Question 1
Private capital expenditure for 12 successive quarters are presented in the following table:
|
Quarter
|
Millions
|
|
|
|
|
1
|
31,920
|
|
2
|
25,120
|
|
3
|
30,350
|
|
4
|
24,650
|
|
5
|
30,090
|
|
6
|
23,980
|
|
7
|
28,450
|
|
8
|
26,710
|
|
9
|
31,380
|
|
10
|
27,260
|
|
11
|
34,380
|
|
12
|
34,800
|
Required
a) Please present the time series data with a line chart.
b) Please comment on the secular trend.
c) Does the line chart display a cyclical trend or a seasonal trend? Please explain.
d) Use the line chart to predict the expenditure for Quarter 13.
Question 2
A farmer recorded rainfall (in mm) and average yield of crop (bushels / hectare) for 6 successive years as follows:
|
Year
|
Rainfall
|
Average Yield
|
|
|
|
|
|
1
|
350
|
240
|
|
2
|
180
|
100
|
|
3
|
150
|
90
|
|
4
|
400
|
280
|
|
5
|
580
|
60
|
|
6
|
140
|
80
|
Required
a) Is there a correlation between rainfall and average yield to suggest a linear relationship? Please explain the correlation, if it exists.
b) Draw a scatter plot and the least square line.
c) Is the least square line a good fit for the data? Please explain.
d) Re-draw the scatter plot and the least square line without Year 5 data.
e) Is the least square line in d) a good fit for the data? Please explain.
f) Please suggest a plausible reason why Year 5 had the highest rainfall and yet the lowest average yield.