Critical Element IV: Analyze data to determine the appropriate decision for the identified problem:
The process of the analysis will start with the Calculation of the Central Tendency and the Dispersion among the values of the Variable. The Descriptive Statistics of the Sales of the Refrigerators and the requirement of the Transformers (Monthly and Quarterly) is calculated for different years. From the evaluate Central Tendency and the Dispersion among the values from the Descriptive Statistics.
The Data will than further taken for the test for the validity and reliability. The overall data for the requirement of the transformers (quarterly) and the sales of the refrigerators are assumed as valid. The Correlations were taken into considering for checking the validity of the data. The average correlation in the data of the requirements of the transformers is 72 percent and the sales of the refrigerators are 60.6 percent.
The Hypotheses for the requirement of the Transformers are: H0: μ1 = μ2 = μ3 = μ4 = μ5, H1: Means are not all equal and the Hypotheses for the sales of the Refrigerators are: H0: μ1 = μ2 = μ3 = μ4 = μ5, H1: Means are not all equal. And the Hypotheses for both the Variables are: H0: μ1 = μ2 = μ3 = μ4 = μ5, H1: Means are not all equal. The ANOVA is used to test these hypotheses and the Significant Value is less than 0.05 in first two data sets that reject the Null Hypotheses and the Significant in the third data set are greater than 0.05 that accepts the Null Hypothesis for the data.
The Regression is then done to make a model for the forecasting of the requirement of the transformers from the Sales of the Refrigerators. The Regression Analysis is done twice, first sets the intercept as nonzero and the second assumes zero intercepts. The First Regression analysis shows a model as the "y= a + bx" that identifies "y" as the requirement of the Transformers, "a" as the intercept, "b" as the coefficient and "x" as the sales of the refrigerators. "Y = 1491.57 + .257 X" the model shows the minimum requirement of the transformers will be referred as the intercept (1491.57). The model from the second regression analysis is "Y= 0.506 X". The reliability test will evaluate the best model for the data. The Adjusted R Square for the first model is 76% and the Adjusted R Square for the second model is 92 percent. The second model is assumed to be a better fit for the Case.
Appendix
Exhibit 1: Transformer requirements during the period quarterly (taken from the sales of voltage regulators)
Quarter  2006  2007  2008  2009  2010 
I  2399  2455  2675  2874  2776 
II  2688  3184  3477  3774  3571 
III  2319  2804  2918  3247  3354 
IV  2208  2343  2814  3107  3533 
Exhibit 2: Sales figures of refrigerators during the period
Quarter  2006  2007  2008  2009  2010 
I  3832  4007  4826  5411  6290 
II  5032  5903  6492  7678  8332 
III  3947  4274  4785  5774  8107 
IV  3291  3692  4972  8007  6729 
Exhibit 3: Data of both Variables Quarterly
Transformers Requirement  Sales Of Refrigerators  
2006  I  2399  3832 
II  2688  5032  
III  2319  3947  
IV  2208  3291  
2007  I  2455  4007 
II  3184  5903  
III  2804  4274  
IV  2343  3692  
2008  I  2675  4826 
II  3477  6492  
III  2918  4785  
IV  2814  4972  
2009  I  2874  5411 
II  3774  7678  
III  3247  5774  
IV  3107  8007  
2010  I  2776  6290 
II  3571  8332  
