QUANTITATIVE AND ANALYTICAL TECHNIQUES

Quantitative and Analytical Techniques

Quantitative and Analytical Techniques

Section 1

Province

Gross Regional Product per Capita 2007 (Yuan)

Gross Fixed Capital Formation per Capita in 2007 (Yuan)

(X-MeanX)2

(Y- MeanY2)

(x-MEANX)

(Y-MeanY)

(x-MEANX)(y-MEANY)

Y

X

Beijing

58204

25000.37

200145595

1312654974

14147.2823

36230.5806

512564250.8

Tianjin

46122

24047.98

174105182

583153947.2

13194.8923

24148.5806

318637919.8

Hebie

19877

8947.05

3632979.87

4394974.111

-1906.0377

-2096.4194

3995854.413

Shanxi

16945

8575.33

5188180.33

25285001.21

-2277.7577

-5028.4194

11453521.12

Inner Mongolia

25393

18113.89

52719249.4

11693531.79

7260.80226

3419.58065

24828898.87

Liaoning

25729

14032.81

10110633.6

14104385.98

3179.72226

3755.58065

11941703.37

Jilan

19383

14663.66

14520460.9

6710272.434

3810.57226

-2590.4194

-9870980.13

Heilongjiang

18478

7525.73

11071309.5

12217956.47

-3327.3577

-3495.4194

11630510.65

Shanghai

66367

27133.48

265051172

1970790002

16280.3923

44393.5806

722744906.6

Jiangsu

33928

15206.06

18948367.5

142911998.4

4352.97226

11954.5806

52037957.91

Zhejiang

37411

16208.06

28675727.9

238318896.2

5354.97226

15437.5806

82667816.09

Anhui

12045

5469.53

28982694

98573510.89

-5383.5577

-9928.4194

53450218.88

Fujian

25908

12133.15

1638559.38

15480924.85

1280.06226

3934.58065

5036508.185

Jiangxi

12633

6154.6

22075787.1

87243433.72

-4698.4877

-9340.4194

43885845.84

Shangdong

27807

12580.94

2985473.43

34030663.14

1727.85226

5833.58065

10079565.49

Henan

16012

8593.32

5106550.25

35538520.72

-2259.7677

-5961.4194

13471423.15

Hubei

16206

7670.01

10131983.9

33263126.01

-3183.0777

-5767.4194

18358144.18

Hunan

14492

6208.42

21572938.4

55971635.56

-4644.6677

-7481.4194

34748707.14

Guangdong

33151

10499.51

125017.22

124938309.1

-353.57774

11177.5806

-3952143.72

Guangxi

12555

5938.8

24150224

88706623.14

-4914.2877

-9418.4194

46284822.78

Hainan

14555

5863.91

24891894.5

55032945.72

-4989.1777

-7418.4194

37011812.73

Chongqing

14660

9189.84

2766393.05

53486102.66

-1663.2477

-7313.4194

12164028.23

Sichuan

12893

6159.04

22034084.2

82454015.66

-4694.0477

-9080.4194

42623921.97

Guizhou

6915

3619.86

52319583.6

226755993.5

-7233.2277

-15058.419

108920976.6

Yunnan

10540

5797.01

25563922.1

130723078.1

-5056.0777

-11433.419

57808257.11

Tibet

12109

9565.85

1656981

97306769.21

-1287.2377

-9864.4194

12697852.9

Shaanxi

14607

8410.57

5965892.92

54264134.11

-2442.5177

-7366.4194

17992609.97

Gansu

10346

4669.32

38238983.5

135196880.9

-6183.7677

-11627.419

71901260.73

Qinghai

14257

8703.44

4620985.41

59543127.66

-2149.6477

-7716.4194

16587583.44

Ningxia

14649

10193.77

434699.885

53647118.89

-659.31774

-7324.4194

4829119.63

Xinjiang

16999

9570.41

1645262.19

24744847.92

-1282.6777

-4974.4194

6380576.986

Total

1081076768

5869137702

2352913452

Section 1.1

From the above calculation, it can be said that;

Y

X

Mean

21973.4194

10853.0877

Median

16206

8947.05

Range

59452

23513.62

From the calculation of the Mean value of X, it can be observed that which provinces lie in the upper quartile which is Mongolia, Zhejiang, Beijing, Tianjin, Liaoning, Jilan, Shanghai, Jiangsu, Fujian and Shangdong. Moreover, from the abobe table, it can be observed that the dispersion in the two variables across regions is higha as the range of the both the variables that are Gross Regional Product per Capita 2007 and Gross Fixed Capital Formation per Capita in 2007 varies a lot.

For Gross Regional Product per Capita 2007, the regions that lie in the lower quartile are Mongolia, Zhejiang, Beijing, Tianjin and Liaoning; however, for Gross Fixed Capital Formation per Capita in 2007 the regions that lie in the lower quartile are Jilan, Shanghai, Jiangsu, Fujian and Shangdong.

Variance of X

=

1081076768/31

=

34873444.14

Variance of Y

=

5869137702/31

=

189327022.6

Standard Deviation of X =

Square root of variance of X =

5905.374174

Standard Deviation of Y =

Square root of variance of Y =

13759.61564

The values of the standard deviations and the mean of X and Y reflects that how further away is the data set from the mean and with the calculated result, it can be observed that the data set is very close to the Mean value.

Section 1.2

Covariance of XY

(X-MEAN OF X)(Y-MEAN OF Y)/N-1

Cov (x,y)

=

2352913452

31

Cov (x,y)

=

75900433.9

Correlation

75892804

=

0.934

5905.37417

x

13759.61564

75892804

=

0.934

81255678.8

From the calculation of the correlation, it is observed that there is a strong positive relationship between X and Y, reflecting as increase in the value of Y will increase the value of X which shows positive relationship between the variables.

Correlations

VAR00001

VAR00002

Gross Regional Product per Capita 2007 (Yuan)

Pearson Correlation

1

.934 **

Sig. (2-tailed)

.000

N

31

31

Gross Fixed Capital Formation per Capita in 2007 (Yuan)

Pearson Correlation

.934 **

1

Sig. (2-tailed)

.000

N

31

31

**. Correlation is significant at the 0.01 level (2-tailed).

The above result for the data shows that there is correlation between Gross Regional Product per Capita 2007 (Yuan) and Gross Fixed Capital Formation per Capita in 2007 (Yuan). In addition to this, the value of the Pearson correlation coefficient shows that the value is in positive that is 0.934 as the value of Pearson correlation coefficient is significant that is it is are less than 0.05 which shows that the value is significant. Therefore, it can be said that there is a relationship between the two variables. In addition to this, the correlation between the variables is high as the value of Pearson Correlation is above 0.5 which reflecst that that more the value of the Pearson Correlation is graeter the more correlation exist between the variables.

Section 1.3

(a)

A common statistical way of standardizing data on one scale so a comparison can take place is using a z-score. The z-score is like a common yard stick for all ...