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HI6007 Statistics and Research Methods for Business Decision Making Assignment, Holmes Institute, Australia

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Question 1 -

(a) Use an appropriate graphical technique to compare the value of Australian exports (in A\$ bn) in 2004-05 and 2014-15, broken down by country of export destination.

(b) Use an appropriate graphical technique to compare the percentage value of Australian exports (in %) in 2004-05 and 2014-15, broken down by country of export destination.

(c) Comment your observations in parts (a) and (b).

In part a), China recorded the highest export of goods and service in 2014-2015 and United States recorded the least in that year. In 2004-05, Japan recorded the highest export and the least was Singapore.

In part b) China was still the highest in percentage value of exports with 40.4% in 2014-15. United Kingdom recorded the lowest percentage value of exports in 2014-15.Japan recorded the highest percentage value of exports in 2004-05and the lowest vas Singapore.

Question 2 -

a. Construct a frequency distribution and a relative frequency distribution for the data.

b. Construct a cumulative frequency distribution and a cumulative relative frequency distribution for the data.

 Classes frequency Relative frequency Cumulative frequency Cumulative Relative frequency 30-40 2.00 0.05 2.00 0.05 40-50 4.00 0.10 6.00 0.15 50-60 8.00 0.20 14.00 0.35 60-70 11.00 0.28 25.00 0.63 70-80 8.00 0.20 33.00 0.83 80-90 5.00 0.13 38.00 0.95 90-100 2.00 0.05 40.00 1.00 40.00

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c. Plot a relative frequency histogram for the data.

d. Construct an ogive for the data.

Relative frequency histogram for the data

e) What proportion of the grades is less than 60?

14/40 = 0.35

f) What proportion of the grades is more than 70?

15/40 =0.375

Question 3 -

a. Using an appropriate graphical descriptive measure (relevant for time series data) describe the two variables.

Both graphs of the times series data appears to be in rising gradually since 1993 to 2014.

b. Use an appropriate plot to investigate the relationship between FINAL CONSUMPTION EXPENDITURE and RETAIL TURNOVER PER CAPITA. Briefly explain the selection of each variable on the X and Y axes and why?

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c. Prepare a numerical summary report about the data on the two variables by including the summary measures, mean, median, range, variance, standard deviation, coefficient of variation, smallest and largest values, and the three quartiles, for each variable.

x- variable is retail turnover per capita and y-axis is Final expenditure.

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d. Calculate the coefficient of correlation (r) between FINAL CONSUMPTION EXPENDITURE and RETAIL TURNOVER PER CAPITA. Then, interpret it.

Descriptive Statistics Return per capita

 Mean 2205.76 Median 2180.2 Range 1558.7 Variance 295060 Standard deviation 543.194 Co-efficient of Variation 24.63 Minimum 1455.9 Maximum 3014.6 1st Quartile 1641.8 2nd Quartile 2180.2 3rd Quartile 2799.7

Descriptive Statistics Final expenditure

 Mean 146020 Median 139137 Range 151259 Variance 2.2 Standard deviation 46904 Co-efficient of Variation 32.12 Minimum 81889 Maximum 233148 1st Quartile 103169 2nd Quartile 139137 3rd Quartile 192828

Coefficient of correlation

Correlation coeff, r: 0.9876971

Critical r: ±0.1716148

P-value (two-tailed): 0.000

The co-efficient of correlation indicate the strength and direction of the relationship between variables (Bluman, 2009).

The coefficient of correlation is 0.988 which means that there is a strong positive correlation between Return per capita and final expenditure.

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e. Estimate a simple linear regression model and present the estimated linear equation. Then, interpret the coefficient estimates of the linear model.

Simple linear regression

Linear equation is given by Y= B0 +BX1

Regression Results:

Y= b0 + b1x:

Y Intercept, b0: -42102.53

Slope, b1: 85.28681

The linear equation is Y= -42102.53 +85.29X1

f. Determine the coefficient of determination R2 and interpret it.

The coefficient of determination R2

Coeff of Det, R^2: 0.9755456

Regression analysis show the relationship between variables(Patten & Newhart, 2017).

Coefficient of Det R^2 is 0.976 meaning that 97.6% of the variation of the dependent variable (Final expenditure) can be explained by the independent variable (return in capital).

The p-value 0.000< 0.05 appears to be significant.

g. What is the value of the standard error of the estimate (se). Then, comment on the fitness of the linear regression model?

Standard error

Standard error is 7363.225. The linear regression is a strong fit for the prediction.

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