III  3354  8107  
IV  3533  6729 
Exhibit 4: Descriptive Statistics of Exhibit 1
2006  2007  2008  2009  2010  
Mean  2403.5  2696.5  2971  3250.5  3308.5 
Standard Error  102.6  189.8458  175.8574  190.7024  183.6965 
Median  2359  2629.5  2866  3177  3443.5 
Standard Deviation  205.1999  379.6915  351.7148  381.4049  367.3931 
Sample Variance  42107  144165.7  123703.3  145469.7  134977.7 
Kurtosis  1.659048  1.37015  2.58591  1.562373  2.544941 
Skewness  1.153657  0.716629  1.526163  1.04707  1.63335 
Range  480  841  802  900  795 
Minimum  2208  2343  2675  2874  2776 
Maximum  2688  3184  3477  3774  3571 
Sum  9614  10786  11884  13002  13234 
Count  4  4  4  4  4 
Exhibit 5: Descriptive Statistics of Exhibit 2
2006  2007  2008  2009  2010  
Mean  4025.5  4469  5268.75  6717.5  7364.5 
Standard Error  364.7073  492.5744  409.7197  657.1723  503.8 
Median  3889.5  4140.5  4899  6726  7418 
Standard Deviation  729.4146  985.1487  819.4394  1314.345  1007.6 
Sample Variance  532045.7  970518  671480.9  1727502  1015258 
Kurtosis  2.028929  2.920948  3.799095  5.32137  4.84535 
Skewness  1.057582  1.655113  1.94373  0.01166  0.11876 
Range  1741  2211  1707  2596  2042 
Minimum  3291  3692  4785  5411  6290 
Maximum  5032  5903  6492  8007  8332 
Sum  16102  17876  21075  26870  29458 
Count  4  4  4  4  4 
Exhibit 6: Correlation Matrix of Exhibit 1
2006  2007  2008  2009  2010  
2006  1  
2007  0.854829  1  
2008  0.833478  0.918457  1  
2009  0.762289  0.91261  0.991583  1  
2010  0.12974  0.435133  0.652096  0.726801  1 
Exhibit 7: Correlation Matrix of Exhibit 2
2006  2007  2008  2009  2010  
2006  1  
2007  0.98283  1  
2008  0.87713  0.94293  1  
2009  0.120468  0.299397  0.565491  1  
2010  0.721217  0.749792  0.600981  0.204654  1 
Exhibit 8: ANOVA of Exhibit 1
ANOVA  
Source of Variation  SS  df  MS  F  Pvalue  F crit 
Between Groups  2317232  4  579308  4.90587  0.0099  3.055568 
Within Groups  1771270  15  118084.7  
Total  4088502  19 
Exhibit 9: ANOVA of Exhibit 2
ANOVA  
Source of Variation  SS  df  MS  F  Pvalue  F crit 
Between Groups  32901659  4  8225415  8.364595  0.000936  3.055568 
Within Groups  14750412  15  983360.8  
Total  47652071  19 
Exhibit 10: ANOVA of Exhibit 3
ANOVA  
Source of Variation  SS  df  MS  F  Pvalue  F crit 
Between Groups  69857133  1  69857133  51.30541  1.48E08  4.098172 
Within Groups  51740573  38  1361594  
Total  1.22E+08  39 
Exhibit 11: Regression Analysis 1
SUMMARY OUTPUT  
Regression Statistics  
Multiple R  0.87934  
R Square  0.773239  
Adjusted R Square  0.760641  
Standard Error  226.9501  
Observations  20  
Coefficients  Standard Error  t Stat  Pvalue  Lower 95%  Upper 95%  Lower 95.0%  Upper 95.0%  
Intercept  1491.571  189.9953  7.850569  3.2E07  1092.406  1890.736  1092.406  1890.736  
Sales Of Refrigerators  0.257572  0.032877  7.834448  3.3E07  0.1885  0.326643  0.1885  0.326643  
Exhibit 12: Regression Analysis 2:
SUMMARY OUTPUT  
Regression Statistics  
Multiple R  0.98823  
R Square  0.97660  
Adjusted R Square  0.92397  
Standard Error  464.617  
Observations  20  
Coefficients  Standard Error  t Stat  Pvalue  Lower 95%  Upper 95%  Lower 95.0%  Upper 95.0%  
Intercept  0  
Sales Of Refrigerators  0.506296  0.017977  28.16287  5.86E17  0.468669  0.543923  0.468669  0.543923

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