Pixel | Hue angle° |
---|---|

0 | 9 |

15 | 17 |

30 | 24 |

45 | 24 |

60 | 26 |

75 | 30 |

90 | 36 |

105 | 43 |

120 | 48 |

135 | 52 |

150 | 64 |

165 | 77 |

180 | 88 |

195 | 111 |

210 | 137 |

225 | 165 |

240 | 184 |

255 | 200 |

270 | 217 |

285 | 230 |

300 | 236 |

315 | 239 |

330 | 250 |

345 | 270 |

360 | 303 |

This section explores whether the hue angle changes linearly as one moves from red to magenta across a rainbow.
The image of a rainbow was analyzed from red to purple.
The hue angle for every 15^{th} picture element (pixel) was measured and recorded. A spreadsheet with the data should be available at: http://www.comfsm.fm/~dleeling/statistics/s53/rainbow.xls

- _________ Calculate the slope of the best fit (least squares) line for the data.
- _________ Calculate the y-intercept of the best fit (least squares) line.
- _________ Is the correlation positive, negative, or neutral?
- _________ Use the equation of the best fit line to calculate the predicted hue angle for pixel 145.
- _________ Use the inverse of the best fit line to calculate the predicted pixel for a hue angle of 220°.
- _________ Calculate the linear correlation coefficient r for the data.
- _________ Is the correlation none, low, moderate, high, or perfect?
- _________ Calculate the coefficient of determination.
- _________ What percent of the variation in the pixel data explains the variation in the hue angle data?
- _________ Is there a relationship between the pixels and the hue angles?
- _________ Can we use a linear regression to predict hue angles from pixels?
- Why or why not?

Linear Regression Statistics | |||
---|---|---|---|

Statistic or Parameter | Symbol | Equations | Excel |

Slope | b | =SLOPE(y data, x data) | |

Intercept | a | =INTERCEPT(y data, x data) | |

Correlation | r | =CORREL(y data, x data) | |

Coefficient of Determination | r^{2} |
=(CORREL(y data, x data))^2 |