# Quadratic Regression

The following table lists the tuition cost per quarter for
taking 15 credits at Green River Community

College since 1980.

Year |
Cost |
||

1980 | $102 | Year |
Cost |

1981 | 102 | 1994 | $432 |

1982 | 173 | 1995 | 450 |

1983 | 173 | 1996 | 467 |

1984 | 193 | 1997 | 486 |

1985 | 193 | 1998 | 505 |

1986 | 233 | 1999 | 528 |

1987 | 253 | 2000 | 547 |

1988 | 260 | 2001 | 581 |

1989 | 274 | 2002 | 661 |

1990 | 294 | 2003 | 714 |

1991 | 320 | 2004 | 771 |

1992 | 333 | 2005 | 815 |

1993 | 375 | 2006 | 862 |

Use your calculator ’s
linear regression function to find a line of best fit for the data. What is

the linear function of best fit? (*Hint:* It might make things easier if
you use ‘years since 1980’ as

the variable x instead of the year number – so 1980 would be x = 0, and 2006
would be x = 26.)

Use the function you
found in part 1 to estimate the cost of taking 15 credits at GRCC in 2007.

Also estimate the cost in 2010 and 2020.

Plot both the data and
the line on your calculator to see how well it fits. Does it look like a

good fit to you?

Next, use your
calculator to find a quadratic regression for the data. What is the quadratic

function of best fit?

Plot the data and your
quadratic function on your calculator. How well does it fit? Does it look

like it fits better than the line does?

Now use the quadratic
function to try to predict the cost of taking 15 credits at GRCC in 2007,

2010 and 2020.

Do you think the linear function or the quadratic function gives a better prediction? Why?

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