Selecting the appropriate family of statistic
Introduced to the case study and the statistical requirements, we believe that amongst all the family of statistics, regression analysis will be the most appropriate data analysis method to achieve the desired outcome. Important to note, regression analysis belongs to family of statistical techniques and includes methods which are used for forecasting, variance analysis, et cetera. Henceforth, considering the two requirements laid down by Mittra for his operations head as part of which she is required to forecast the sales and explain the past variance, regression analysis and related tools will be the most appropriate statistical tools to perform the analysis.
Type of data
Before performing the statistical analysis the given data, it is important for the analyst to understand the type of data involved in the analysis. Referring to the given case study details, we see that the case involves discrete data. Important to note, discrete data are represented by items or variables that are countable. Henceforth, here the two variables, i.e., number of transformers and sales units are both countable and are covered under discrete data.
Accordingly, to understand any kind of statistical relationship between these two variables, it is important that we use regression analysis.
Selecting the tools of regression analysis
Regression analysis includes a wide array of multiples with each multiple having its own relevance in terms of explaining the relationship of the variables in the given data. However, for the given case study where the operations head is required to develop a forecast model for transformer requirement (dependent variable) based on the sales of refrigerators (independent variables) we will use the linear regression model as the forecast is based on a single variable, i.e. sales of refrigerators. In addition, we will use the data from 2006-2010 (on a quarterly basis) to evaluate whether the mean requirement of transformers has changed over the years. For this purpose, we will rely on the outcome of the single-factor ANOVA table because the outcome of the table helps the analysts to gauge whether the variance of the data set over the period has changed or not.
Description of quantitative method
In order to proceed with the forecasting model, we will use the transformer requirement as the dependent variable while sales of refrigerators will be used as an independent variable. Thereafter, we will use the ‘Data Analysis’ tool for conducting the linear regression model and creating a regression equation to forecast the transformer requirement. However, a considerable point is that in order to reduce the coefficient error residual term, a daily data of transformer usage and sales refrigerator would have been more useful.
Similarly, for explaining the variance of transformer usage over the years, a daily based data would have been more explanatory and with the least error term, thus enhancing the validity of single-factor ANOVA.
Data Analysis
Forecasting Model:
Therefore, using the regression analysis, we found the forecasting model:
Y= 1233.5+ 0.3149X
In addition, we can also see that the R-square multiple of the model is at 85.73%. This confirms a strong validity of the regression model in forecasting the transformer requirement as it shows that the sales of refrigerators explains 85.73% of the variation in requirement of transformers.
Variance Analysis
As explained in the previous sections, for the purpose of analyzing the variance amongst the transformer requirement data from 2006-2010, we have decided to use single-factor ANOVA table. Important to note, we will be using quarterly data presented in Exhibit 2 for the analysis.
-Hypothesis
Here, Null Hypothesis(Ho): Variance is same
And, Alternative Hypothesis(HA): Variance is not same
Data
ANOVA Table
Referring to the above table, we can see that at 5% level confidence, F-Statistic is greater than F-Critical, we reject the null hypothesis a conclude that the variance of data, i.e. transformer requirement has changed from 2006-2010.
Using Data for decision making
Using the above analysis, we have developed a forecasting model for the transformer requirement. The model is highly credible as it carries a high R2 multiple of 85.73% indicating that the sales of refrigerators largely explains the variation in the requirement of transformers. Hence, the operation staff can largely rely on this forecasting model for estimating the amount of transformers required.
Secondly, ANOVA table also confirms that the transformer requirement has changed from 2006-2010 and all of the further decisions should be taken accordingly. We are also assured of the reliability of the ANOVA table as both the p-value and F-Statistic confirms the rejection of null hypothesis at 5% level of significance.
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/
Linear Regression. (n.d.). Retrieved January 24, 2015, from http://www.stat.yale.edu/Courses/1997-98/101/linreg.htm
One-Way ANOVA. (n.d.). Retrieved February 7, 2016, from http://www.reliasoft.com/newsletter/v9i1/doe_techniques.htm
One-Way ANOVA. (n.d.). Retrieved February 7, 2016, from https://explorable.com/one-way-anova
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
