For my regression I observed food consumption rates in dollars, plotted against income level as the explanatory variable. I used a measurement of income before taxes separated into 9 different brackets: <$15,000, <$30,000, <$40,000, <$50,000, <$70,000, <$100,000, <$150,000, <$200,000, and <$250,000. I ran a cross sectional regression to observe changes in food consumption due to increases in annual income. For a second regression, I included alcohol consumption in dollars to observe its effect on food consumption under the same income brackets.

In my first test, I found that each additional dollar of income will lead to a $0.04 dollar increase in food consumption. For my second model, I found that each additional dollar spent on alcohol consumption causes a $1.95 decrease in spending on food, holding the other variable (income) constant. My R squared statistics of .993 and .995 (respectively) suggests this regression, and its independent variables, hold a high strength of explanation for the dependent variable (food consumption). These findings align with our common assumptions about food, that it is a highly normal good.

Output information is presented below.

The SAS System |

Number of Observations Read | 9 |
---|---|

Number of Observations Used | 9 |

Analysis of Variance | |||||
---|---|---|---|---|---|

Source | DF | Sum of Squares |
Mean Square |
F Value | Pr > F |

Model | 1 | 133051467 | 133051467 | 1059.56 | <.0001 |

Error | 7 | 879010 | 125573 | ||

Corrected Total | 8 | 133930477 |

Root MSE | 354.36261 | R-Square | 0.9934 |
---|---|---|---|

Dependent Mean | 8111.88889 | Adj R-Sq | 0.9925 |

Coeff Var | 4.36844 |

Parameter Estimates | |||||
---|---|---|---|---|---|

Variable | DF | Parameter Estimate |
Standard Error |
t Value | Pr > |t| |

Intercept | 1 | 3126.16650 | 193.42381 | 16.16 | <.0001 |

Inc | 1 | 0.04958 | 0.00152 | 32.55 | <.0001 |

The SAS System |

Number of Observations Read | 9 |
---|---|

Number of Observations Used | 9 |

Analysis of Variance | |||||
---|---|---|---|---|---|

Source | DF | Sum of Squares |
Mean Square |
F Value | Pr > F |

Model | 2 | 133279356 | 66639678 | 614.08 | <.0001 |

Error | 6 | 651121 | 108520 | ||

Corrected Total | 8 | 133930477 |

Root MSE | 329.42404 | R-Square | 0.9951 |
---|---|---|---|

Dependent Mean | 8111.88889 | Adj R-Sq | 0.9935 |

Coeff Var | 4.06100 |

Parameter Estimates | |||||
---|---|---|---|---|---|

Variable | DF | Parameter Estimate |
Standard Error |
t Value | Pr > |t| |

Intercept | 1 | 3154.80047 | 180.89387 | 17.44 | <.0001 |

Inc | 1 | 0.06212 | 0.00877 | 7.08 | 0.0004 |

Alc | 1 | -1.95538 | 1.34935 | -1.45 | 0.1975 |