QUESTION 1[50%]
You have been consulted by the government to investigate the demand for trans-Malaysia
Express bus services. It is believed that demand is positively related to petrol prices and the
percentage of buses arriving on time during peak periods. The following monthly data were
recorded for 2013-14.
Bus tickets sales Petrol Price Percentage of
Month (million) ($/litre) buss on time
July 22.60 1.35 93.9
August 24.80 1.33 91.3
September 23.00 1.20 92.1
October 24.09 1.13 93.9
November 23.93 1.12 93.7
December 21.08 1.16 94.7
January 21.53 1.12 94.0
February 22.41 1.13 91.7
March 26.11 1.22 91.2
April 22.80 1.24 91.2
May 25.90 1.29 91.6
June 23.00 1.28 86.6
a. Use Excel’s “Data Analysis” functions to determine the predictive model for the
above data. [8 marks]
b. Interpret the meaning of the slope coefficient, b1 and b2. [2 marks]
c. Explain why coefficient b0 would have no practical meaning in the context of this
problem. [1 marks]
d. Predict the bus ticket sales for a month with a petrol price of $1.30/litre and 90% of
buses being on time. [4 marks]
e. Construct a 95% confidence interval estimate for the mean bus ticket sales for a
month with a petrol price of $2.30/litre and 90% of the buses being on time.
[4 marks]
f. Determine whether there is a significant relationship between ticket sales and the two
independent variables at the 0.05 level of significance. [5 marks]
g. Interpret the meaning of the p-value. [2 marks]
2
h. Calculate the coefficient of multiple determination, R2
and interpret it's meaning.
[4 marks]
i. Calculate the adjusted R2
. [2 marks]
j. Perform a residual analysis on your results and determine the adequacy of this model.
[3 marks]
k. Plot the residuals against the time. Is there evidence of a pattern in the residuals?
Explain. [4 marks]
l. Determine the Durbin-Watson statistics. [8 marks]
m. At the 0.05 level of significance, is there evidence of positive autocorrelation in the
residuals? [3 marks]
QUESTION 2 [50%]
Use the Excel file – Assignment_Olympic for this question.
PART A
Suppose you think that the relationship between the number of Olympic medals regressed on
GDP per capita is likely heteroskedastic.
a. First use informal graphical methods to investigate heteroskedasticity. Create a
scatter plot with Olympic medals on the y-axis and GDP per capita on the x-axis.
[5 marks]
b. Now use another graph to investigate the same issue. Regress Olympic medals on
GDP per capita and save the residuals. Create a scatter plot with the residuals on the
y-axis and GDP per capita on the x-axis. [10 marks]
c. Looking at the two scatter plots, do you think heteroskedasticity exist? What are the
implications of heteroskedasticity on your regression analysis? [5 marks]
PART B
a. Use the Breaush – Pagan test to formally test if heteroskedasticity exists in these data.
What do you conclude? [8 marks]
b. Use the modified White’s test to formally test if heteroskedasticity exists in these
data. What do you conclude? [8 marks]
c. Use the Goldfeld-Quandt test to formally test if heteroskedasticity exists in these data.
What do you conclude? [8 marks]
d. Do you thnk it is necessary to use three different test to see if heteroskedasticity
exists in these data? Comment on the conditions under which each of these three tests
would be preferred. [6 marks]
Sample Solution