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.
278 exam-style questions on CCEA A Level Maths 2.5 Data presentation and interpretation, covering 2.5.1 Data presentation and interpretation, 2.5.2 Data presentation and interpretation, 2.5.3 Data presentation and interpretation, 2.5.4 Data presentation and interpretation, 2.5.5 Data presentation and interpretation, 2.5.6 Data presentation and interpretation, 2.5.7 Data presentation and interpretation, 2.5.8 Data presentation and interpretation, 2.5.9 Data presentation and interpretation, and 2.5 Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.