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Revision Session
1)
Using the data here, which refers to Australian investment and government
expenditure.
a)
Suggest a model that would enable you to test the hypothesis that government
expenditure affects investment.
b)
Run an OLS regression based on the above model, interpret the coefficients, tstatistics and R2 statistic.
c)
In Excel create 3 lags of each variable, calling them G(-1) G(-2) etc.
d)
Test for causality between these variables by regressing the lags of one
variable against the other variable:
yt   0  1 xt 1   2 xt 2   3 xt 3  ut
Do this for both variables and interpret the t-statistics on the three lags, if any are
significant, it indicates causality from the lagged variable to the dependent variable.
2) a)Find the annual interest rate required for £5,000 to grow to £7,000 in 4 years.
b) Suppose a bank pays annual interest of 6%. How long will it take for £3,000 to
grow to £9,000?
c) £7,000 is invested for three years at 3% per annum. Calculate the total value of the
investment and compare the return on the investment when interest is compounded
semi-annually.
d) With reference to c), calculate the total value of the investment when compounded,
(i) monthly, (ii) daily, (iii) continuously
3)A firm has a production function given by: y = 20*(K^0.6)*(L^0.7), and it wants to
know how output will vary with labour and capital inputs. For labour and capital
input levels of 1,2,…,20 show in a table the firm's output.
4) Given the following data on the exchange rate (cne and uce) found here, produce a
histogram of the data to determine if it is normally distributed.
b) Determine the mean, median and mode, are they similar?
c) What is the series variance
d) What are the levels of kurtosis and skewness of this distribution.
5) a) Set up a worksheet with time in the first column running from 1980 to 2005 and
GDP in the second column. In a parameter box away to the side put entries for the
initial value of GDP and for the growth rate. In the parameter cells set these values
initially to 7000 and 0.015 respectively. In the table put a formula for GDP in 1981
that refers to these initial values.
b) Document the time path for GDP for the period 1980-2005. Then change the
growth rate to 4% per annum via the parameter box. Plot a chart of GDP for the two
growth rates specified.
6) 7) Given the following equations, use the matrix methodology in Excel to
determine the values for x, y and z.
7x + 4y – 2z = 2
x – 7y + 4z = 36
2x – 4y -7z = -4
7) The conclusion from a 40-state poll conducted by the Joint Council on Economic
Education is that students do not learn enough maths. The findings were based on test
results from students who took a 46 question, multiple-choice test on basic concepts
such as calculus and matrix algebra. The following table gives sample data on the
number of questions answered correctly.
17 17 12 24 12 14 18 23 31 14 19 19 17 9 19
28 24 16 28 13 20 12 27 18 22 18 30 16 29 18
16 14 8 25 22 15 34 24 17 9
Summarise these data in Excel using:
a) A frequency distribution (use Data>Sort to arrange the data in order). Use
class intervals 0,8,16,24,32,40. Are the data ‘Normally’ distributed in a bellshape, or are they ‘skewed’?
b) Calculate a cumulative frequency distribution, where each row adds all
previous frequencies to the current frequency. (note that you need a start value
in C2).
(Solutions will follow next week)