A uranium mining company has recorded its monthly profit and the average price of uranium for each month over a period of 24 months.
It is assumed that a simple linear regression will determine the relationship between the average monthly uranium price and monthly profit. The following values have been calculated:
SSxx= 707.1967 SSxy= 8435.9392 SSyy= 114003.8333
SSE= 13374.02264 x= 46.4496 y= 55.9167
Using the calculations given above:
i) Derive the simple linear regression for this data and explain the equation in words.
ii) Assuming that the model is correct calculate the predicted monthly profit next month if the average uranium price is assumed to be $59.
iii) Calculate the value r2 and explain what this value represents.
| Price of uranium $ |
Profit $ (in thousands) |
| 47.5 |
78 |
| 44.5 |
42 |
| 42 |
35 |
| 44.5 |
18 |
| 49 |
62 |
| 51.5 |
93 |
| 47 |
36 |
| 46 |
47 |
| 42.88 |
8 |
| 48 |
101 |
| 45.38 |
55 |
| 44.5 |
59 |
| 42.38 |
-4 |
| 41.13 |
-4 |
| 41.88 |
59 |
| 41.75 |
-3 |
| 40.75 |
-54 |
| 41.75 |
-46 |
| 45.63 |
65 |
| 45.25 |
25 |
| 46.63 |
65 |
| 52 |
137 |
| 60.63 |
212 |
| 62.25 |
256 |