A researcher is studying the relationship between the daily average temperature, ttt in ∘C^{\circ}\text{C}∘C, and the daily electricity consumption, eee in megawatt-hours (MWh), for a small town. A random sample of 10 days is taken and the results are recorded.
The data are summarised as follows:
n=10,∑t=184,∑e=412,∑e2=17540,Stt=226.4,Ste=−198.8 n = 10, \quad \sum t = 184, \quad \sum e = 412, \quad \sum e^2 = 17540, \quad S_{tt} = 226.4, \quad S_{te} = -198.8 n=10,∑t=184,∑e=412,∑e2=17540,Stt=226.4,Ste=−198.8Calculate the product moment correlation coefficient between ttt and eee.
Give an interpretation of your product moment correlation coefficient in the context of the study.
Find the equation of the least squares regression line of eee on ttt in the form e=a+bte = a + bte=a+bt.
Give an interpretation of the value of bbb in your regression line.
(i) Use the regression line from part (c) to estimate the electricity consumption for a day with an average temperature of 25∘C25^{\circ}\text{C}25∘C.
(ii) Comment on the reliability of your answer in part (i) given that the range of temperatures in the sample was 12∘C12^{\circ}\text{C}12∘C to 22∘C22^{\circ}\text{C}22∘C.
Using the regression line from part (c), the researcher estimates that for a temperature decrease of x ∘Cx \, ^{\circ}\text{C}x∘C there will be an increase of 555 MWh in electricity consumption.
Find the value of xxx.
