4.1 Electricity consumption was recorded for a small town on 12 randomly chosen days. The following maximum temperatures (degrees Celsius) and consumption

(megawatt-hours) were recorded for each day.

Day 1 2 3 4 5 6 7 8 9 10 11 Mwh 16.3 16.8 15.5 18.2 15.2 17.5 19.8 19.0 17.5 16.0 19.6 temp 29.3 21.7 23.7 10.4 29.7 11.9 9.0 23.4 17.8

(a) Plot the data and find the regression model for Mwh with temperature as an explanatory variable. Why is there a negative relationship?

(b) Produce a residual plot. Is the model adequate?

Are there any outliers or influential observations?

(c) Use the model to predict the electricity consumption that you would expect for a day with maximum temperature 10° and a day with maximum temperature 35° . Do you believe these predictions?

(d) Give prediction intervals for your forecasts.

The following R code will get you started:

plot(Mwh - temp, data=econsumption)

30.0 fit <- lm(Mwh - temp, data=econsumption)

plot(residuals(fit) - temp, data=econsumption)

forecast(fit, newdata=data .frame(temp=c(10,35)))