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Statistics And Research Methods, Holmes Institute, Australia

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Question 1: Australian exports (goods and services) along with its top 8 export markets in 2004-05 and 2014-15. Using this data, answer the questions below.

(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).

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

In part b) the highest in percentage value of exportswas China 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 2004-05 and the lowest was Singapore.

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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

c. Plot a relative frequency histogram for the data.

d. Construct an ogive for the data.

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

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

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Question 3: a. Using an appropriate graphical descriptive measure (relevant for time series data) describe the two variables.

The first graph of retail turn over per capita seems to be rising from 1983-2014. The second graph of final consumption expenditure is also in an uptrend since 1983-2014.

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?

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.

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

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

Answer: 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

Coefficient of correlation indicate the strength of relationship between two variables.

Correlation coeff, r: 0.9876971

P-value (two-tailed): 0.000

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

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

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

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

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

Answer: The coefficient of determination R2

Coeff of Det, R^2: 0.9755456

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).

g. Test whether FINAL CONSUMPTION EXPENDITURE positively and significantly increases with RETAIL TURNOVER PER CAPITA at the 5% significance level.

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

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

The linear regression is a strong fit for the prediction.

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