An operations manager at a data centre is monitoring the relationship between the external ambient temperature (TTT ∘C^\circ\text{C}∘C) and the daily energy consumption of the cooling system (EEE kWh). The following data were recorded over 10 separate days:
| Temperature (TTT) | 18 | 22 | 25 | 28 | 30 | 32 | 35 | 38 | 40 | 42 |
|---|---|---|---|---|---|---|---|---|---|---|
| Energy (EEE) | 14 | 16 | 18 | 19 | 21 | 22 | 23 | 25 | 26 | 28 |
[You may use: ∑T=310\sum T = 310∑T=310, STT=564S_{TT} = 564STT=564, ∑E=212\sum E = 212∑E=212, ∑E2=4676\sum E^2 = 4676∑E2=4676, STE=319S_{TE} = 319STE=319]
Calculate SEES_{EE}SEE.
Calculate the product moment correlation coefficient (PMCC) for these data.
Interpret the value of the correlation coefficient in context.
State, giving a reason, whether or not your value of the correlation coefficient supports the use of a linear regression model for these data.
Find the equation of the regression line of EEE on TTT, in the form E=a+bTE = a + bTE=a+bT.
The manager notes that the forecast for the following day is 36 ∘C^\circ\text{C}∘C.
(i) Use your regression line to estimate the energy consumption for this forecasted temperature. (ii) Comment, giving a reason, on the reliability of your estimate.
