a regression model for use in the prediction of the future requirements of transformers. This report will be directed to the vice president Arun Mittra through the company’s operations manager who is Ratnaparkhi. The report is also designed in a manner that can easily be understood by all employees in the organization and especially the employees at the operational and tactical levels of the organization who will be involved directly in placing the requisitions for the purchase of transformers.
Analysis Plan
Quantifiable Factors Affecting the Performance of the Operational Processes.
The number of Transformers. A-Cat Corporation has always been involved in estimation of the number of transformers that are required to meet the demand for refrigerators. From the data above, the number of transformers required is not equal to the number of refrigerators sold. However, it is quantifiable as there is a hypothesized positive relationship between the number of refrigerators sold and the number of transformers that the organization requires. In the analysis, we plan to use the number of transformers as the dependent variable (Sharpe, De Veaux, & Velleman, 2015).
The Amount of Sales in Units. The second quantifiable element in the analysis is the number of unit sales for the refrigerators for a given period. Considering that the refrigerators are sold as whole units and not as subparts makes it easy for the analysis to consider the modeling of the quantifiable data provided herein. Based on the number of refrigerators that A-Cat Corporation sells, it is, therefore, possible to predict the amount of transformers that the company requires to its inventory. In the proposed regression analysis we propose to use the sales units as the independent variable.
Problem Statement
The ability to accurately estimate the inventory levels is one of the most important roles of the operations manager. It does not only enhance the competitiveness of the company but also ensures that shortage and excess capacity related problems are also avoided. A-Cat Corporation had been continuously involved in the estimation of the number of transformers required for a specified level of sales. The usual method used by the corporation was looking at the sales figures for three months and also the sales figures of the last two years for the same month. Next, the company would make a guess on how many transformers the company would be required. The guess work resulted in either too many transformers in stock or at times; the company would find that there were not enough transformers to meet the normal production levels. When tasked with the role of developing a more accurate model for predicting the demand for the transformers, the operations manager resulted in using ANOVA and descriptive statistics but even with the two measures, the company still used some level of guesswork hence warranting the need to develop a more accurate prediction model.
Statistical Tools and Methods of analysis
The operations manager at A-Cat Corporation collected and summarized the data for the sales units and the matching number of transformers that the company required. The data is provided in a table provided in section one of this report. Using the data, the report presents the regression model that would be appropriate for the prediction of future needs for transformers (Sharpe, De Veaux, & Velleman, 2015).
The regression model was the most preferred statistical tool for data analysis. There are two types of regression which include the multivariate linear regression model and the linear regression model. In this analysis, we assume that the only factor affecting the demand for the transformers at A-Cat Corporation is the number of refrigerators sold; hence, the resolve to use linear regression model (Applied Regression & Analysis of Variance).
The data used in this analysis is discrete in nature meaning that the data can be classified into categories based on counts. Consequently, only finite numbers will be accepted in the development of the model and return, it is expected that a discrete number will always result from the model thus developed (Slack, Chambers, & Johnston, 2010).
The regression model alone does not provide adequate information. It is based on this observation that the analysis also includes the r-squared value. The R-squared value is a statistical measure that shows how close a certain dataset set fits the regression line. It is also referred to as the coefficient of determination and in the case of the multiple linear regression model, the coefficient of determination for multiple regression. Notably, the r-squared value shows to what extent the organization should depend on the model or in other words, what number of data points are represented by the regression model. Statistically, the r-squared value is an indicator of the explanatory power of the developed regression model. Rationally, the use of the coefficient of determination is justified by the fact that it is an appropriate indicator of the level of dependence that the management at A-Cat Corporation can give to the model (Chiarini, 2015).
The quantitative method that will best inform data decisions is the t-value. The f-statistic indicates whether or not the model should be accepted. The f-statistic is used alongside the confidence level, which is an indicator of the maximum margin of error that the company is ready to accept. Statistically, the appropriate significance level is the 5% confidence interval, which means that the model should be accepted only if it can be used to explain 95% of all the movements in the data (Applied Regression & Analysis of Variance).
Data Analysis
The determination of the regression model can be completed using two procedures. The first procedure presents the data in the form of a chart or a scatter plot. On the scatter plot, adding a trend line together with the regression equation and the value of the coefficient of determination presents the easiest way to present the equation, and it also provides a visual on where the data points lie on the graph. However, this method does not include the margin of error in the prediction, hence the need to use the second method. The scatter plot together with the regression model is as presented below:
Based on the data analysis as shown in the scatter plot above, the regression model can be expressed as y = 0.2809x + 1270.3. The number of transformers required (Y) is the dependent variable while the sales units (X) is the independent variable. BY replacing the value of X with the amount of sales in the equation, the analyst can determine the amount of transformers that the company requires in its stock.
