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)|
- ______________ 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||r2
||=(CORREL(y data, x data))^2|
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.