12 Simple Linear Regression

Madrid Manufacturing has encountered problems in determining the proper amount of coal to order each week to heat its complex adequately. Because of this, the firm has requested to develop an accurate way to predict the amount of fuel (in tons of coal) that will be used to heat the nine-building complex in future weeks.

It is known that weekly fuel consumption mainly depends on:

• the mean hourly temperature (in degrees Fahrenheit (ºF) ) during the week, and
• other factors that contribute to an overall ``chill factor’’ like:
  • Wind velocity during the week
  • Cloud cover
  • Variations in temperature, wind velocity and cloud cover durng the week (perhaps cause by the movement of weather fronts)

We can use Regression Analysis to predict the dependent variable weekly fuel consumption (\(y\)) on the basis of the independent variable mean hourly temperature (\(x\)).

Suppose that we have gathered concerning \(y\) and \(x\) for \(n=8\) weeks prior to the current week.

Week	Temperature	Fuel
1	28.0	12.4
2	28.0	11.7
3	32.5	12.4
4	39.0	10.8
5	45.9	9.4
6	57.8	9.5
7	58.1	8.0
8	62.5	7.5

Let’s see how it works …

Source: Bowerman, Bruce and O’COnnell, Richard (1990).Linear Statistical Models: an applied approach. 2nd Edition. ISBN 0-534-91796-8.