Heating Oils at Dupree Fuels Company

Case 11.2 – Dupree Fuels Company

Three Factor Model

In order to determine whether Dupree’s oil consumption model is statistically reliable, a three-factor model regression had to be run for the 3 variables, degree days, home index and number people as follows.

Dependent Variable | Oil usage |

Independent Variable | Degree days, Home index, Number people |

This generated the following regression results.

Regression Table | Coefficient | Standard Error | t-Value | p-Value |

Constant | -218.31 | 63.96 | -3.4133 | 0.0016 |

Degree Days | 0.28 | 0.036 | 7.5711 | < 0.0001 |

Home Index | 86.99 | 9.63 | 9.0327 | < 0.0001 |

Number People | 5.267 | 10.56 | 0.4987 | 0.6210 |

However, as observed in the table above, this resulted in a negative intercept of -218.31, which implies that when there is temperate is good (zero degree days) and no people are using the oil (zero home index and number people), oil consumption would automatically revert to zero. This is evidently an unrealistic as it is not possible for oil consumption to be negative. Therefore, the regression was run once more, with the constant set to zero.

The results differed as follows.

Two Factor Model

Regression Table | Coefficient | Standard Error | t-Value | p-Value | Results Significant? |

Constant | 0.00 | NA | NA | NA | |

Degree Days | 0.21 | 9.46 | 5.9967 | < 0.0001 | Yes |

Home Index | 70.81 | 7.16 | 7.4839 | < 0.0001 | Yes |

Number People | -23.55 | 0.04 | -3.2871 | 0.0022 | Yes |

All variables have a p-value below 0.05 and hence statistically significant. The estimate model hence is

Oil usage = 0.21 * degree days + 70.81 * home index – 23.55* number of people.

The negative correlation between oil usage and number of people can be explained that as the number of people increase, the less heat is required to heat up the room.