# Standard Deviation

The descriptive statistics data of the daily return calculated by excel are the following:

• Mean 0. 04%
• Standard Error 0. 03%
• Median 0. 08%
• Mode -0. 16%
• Standard Deviation 0. 010444
• Sample Variance 0. 000109
• UK rotors 1. 102023
• Keenness -0. 23502
• Range 0. 077052
• Minimum -0. 04209
• Maximum 0. 034966
• Sum 0. 4047 Coo NT 1087

Among all the 1 087 dates, the returns of all ordinaries index have the mean of 0. 04%, a median of 0. 03%, and the most frequent data of -0. 16%. Also, the range of these returns is 0. 077052. The maximum and minimum return of all ordinaries index is 0. 34966 and -0. 04209 respectively. The descriptive statistics data of the daily return can form a histogram through the excel as well. A display like following:

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Basing on the question, the data has been divided into two separate groups. The first group contains all the positive daily return Art of all ordinaries index. On the other hand, the second group is made up of all the negative returns. As a result of the two groups of data, it is obvious that the two sample hypothesis test should be chosen to perform the statistical test.

The t-test is chosen to perform the two sample hypothesis test because the population standard deviation is unavailable. Additionally, because of the changeable variances, choosing unequal variance is more suitable. Moreover, it is essential to calculate the sample mean and sample standard deviation of these two groups of data before the statistical test. According to the excel result, the sample means of groups and groups are 1169918868 and 1144404303 respectively. On the other side, the sample standard deviations are 357047870. And 388074423. 4 The hypothesis test assumes HO: the trading volume is larger when the all ordinaries index increases than the all ordinaries index decreases HI: he trading volume is less when the el ordinaries index increases than the all ordinaries index decreases. Therefore, HO: Pl-up>O HI: WI-up -1. 646317286), do not reject HO and claim that there is insufficient evidence to say something other than the trading volume is larger when the all ordinaries index increases than the all ordinaries index decreases.

According to the question, the time index t and all ordinaries index Ext are used as the independent variable and dependent variable respectively. By using the excel regression analysis, the result is the following: Coefficients Intercept 4191. 64 X Variable 1 0. 4765 Regression Statistics R Square 0. 131 787415 The intercept of 4191. 64 in the table is the estimate of the regression intercept which is known as BOO. Additionally, the estimate of the regression slope is the value of 0. 4765 which is also called a ball .

Referring to the original formula, the regression equation for this situation is The slope of the regression means that when the time index increases by 1 day, on average, the all ordinaries index will increase by \$0. 4765. Also, the intercept of the regression shows when the time index is O (the day before the first trading day), the average price of the all ordinaries is \$4191. 64. Moreover, the R square (re) is called the coefficient of determination. It has a specific region which is. The value of re in this situation is computed as 0. 131787415 which is involved in the region.

Comparing the re =0. 131787415 with O and 1, it is obvious that the revalue is closer to O. It indicates that the linear relationship between time index and all ordinaries index is not strong or weak. In addition, the regression model captured less variation. Furthermore, the Durbin- Watson (DO) test is applied to check the independence of the residuals over time. HO assumes residuals are not correlated and HI assumes positive autocorrelation exists. By using excel, the result of the DO test is 0. 013607965. In contrast to the critical value ODL= 1. 899 and ODL = 1. 04, DO is less than ODL which rejects the HO and claims that the autocorrelation exist. This result illustrates that the residuals are dependent which is not good. It is also shown through the residual plot below, the dots on the residual plot haven’t formed a straight line. It is said that the errors are not independent. A satisfied regression assumption is that the two variables have a linear relationship. Tests are used to confirm whether the assumptions of the regression are satisfied. HO assumes there is no linear relationship between time index and all ordinaries index.

HI assumes the time index and all ordinaries index have a linear relationship. The null and alternative hypotheses are the following:

HO: џl = 0 HI:

According to the excel result, the equals the slope of this regression model 0. 4765 and equals 0. 0371. The result equals 12. 839226 and it is less than the critical value. So the decision does not reject HO and claims there is insufficient evidence that time index affects all ordinaries index. By looking at the scatter plot above, the relationship between time index and all ordinaries index are weak and almost independent.

To compute the 90% prediction interval for all trading days during the study period, the formula ( Referring to the question equals 0. 1 and equals 0. 05. can be used. In conclusion, the returns of the all ordinaries index are not very good during the study period. Furthermore, it seems unlikely that the variations of the time index will have any impact on the change of the all ordinaries index. Nevertheless, the prediction of the all ordinaries index is almost not influencing by the variation of the time index.

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