Question

Question 1: (24 marks)

Because inflation reduces the purchasing power of the dollar, investors seek investments that will provide protection against inflation; that is, investments that will provide higher returns when inflation is higher. It is frequently stated that ordinary shares provide just such a hedge against inflation. The annual Australian inflation rate (as measured by percentage changes in the consumer price index) and the annual All-Ordinaries Index from 1995 to 2015 are stored in file INFLATION.XLSX.
Using EXCEL, answer below questions:
a. Using an appropriate graphical descriptive measure (relevant for time series data) describe the two variables. (2 marks)
b. Use an appropriate plot to investigate the relationship between RATE OF INFLATION and ALL-ORDINARIES INDEX. Briefly explain the selection of each variable on the X and Y axes and why? (3 marks)
c. Prepare a numerical summary report about the data on the two variables by including the summary measures, mean, median, range, variance, standard deviation, and coefficient of variation, smallest and largest values, and the three quartiles, for each variable. (4 marks)
d. Calculate the coefficient of correlation (r) between RATE OF INFLATION and ALL-ORDINARIES INDEX. Then, interpret it. (2 marks)
e. Estimate a simple linear regression model and present the estimated linear equation. Then, interpret the coefficient estimates of the linear model. (5 marks)
f. Determine the coefficient of determination R2 and interpret it. (2 marks)
g. Test the significance of the relationship at the 5% significance level. (4 marks)
h. What is the value of the standard error of the estimate (se). Then, comment on the fitness of the linear regression model? (2 marks)

Year 1995 Rate of inflation (%) 1.9 4.6 2.6 1996 1997 1998 0.3 All-Ordinaries index 2000.8 2231.7 2662.7 2608.2 2963.0 3115.9 3352.4 3241.5 3032.0 1999 1.3 2.4 2000 5.9 2001 2002 2003 2.9 3.0 2004 2.4 3499.8 2005 2.4 2006 2.9 4197.5 4933.5 6337.6 2.5 4.3 5513.5 2007 2008 2009 2010 2.4 4127.6 4632.8 2.9 2011 3.3 4553.9 2012 1.6 2013 2.5 4385.2 5110.5 5423.9 5713.4 2014 2.9 2015 1.5

Answer 1

The data is:

Rate of inflation (%)	All-Ordinaries index
1.9	2000.8
4.6	2231.7
2.6	2662.7
0.3	2608.2
1.3	2963
2.4	3115.9
5.9	3352.4
2.9	3241.5
3	3032
2.4	3499.8
2.4	4197.5
2.9	4933.5
2.5	6337.6
4.3	5513.5
2.4	4127.6
2.9	4632.8
3.3	4553.9
1.6	4385.2
2.5	5110.5
2.9	5423.9
1.5	5713.4

a. Using an appropriate graphical descriptive measure (relevant for time series data) describe the two variables. (2 marks)

The time series plot for Rate of inflation (%) is:

The time series plot for the All-Ordinaries index is:

b. Use an appropriate plot to investigate the relationship between RATE OF INFLATION and ALL-ORDINARIES INDEX. Briefly explain the selection of each variable on the X and Y axes and why? (3 marks)

The appropriate plot to investigate the relationship between RATE OF INFLATION and ALL-ORDINARIES INDEX is:

The All-Ordinaries index is dependent on the Rate of inflation (%).

So, the All-Ordinaries index is on the Y-axis and the Rate of inflation (%) is on the X-axis.

c. Prepare a numerical summary report about the data on the two variables by including the summary measures, mean, median, range, variance, standard deviation, and coefficient of variation, smallest and largest values, and the three quartiles, for each variable. (4 marks)

The summary statistics of Rate of inflation (%) is:

	Rate of inflation (%)
count	21
mean	2.690
sample standard deviation	1.193
sample variance	1.424
minimum	0.3
maximum	5.9
range	5.6
skewness	0.798
kurtosis	2.038
coefficient of variation (CV)	44.35%
1st quartile	2.400
median	2.500
3rd quartile	2.900
interquartile range	0.500
mode	2.400

The summary statistics of the All-Ordinaries index is:

	All-Ordinaries index
count	21
mean	3,982.733
sample standard deviation	1,237.248
sample variance	15,30,783.220
minimum	2000.8
maximum	6337.6
range	4336.8
skewness	0.183
kurtosis	-1.010
coefficient of variation (CV)	31.07%
1st quartile	3,032.000
median	4,127.600
3rd quartile	4,933.500
interquartile range	1,901.500
mode	#N/A

d. Calculate the coefficient of correlation (r) between RATE OF INFLATION and ALL-ORDINARIES INDEX. Then, interpret it. (2 marks)

r²	0.002
r	0.039
Std. Error	1268.430
n	21
k	1
Dep. Var.	All-Ordinaries index

The coefficient of correlation (r) between RATE OF INFLATION and ALL-ORDINARIES INDEX is 0.039.

There is a very weak positive relationship between RATE OF INFLATION and ALL-ORDINARIES INDEX.