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 non-zero 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 | P-value | 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 | P-value | 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 | P-value | F crit |
Between Groups | 69857133 | 1 | 69857133 | 51.30541 | 1.48E-08 | 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 | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |||
Intercept | 1491.571 | 189.9953 | 7.850569 | 3.2E-07 | 1092.406 | 1890.736 | 1092.406 | 1890.736 | ||
Sales Of Refrigerators | 0.257572 | 0.032877 | 7.834448 | 3.3E-07 | 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 | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | ||
Intercept | 0 | ||||||||
Sales Of Refrigerators | 0.506296 | 0.017977 | 28.16287 | 5.86E-17 | 0.468669 | 0.543923 | 0.468669 | 0.543923
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