- 20 Marks
Question
The Branch Manager of a building material production plant feels that the demand for iron rod shipments may be related to the number of construction permits issued in the country during the previous quarter. The Manager has collected the data shown in the table below:
| Construction Permits | Iron Rods |
|---|---|
| 15 | 6 |
| 9 | 4 |
| 40 | 16 |
| 20 | 6 |
| 25 | 13 |
| 25 | 9 |
| 15 | 10 |
| 35 | 16 |
Required:
i) Use the normal equations of the least square regression method to derive a regression forecasting equation for the data. (9 marks)
ii) Interpret your regression coefficient in (i) above. (1 mark)
iii) Using the regression line in (a) above, determine a point estimate for Iron Rods when the number of construction permits is 30. (2 marks)
iv) Is your estimate in (iii) above reliable? Give reason(s) for your answer. (2 marks)
v) Calculate the coefficient of determination and interpret it. (6 marks)
Answer
a
i)
ii) on average, for each additional construction permit issued, 0.78 iron rods will be demanded.
iii) When the number of construction permits is 30: y = −0.67 + 0.78 (30) = 22.73
iv) Yes, the estimate is reliable because the value of 30 is within the range of the data used to derive the regression equation.
v) R = 
= 
= 
= 0.2%
This indicates that roughly 0.2% of the variation in iron rod demand is explained by the variation in construction permits.
- Tags: Construction Permits, Forecasting, Iron Rods, Regression
- Level: Level 1
- Topic: Forecasting
- Series: NOV 2016
- Uploader: Kwame Aikins