Quantitative and Analytical Techniques for Managers

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The regions that lie below the lower quartile of Gross Fixed Capital Formation per Capita in 2007 (Yuan) are Guangxi, Hainan, Sichuan, Guizhou, Yunnan and Gansu. However, the regions that fall below the lower quartile of the Gross Regional Product per Capita 2007 (Yuan) are Anhui, Jiangxi, Guangxi, Guizhou, Yunnan, Yunnan, Tibet and Gansu. The measures of central tendency have both strengths and weaknesses, for example, if the range between the highest and lowest figures is high, then the measures may be skewed. There are also effects of the outliers that may lead to wrong conclusion. However, the measures of central tendency are more advantageous because they help in working out the average score effectively and efficiciently. Table 1: descriptive statistics for Gross Regional Product per Capita 2007 (Yuan) Anderson-Darling A-Squared 2.450 p 0.000 95% Critical Value 0.787 99% Critical Value 1.092 Mean 21973.419 Mode #N/A Standard Deviation 13987.063 Variance 195637923.385 Skewedness 1.852 Kurtosis 3.263 N 31.000 Minimum 6915.000 1st Quartile 13575.000 Median 16206.000 3rd Quartile 25818.500 Maximum 66367.000 Confidence Interval 5130.496 for Mean (Mu) 16842.923 0.95 27103.915 For Stdev (sigma) 11177.229 18696.134 for Median 14492.000 19877.000 Table 2: descriptive statistics for Gross Fixed Capital Formation per Capita in 2007 (Yuan) Gross Fixed Capital Formation per Capita in 2007 (Yuan) Anderson-Darling A-Squared 1.632 p 0.000 95% Critical Value 0.787 99% Critical Value 1.092 Mean 10853.088 Mode #N/A Standard Deviation 6002.990 Variance 36035892.274 Skewedness 1.412 Kurtosis 1.492 N 31.000 Minimum 3619.860 1st Quartile 6183.730 Median 8947.050 3rd Quartile 13306.875 Maximum 27133.480 Confidence Interval 2201.915 for Mean (Mu) 8651.173 0.95 13055.002 For Stdev (sigma) 4797.061 8024.037 for Median 7525.730 10499.510 1 Calculate Pearson’s correlation coefficient between Gross Regional Product per Capita and Gross Fixed Capital Formation per Capita and discuss its size, sign and significance. Why do you think the correlation is high? In statistics, Pearson product-moment correlation coefficient (denoted by r) measures the linear correlation or linear dependence that occurs between linear variables. For example, in this case, the Gross Regional Product per Capita and Gross Fixed Capital Formation per Capita are the main variables. This measure shows then strength of the correlation or linear dependence between the main variables. The variable may take the value of +1 and ?1 both inclusive. If the correlation is +1 or -1, then variables are perfectly correlated. However, the inference is always the bone of contention as it depends on these rules. In this case the correlation is 0.934093899531846, this is strong correlation. It indicates that the Gross Regional Product per Capita 2007 (Yuan) and the Gross Fixed Capital Formation per Capita in 2007 (Yuan) are strongly correlated Pearson Product Moment Correlation – Ungrouped Data Statistic Gross Regional Product per Capita Gross Fixed Capital Formation per Capita Mean 21973.4193548387 10853.0877419355 Biased Variance 189327022.630593 34873444.1364433 Biased Standard Deviation 13759.6156425459 5905.37417412676 Covariance 78430448.3909785 Correlation 0.934093899531846 Determination 0.87253141314261 T-Test 14.089252394164 p-value (2 sided)