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ECON1030 - Business Statistics, RMIT University, Australia

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Question 1: Locate the data file (Assignment_BusStats.xls) on CANVAS.

A. Use the most appropriate type of graph to present the weekly closing price of Bitcoin (BIT) and provide a general description, commenting on the trend. [Topic 1]

B. Calculate the weekly return for BIT and construct a histogram. Does the data on return rates appear normally distributed? On the basis of z-scores do you find evidence of outliers? Hint: the formula for a return is (Current Price - Previous price)/Previous price multiplied by 100. [Topics 1-4]

C. Calculate and interpret the three aspects of Descriptive Analysis for weekly return: Location, Shape and Spread. Hint: make sure you interpret these measures in the context of the data and pay attention to the unit of measurement.

D. Construct a 95% confidence interval for BIT return and interpret the interval.

E. An investment advisor claimed that BIT return is 2%. Do you agree? Justify your reasoning using a two-tailed hypothesis test approach at the significance level of 5%.

F. Repeat steps 1-5 above for another financial stock traded at the Australia Securities Exchange: the Macquarie Group Limited (MAC).

G. Explore the association between BIT and MAC returns. Specifically, construct a contingency table for the positive and non-positive returns of the two stocks and calculate the following: a) Prob (BIT return is positive), b) Prob (MAC return is positive), and c) Prob (positive BIT return conditional on positive MAC return). Are returns to BIT and MAC statistically independent? Hint: use the IF function in excel to construct the four joint events: +ve and +ve returns, +ve and -ve returns, -ve and +ve returns, -ve and -ve returns.

Answer: Executive Summary: The main objective of this study is to determine the proper use of statistical tools. The variables taken into consideration for this study is BIT and MAC. The mean BIT is 3645.45 ± 4935 and the median BIT value is 829.08 and mean MAC is 82.09 ± 25.75 and the median MAC value is 81.36. The study findings suggest that there is no linear relationship between BIT and MAC, indicating that there exists nonlinear relationship between BIT and MAC. Thus, we can say that these variables depends on time

Introduction: The main objective of this study is to determine the proper use of statistical tools. The random variables are normally classified as either qualitative or quantitative variables. The use of statistical tools will differ based on the variables taken into consideration. If we are trying to find the relationship between one continuous variable and one categorical variable, then, the appropriate statistical test is either independent sample t test (comparing two group mean) or one way ANOVA

Statistical Analysis: Descriptive statistics was used for continuous variables and frequency distribution and bar chart was used for qualitative variables to assess the distribution of those variables. Pearson correlation coefficient was used to determine the relationship between two continuous variables. Independent sample t test or Mann Whitney U test was used to find the difference in mean between two groups. Sensitivity and specificity analysis was used to assess the ability of the test used.

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Descriptive Statistics: The descriptive statistics for the variables BIT and MAC is given below

 BIT MAC Mean 3645.45 82.09 Standard Error 269.23 1.40 Median 829.08 81.36 Mode 58.30 Standard Deviation 4935.00 25.75 Sample Variance 24354245.71 663.20 Kurtosis 2.28 -0.87 Skewness 1.64 0.27 Range 25934.49 101.13 Minimum 52.06 34.86 Maximum 25986.55 135.99 Sum 1224872.23 27580.87 Count 336 336

The mean BIT is 3645.45 ± 4935 and the median BIT value is 829.08, indicating that nearly 50% of the sample BIT value falls below 829.08 and nearly 50% of the sample BIT value falls above 829.08. The recorded minimum and maximum BIT value 52.06 and 25986.55 respectively. On comparing the mean and median of BIT, we can say that the distribution of BIT has longer tail towards the right side of the normal curve, indicating that the distribution of BIT is skewed right or positively skewed The descriptive statistics for the variables BIT and MAC is given below

 BIT MAC Mean 3645.45 82.09 Standard Error 269.23 1.40 Median 829.08 81.36 Mode 58.30 Standard Deviation 4935.00 25.75 Sample Variance 24354245.71 663.20 Kurtosis 2.28 -0.87 Skewness 1.64 0.27 Range 25934.49 101.13 Minimum 52.06 34.86 Maximum 25986.55 135.99 Sum 1224872.23 27580.87 Count 336 336

