Forecasting for Business, Semester 2 2012
Assessment Assignment 2
Due date: Friday 19 October 2012
This assignment contributes 20% towards assessment in this unit.
Please note that your answers must be accompanied by graphs and Excel/ EViews outputs. Relevant
outputs must be annotated for clarity of information and for drawing marker’s attention on which you
have based your comments and discussion. Do not expect the marker to interpret computer output on
your behalf.
Question 1 (It is an open-ended question.)
A builder wishes to determine the type of homes that would be attractive to residents of the community in
a regional university town. The builder has collected the following data from a local real estate agency
that is also provided in file “ETW3232Ass2-2012dat.xls”. The data includes the sales price Y in units of
ten thousand dollars, house size X 1 in square metres, number of bedrooms X 2 , number of bathrooms X 3 ,
and age X 4 in months for each of the 60 single-family residences recently sold in the community.
(a) Develop a regression model that can be used for predicting sales price of houses in the
University town.
Note: Your modeling process should include, among other things, plots of data to ascertain the type of
relationship that exists among variables, and matrix of inter-correlations to identify any collinearity
problems.
(b) Perform residual analysis to make sure no pattern is left in the errors. (This should include
plot of residuals, and checking of model assumptions.)
(c) Predict sale price of a 48 months old house with 4 bedrooms and 2 bathrooms of size 190
square metres, and obtain 95% prediction interval.
(d) Write a brief (non-technical) report (not exceeding 500 words) that includes an explanation of
results as well as a summary of findings for the builder.
Res
No.
Size
(Sq
metres) BedRms BathRms
Age
(months)
Price
($’10, 000)
1 94 2 1 35 143.5
2 120 3 1 36 139.0
3 80 5 2 36 140.5
4 85 2 2 41 139.9
5 112 3 2 40 142.0
6 112 2 1 10 145.0
7 164 5 3 64 170.5
8 149 4 2 19 176.0
9 117 2 2 16 159.0
10 80 2 1 37 136.0
11 67 1 1 41 128.0
12 94 3 2 35 139.5
13 181 5 2 52 195.0
14 194 4 2 12 242.5
15 187 5 3 76 175.0
16 136 3 2 102 150.0
2
17 114 2 1 69 148.5
18 161 4 2 67 198.0
19 120 3 2 11 169.4
20 185 4 2 9 215.0
21 174 2 1 14 177.9
22 147 2 2 11 170.0
23 178 2 2 14 184.0
24 133 5 2 16 164.0
25 138 3 2 27 159.0
26 94 2 1 35 153.0
27 119 2 2 20 157.5
28 105 2 1 74 125.0
29 223 5 3 15 232.5
30 158 2 2 15 182.2
31 95 3 2 16 146.0
32 98 2 1 24 153.0
33 161 3 2 26 150.0
34 80 1 1 42 124.0
35 97 2 1 9 142.0
36 139 3 2 30 165.0
37 180 5 3 39 183.0
38 177 4 3 32 150.0
39 100 2 1 24 163.0
40 164 4 3 74 161.0
41 140 3 2 14 173.0
42 161 4 2 16 180.0
43 157 3 2 12 173.0
44 203 5 3 12 205.0
45 82 2 1 34 140.0
46 104 3 2 29 145.2
47 130 2 2 33 151.0
48 201 4 2 2 237.0
49 143 3 2 36 150.0
50 183 5 2 37 190.0
51 104 2 2 27 134.5
52 155 4 2 79 145.0
53 86 2 1 20 143.4
54 120 2 2 2 155.0
55 130 2 2 2 163.0
56 128 3 2 103 130.0
57 189 4 3 62 231.0
58 146 3 1 29 158.0
59 185 3 2 4 230.0
60 105 2 1 21 145.0
3
Question 2
Refer to data sets of Question 2, Assignment 1. To each data set fit a suitable regression model that can be
used for prediction purposes. Comment on the performance of the fitted model as judged by the value of
R 2 .
Question 3
(a) Using the first 13 years of data from Assignment 1, Question 3, fit a suitable regression model.
(b) Forecast average room occupancy for each of the 12 months of 2010.
(c) Prepare a time plot of forecasts obtained using the decomposition model and the Holt-Winter
method (Questions 3 & 4) in Assignment 1, and forecast values from part (b) above and the actual
values for the 12 months of 2010. Which model seems to provide the closest fit to data?
Question 4
The following table lists weekly sales of thermostats and data are provided in file
“ETW3232Ass2-2012dat.xls”.
Weekly Thermostat Sales
time
index X_t
time
index X_t
time
index X_t
time
index X_t
1 206 14 189 27 172 40 255
2 245 15 244 28 210 41 303
3 185 16 209 29 205 42 282
4 169 17 207 30 244 43 291
5 162 18 211 31 218 44 280
6 177 19 210 32 182 45 255
7 207 20 173 33 206 46 312
8 216 21 194 34 211 47 296
9 193 22 234 35 273 48 307
10 230 23 156 36 248 49 281
11 212 24 206 37 262 50 308
12 192 25 188 38 258 51 280
13 162 26 162 39 233 52 345
(a) Obtain time series plot and the estimated ACF for the above series. Do the graphs
suggest that differencing is required to make the series stationary? If so, what order of
differencing is sufficient to induce a stationary mean?
(b) Identify an ARIMA model underlying this series and fit it.
(c) Perform autocorrelation analysis on the residuals of your final fitted model to check
the adequacy of the fitted model.
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