(Sample) Curve-Fitting Project - Linear Model: Men's 400 Meter Dash

(LR-1) Purpose: To analyze the winning times for the Olympic Men's 400 Meter Dash using a linear model

Data: The winning times were retrieved from http://www.databaseolympics.com/sport/sportevent.htm?sp=ATH&enum=130

The winning times were gathered for the most recent 16 Summer Olympics, post-WWII. (More data was available, back to 1896.)

DATA: Summer Olympics:

Men's 400 Meter Dash

Winning Times |

Year | Time (seconds) |

1948 | 46.20 |

1952 | 45.90 |

1956 | 46.70 |

1960 | 44.90 |

1964 | 45.10 |

1968 | 43.80 |

1972 | 44.66 |

1976 | 44.26 |

1980 | 44.60 |

1984 | 44.27 |

1988 | 43.87 |

1992 | 43.50 |

1996 | 43.49 |

2000 | 43.84 |

2004 | 44.00 |

2008 | 43.75 |

| (LR-2) SCATTERPLOT:As one would expect, the winning times generally show a downward trend, as stronger competition and training methods result in faster speeds. The trend is somewhat linear. |

(LR-3)

Line of Best Fit (Regression Line)

y = 0.0431x + 129.84 where x = Year and y = Winning Time (in seconds)

(LR-4) The slope is 0.0431 and is negative since the winning times are generally decreasing.

The slope indicates that in general, the winning time decreases by 0.0431 second a year, and so the winning time decreases at an average rate of 4(0.0431) = 0.1724 second each 4-year Olympic interval.

(LR-5) Values of r2 and r:

r2 = 0.6991

We know that the slope of the regression line is negative so the correlation coefficient r must be negative.

r=-0.6991=-0.84

Recall that r = 1 corresponds to perfect negative correlation and so r = 0.84 indicates moderately strong negative correlation (relatively close to -1 but not very strong).

(LR-6) Prediction: For the 2012 Summer Olympics, substitute x = 2012 to get y = 0.0431(2012) + 129.84 43.1 seconds.

The regression line predicts a winning time of 43.1 seconds for...

(LR-1) Purpose: To analyze the winning times for the Olympic Men's 400 Meter Dash using a linear model

Data: The winning times were retrieved from http://www.databaseolympics.com/sport/sportevent.htm?sp=ATH&enum=130

The winning times were gathered for the most recent 16 Summer Olympics, post-WWII. (More data was available, back to 1896.)

DATA: Summer Olympics:

Men's 400 Meter Dash

Winning Times |

Year | Time (seconds) |

1948 | 46.20 |

1952 | 45.90 |

1956 | 46.70 |

1960 | 44.90 |

1964 | 45.10 |

1968 | 43.80 |

1972 | 44.66 |

1976 | 44.26 |

1980 | 44.60 |

1984 | 44.27 |

1988 | 43.87 |

1992 | 43.50 |

1996 | 43.49 |

2000 | 43.84 |

2004 | 44.00 |

2008 | 43.75 |

| (LR-2) SCATTERPLOT:As one would expect, the winning times generally show a downward trend, as stronger competition and training methods result in faster speeds. The trend is somewhat linear. |

(LR-3)

Line of Best Fit (Regression Line)

y = 0.0431x + 129.84 where x = Year and y = Winning Time (in seconds)

(LR-4) The slope is 0.0431 and is negative since the winning times are generally decreasing.

The slope indicates that in general, the winning time decreases by 0.0431 second a year, and so the winning time decreases at an average rate of 4(0.0431) = 0.1724 second each 4-year Olympic interval.

(LR-5) Values of r2 and r:

r2 = 0.6991

We know that the slope of the regression line is negative so the correlation coefficient r must be negative.

r=-0.6991=-0.84

Recall that r = 1 corresponds to perfect negative correlation and so r = 0.84 indicates moderately strong negative correlation (relatively close to -1 but not very strong).

(LR-6) Prediction: For the 2012 Summer Olympics, substitute x = 2012 to get y = 0.0431(2012) + 129.84 43.1 seconds.

The regression line predicts a winning time of 43.1 seconds for...