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)
00
575
10588
151980
204700
259190
3015876
  1. ______________ Calculate the slope of the linear regression (trend line) for the data.
  2. ______________ Calculate the y-intercept of the linear regression (trend line) for the data.
  3. ______________ Is the correlation positive or negative?
  4. ______________ 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
  5. ______________ Use the slope and intercept to calculate the wind speed for which power production is 1000 Watts.
  6. __________ Determine the correlation coefficient r.
  7. __________ Is the correlation none, low, moderate, high, or perfect?
  8. __________ Does the relationship appear to be linear or non-linear?
  9. __________ Determine the coefficient of determination.
  10. __________ What percent in the variation in wind speed accounts for the variation in the kilowatt hours variable?
  11. In this case, is there causation?

    Why or why not?
Linear Regression Statistics
Statistic or ParameterSymbolExcel
Slopeb=SLOPE(y data, x data)
Intercepta=INTERCEPT(y data, x data)
Correlationr=CORREL(y data, x data)
Coefficient of Determinationr2 =(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.