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The mean MAC is 82.09 ± 25.75 and the median MAC value is 81.36, indicating that nearly 50% of the sample MAC value falls below 81.36 and nearly 50% of the sample MAC value falls above 81.36. The recorded minimum and maximum MAC value 34.86 and 135.99 respectively. On comparing the mean and median of MAC, we can say that the distribution of MAC has equal tail width on both sides of the normal curve, indicating that the distribution of MAC follows normal distribution Relationship between BIT and MAC: In order to determine the relationship between BIT and MAC, we construct scatter plot From the above scatter plot, we see that there is no linear relationship between BIT and MAC, indicating that there exists nonlinear relationship between BIT and MAC. Thus, we can say that these variables depends on time

Regression Model: The regression model was constructed to predict the MAC value based on BIT and time. The regression equation is

MAC = b0 + b1 * Time + b2 * BIT

The regression output is given below

SUMMARY OUTPUT

 Regression Statistics Multiple R 0.95863911 R Square 0.91898894 Adjusted R Square 0.91850238 Standard Error 7.35179654 Observations 336

ANOVA

 df SS MS F Significance F Regression 2 204172.5 102086.2 1888.775 1.9E-182 Residual 333 17998.29 54.04891 Total 335 222170.7

 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 40.4475901 0.860686 46.99458 5.1E-149 38.75452 42.14066 Time 0.24124253 0.00612 39.41963 1.8E-127 0.229204 0.253281 BIT 0.00033746 0.00012 2.801396 0.005386 0.0001 0.000574

From the above output, we see that

MAC = 40.448 + 0.241 * Time + 0.00034 * BIT

The coefficient of determination is 0.919, which clearly indicates that the dependent variable MAC variation of 91.9% was clearly explained by the regression model while the left out variation of 8.1% remains unexplained
The overall significance model was validated using F test for overall significance. Here, the p - value was found to be less than 0.05, indicating that the estimated regression model is good fit in predicting MAC

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Conclusion: The main objective of this study is to determine the proper use of statistical tools. The random variables are normally classified as either qualitative or quantitative variables. The mean BIT is 3645.45 ± 4935 and the median BIT value is 829.08, indicating that nearly 50% of the sample BIT value falls below 829.08 and nearly 50% of the sample BIT value falls above 829.08. The mean MAC is 82.09 ± 25.75 and the median MAC value is 81.36, indicating that nearly 50% of the sample MAC value falls below 81.36 and nearly 50% of the sample MAC value falls above 81.36. The regression equation to predict MAC using Time and BIT is given below

MAC = 40.448 + 0.241 * Time + 0.00034 * BIT

The coefficient of determination is 0.919, which clearly indicates that the dependent variable MAC variation of 91.9% was clearly explained by the regression model while the left out variation of 8.1% remains unexplained

Question 2: Write a ministerial brief of no more than 200 words containing no more than three graphs on whether you can confidently recommend investing in the Bitcoin, as compared with MAC. Hint: draw on the relevant evidence you have gathered from Part A, as well as other information/evidence not covered here but you believe is useful.

Answer: The main objective of this study is to determine the proper use of statistical tools. The random variables are normally classified as either qualitative or quantitative variables. Descriptive statistics was used for continuous variables and frequency distribution and bar chart was used for qualitative variables to assess the distribution of those variables. Pearson correlation coefficient was used to determine the relationship between two continuous variables. Independent sample t test or Mann Whitney U test was used to find the difference in mean between two groups. Sensitivity and specificity analysis was used to assess the ability of the test used. The Histogram for the two variables BIT and MAC is given below  From the above graph, it clearly shows that the variable BIT has outliers and hence do not follow normal distribution while the variable MAC follows normal distribution approximately. The mean BIT is 3645.45 ± 4935 and the median BIT value is 829.08. The mean MAC is 82.09 ± 25.75 and the median MAC value is 81.36. The study findings suggest that there is no linear relationship between BIT and MAC, indicating that there exists nonlinear relationship between BIT and MAC. Thus, we can say that these variables depends on time.

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