Question

Estimate the following simple regression models (using the given data)

Male Labor Participation = β0 + β1*Average Hourly Earnings + ei

Female Labor Participation = β0 + β1*Average Hourly Earnings + ei

Interpret the estimated parameters of the above two regression models

Year | CLFPRM | CLFPRF | UNRM | UNRF | AHE |

1980 | 77.4 | 51.5 | 6.9 | 7.4 | 6.8 |

1981 | 77.0 | 52.1 | 7.4 | 7.9 | 7.4 |

1982 | 76.6 | 52.6 | 9.9 | 9.4 | 7.9 |

1983 | 76.4 | 52.9 | 9.9 | 9.2 | 8.2 |

1984 | 76.4 | 53.6 | 7.4 | 7.6 | 8.5 |

1985 | 76.3 | 54.5 | 7.0 | 7.4 | 8.7 |

1986 | 76.3 | 55.3 | 6.9 | 7.1 | 8.9 |

1987 | 76.2 | 56.0 | 6.2 | 6.2 | 9.1 |

1988 | 76.2 | 56.6 | 5.5 | 5.6 | 9.4 |

1989 | 76.4 | 57.4 | 5.2 | 5.4 | 9.8 |

1990 | 76.4 | 57.5 | 5.7 | 5.5 | 10.2 |

1991 | 75.8 | 57.4 | 7.2 | 6.4 | 10.5 |

1992 | 75.8 | 57.8 | 7.9 | 7.0 | 10.8 |

1993 | 75.4 | 57.9 | 7.2 | 6.6 | 11.0 |

1994 | 75.1 | 58.8 | 6.2 | 6.0 | 11.3 |

1995 | 75.0 | 58.9 | 5.6 | 5.6 | 11.6 |

1996 | 74.9 | 59.3 | 5.4 | 5.4 | 12.0 |

1997 | 75.0 | 59.8 | 4.9 | 5.0 | 12.5 |

1998 | 74.9 | 59.8 | 4.4 | 4.6 | 13.0 |

1999 | 74.7 | 60.0 | 4.1 | 4.3 | 13.5 |

2000 | 74.8 | 59.9 | 3.9 | 4.1 | 14.0 |

2001 | 74.4 | 59.8 | 4.8 | 4.7 | 14.5 |

2002 | 74.1 | 59.6 | 5.9 | 5.6 | 15.0 |

2003 | 73.5 | 59.5 | 6.3 | 5.7 | 15.4 |

2004 | 73.3 | 59.2 | 5.6 | 5.4 | 15.7 |

2005 | 73.3 | 59.3 | 5.1 | 5.1 | 16.1 |

2006 | 73.5 | 59.4 | 4.6 | 4.6 | 16.7 |

Answer #1

1) Male Labor Participation = β0 + β1*Average Hourly Earnings + ei

Regression Analysis: CLFPRM versus AHE

Analysis of Variance

Source | DF | Adj SS | Adj MS | F-Value | P-Value |

Regression | 1 | 34.097 | 34.0968 | 534.41 | 0.000 |

AHE | 1 | 34.097 | 34.0968 | 534.41 | 0.000 |

Error | 25 | 1.595 | 0.0638 | ||

Total | 26 | 35.692 |

Model Summary

S | R-sq | R-sq(adj) | R-sq(pred) |

0.252593 | 95.53% | 95.35% | 94.80% |

Coefficients

Term | Coef | SE Coef | T-Value | P-Value | VIF |

Constant | 79.885 | 0.201 | 397.27 | 0.000 | |

AHE | -0.3948 | 0.0171 | -23.12 | 0.000 | 1.00 |

Regression Equation

Male Labor Participation =

79.885 - 0.3948 AHE |

β0 = 79.88, β1 = -0.3948

**2)**

**Female Labor Participation = β0 + β1*Average Hourly
Earnings + ei**

Regression Analysis: CLFPRF versus AHE

Analysis of Variance

Model Summary

S | R-sq | R-sq(adj) | R-sq(pred) |

1.38856 | 75.19% | 74.19% | 70.01% |

Coefficients

Term | Coef | SE Coef | T-Value | P-Value | VIF |

Constant | 47.94 | 1.11 | 43.37 | 0.000 | |

AHE | 0.8170 | 0.0939 | 8.70 | 0.000 | 1.00 |

Regression Equation

Female Labor Participation | = | 47.94 + 0.8170 AHE |

β0 = 47.94 , β1 = 0.817

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