Use the following to answer the questions below:

A small university is concerned with monitoring the electricity usage in its Student Center, and its officials want to better understand what influences the amount of electricity used on a given day. They collected data on the amount of electricity used in the Student Center each day and the daily high temperature for nearly a year. They also made note of whether each day was a weekend or not (1 = Saturday/Sunday and 0 = Monday - Friday). Regression output is provided.

Helpful notes: 1) Electricity usage is measured in kilowatt hours, 2) During the cold months, the Student Center is heated by gas, not electricity, and 3) Air conditioning the building during the warm months does use electricity.

The regression equation is Electricity = 83.6 + 0.529 High Temp - 25.2 Weekend

Predictor | Coef | SE Coef | T | P |

Constant | 83.560 | 4.238 | 19.72 | 0.000 |

High Temp | 0.52918 | 0.07020 | 7.54 | 0.000 |

Weekend | -25.168 | 3.724 | -6.76 | 0.000 |

S = 29.8162 R-Sq = 24.7% R-Sq(adj) = 24.2%

Analysis of Variance

Source | DF | SS | MS | F | P |

Regression | 2 | 90481 | 45241 | 50.89 | 0.000 |

Residual Error | 310 | 275592 | 889 | | |

Total | 312 | 366073 | | | |

Another possible predictor they recorded was the average temperature over the course of each day. Regression output for the model that uses

High Temp,

Weekend, and

Avg. Temp is provided. Explain why these results differ so drastically from those for the two-predictor model.

The regression equation is

Sullivan Student Center = 81.9 + 0.839 High Temp - 25.1 Weekend - 0.337 Avg. Temp

Constant | 81.881 | 4.837 | 16.93 | 0.000 |

High Temp | 0.8389 | 0.4351 | 1.93 | 0.055 |

Weekend | -25.053 | 3.730 | -6.72 | 0.000 |

Avg. Temp | -0.3372 | 0.4673 | -0.72 | 0.471 |

S = 29.8393 R-Sq = 24.8% R-Sq(adj) = 24.1%

Analysis of Variance

Regression | 3 | 90945 | 30315 | 34.05 | 0.000 |

Residual Error | 309 | 275129 | 890 |