#### MS 150 Statistics Quiz four 4.2 linear regression • Name:

The following data is the power generated in kilowatt hours by a windmill with a rotor area of 300 square feet and 40% efficiency.^{1} Use this data to find the linear regression (trend line) for this data.

Wind speed (mph) | Power (Watts) |

0 | 0 |

5 | 75 |

10 | 588 |

15 | 1980 |

20 | 4700 |

25 | 9190 |

30 | 15876 |

- ______________ Calculate the slope of the linear regression (trend line) for the data.
- ______________ Calculate the y-intercept of the linear regression (trend line) for the data.
- ______________ Is the correlation positive or negative?
- ______________ Use the slope and intercept to calculate the projected power production in Watts for a wind speed of 40 mph. Go ahead and make this projection even though 40 mph is beyond the data provided.
^{2}
- ______________ Use the slope and intercept to calculate the wind speed for which power production is 1000 Watts.
- __________ Determine the correlation coefficient r.
- __________ Is the correlation none, low, moderate, high, or perfect?
- __________ Does the relationship appear to be linear or non-linear?
- __________ Determine the coefficient of determination.
- __________ What percent in the variation in wind speed accounts for the variation in the kilowatt hours variable?
- In this case, is there causation?

Why or why not?

Linear Regression Statistics |

Statistic or Parameter | Symbol | 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 |

^{1}
http://home.earthlink.net/~fradella/green.htm

^{2} In actual operation the rotor (propeller) is usually designed to feather (rotate in a manner such as to reduce its pitch and thus maintain a constant maximum spin speed) above 30 mph.