Further, the model indicates an R-squared value of 0.2702. The r-squared value, therefore, indicates that the equation thus developed has a predictive value with regard to the goodness of fit of 27%. Consequently, it should be determined that the sales units data that was used in the analysis was fit for the analysis and prediction of the transformers.
Other than using the scatter plot, the use of the data analysis tool in Excel can be used to better predict the demand for the transformers. The output from the data analysis tool is presented as shown below. The process of analysis includes clicking on the data tab, selecting the data analysis tool to access the data analysis tool pack followed by the selection of the regression as the item of analysis. Under regression there are various items that the analyst should select to produce holistic summary output such as the one shown below. These elements include the confidence level, the residuals, and the normal probability plot (Sharpe, De Veaux, & Velleman, 2015).
Y=1270.29+0.280941X+601.9489
Further, the model indicates a p-value of 0.049 or 4.9%. At a confidence level of 95%, the model can be used to predict the future requirements for the transformers. The P-value indicate that the result from the regression model is reliable. It means that there are at least 95% chances of predicting accurately the number of transformers required. Given the p-value, therefore, the regression model provided above should be accepted as it has an appropriate level of explanation (Bansal, 2015).
Recommended Operational Improvements for Stakeholders
Based on the data analysis, this report recommends that the company drops guesswork in the estimation of the number of transformers required and replace it with the regression model herein developed. The model which is expressed as shown below has a p-value of 4.9% which means that it has an explanatory or prediction power of at least 95.1%. It means that the error in the prediction cannot exceed 5% which means that if there are shortages they cannot exceed 5% and if there are excesses they cannot be more than 5% of the value predicted by the model. Consequently, this model shows that the number of refrigerators sold is the best indicator of the number of transformers that the company requires.Y=1270.29+0.280941X+601.9489
Secondly, the paper recommends that the company establishes lasting relationships with the suppliers for just in time management system for the inventory. With the ability to predict the demand for the transformers, the company can precisely design a model for the management of inventory. It would require the company to identify dependable suppliers who would never fail the company with regard to the supply of materials and the transformers. The system should ensure that the transformers and or other required materials are supplied only when needed ensuring that the company does not incur high holding costs for the materials and also that it does not suffer losses due to shortages (Chiarini, 2015).
Thirdly, this report recommends that the company develops a system for determining the optimum order levels. The company can determine this by determining the economic order quantity levels. The economic order quantity refers to the amount of supplies that the company to ensure that the cost of ordering the materials is maintained at the lowest possible while at the same time ensuring that the cost of handling the materials is maintained at the lowest point possible. The company can use the data and the regression model to determine the actual demand for the transformers and based on this data determine the economic order quantity. By creating the system for the determination of the economic order quantity the company will be able to determine the quantity for every order to be placed with the just in time inventory system. In addition to the economic order quantity the company can determine the other measures, including the reorder levels, the maximum inventory levels, and the time it takes for an order to reach the company among other factors (Chiarini, 2015).
Focusing on the possibility of having excess inventory, this has implications for the performance of the company. If the company holds high levels of inventory, it may have a lot of it's the capital tied up in the inventory. As a result of the tied up capital, the company may not be able to meet its current and maturing debt obligations, especially when considered that the company may find it difficult to convert the inventory into cash. Consequently, the company may not be able to pay the wages of the employees and this is just one of the reasons why the employees at the tactical and operational levels of the organization should also be involved in the planning for the inventory. Consequently, it is one of the reasons why the company should use the regression to estimate the demand for the transformers.
References
Applied Regression & Analysis of Variance. (n.d.). Retrieved February 7, 2016, from http://www.enotes.com/research-starters/applied-regression-analysis-variance
Bansal, G. (2015, September 28). What is the difference between coefficient of determination, and coefficient of correlation? Retrieved January 24, 2016, from http://blog.uwgb.edu/bansalg/statistics-data-analytics/linear-regression/what-is-the-difference-between-coefficient-of-determination-and-coefficient-of-correlation/
Chiarini, A. (2015). Sustainable Operations Management: Advances in Strategy and Methodology. New York: Springer.
Linear Regression. (n.d.). Retrieved January 24, 2015, from http://www.stat.yale.edu/Courses/1997-98/101/linreg.htm
Rumsey, D. J. (n.d.). Types of Statistical Data: Numerical, Categorical, and Ordinal. Retrieved February 7, 2016, from http://www.dummies.com/how-to/content/types-of-statistical-data-numerical-categorical-an.html
Sharpe, N., De Veaux, R. & Velleman, P. (2015). Business statistics. 3rd ed. Boston: Addison Wesley.
Slack, N., Chambers, S. & Johnston, R. (2010). Operations management. Harlow, England: Financial Times Prentice Hall.
