Analyze data to determine the appropriate decision for the identified problem Harvard Case Solution & Analysis

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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