The article “Optimization of HVAC Control to Improve Comfort and Energy Performance in a School” (Energy Engr. 2008: 6–22) gives an analysis of the electrical and gas costs for a high school in Austin, Texas after a new heating and air conditioning (HVAC) system was installed. The accompanying data on x = average outside air temperature (°F) and y = electricity consumption (kWh) for a sample of n = 20 months was read from a graph in the article.

a. Does the simple linear regression model specify a useful relationship between outside temperature and electricity consumption?
b. Estimate the true change in expected energy consumption associated with a 1 °F increase in outside temperature using a 95% confidence interval, and interpret the interval.
c. Calculate a 95% CI for μ_lY|70, the true average monthly energy consumption when temperature = 70 °F.
d. Calculate a 95% PI for a single future observation on energy consumption to be made when temperature = 70 °F.
e. Would the 95% CI and PI when temperature = 85 °F be wider or narrower than the corresponding intervals of parts (c) and (d)? Answer without actually computing the intervals.
f. Would you recommend calculating a 95% PI for an outside temperature of 95 °F? Explain.

g. Calculate simultaneous CI’s for true average monthly energy consumption when outside temperature is 60, 70, and 80 °F, respectively. Your simultaneous confidence level should be at least 97%.

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