The table below shows the number of active high-performance servers, sss, and the cooling energy consumption, eee kWh, in a data center over 8 separate observation periods.
| sss | 5 | 12 | 15 | 20 | 25 | 30 | 35 | 42 |
|---|---|---|---|---|---|---|---|---|
| eee | 12 | 18 | 25 | 32 | 40 | 45 | 55 | 61 |
You may use Sss=1076S_{ss} = 1076Sss=1076 and See=2120S_{ee} = 2120See=2120.
Find the exact value of ∑se\sum se∑se.
Find the value of SseS_{se}Sse.
Calculate the product moment correlation coefficient between sss and eee, giving your answer to 3 decimal places.
Interpret the value of the correlation coefficient in the context of the data center.
A ninth observation is added to the data set. On this day, 45 servers were active and the cooling energy consumption was 15 kWh.
Without further calculation, state whether the value of the product moment correlation coefficient will increase, decrease or stay the same when all nine observations are used. Give a reason for your answer.