# Solution Library

# Calculate Linear Regression And Examine The Results

**Question**

A wind farm has collected data on the variability of the power output due to wind speed variation. Part of the observed data consists of the current generated in kA and the corresponding wind speed in mph on each day for 45 days in time order. The data are provided in the attached data file.

For parts (1) through (4), conduct a linear regression analysis in terms of the variables listed. Write out and label each least squares regression equation and the corresponding equation needed to predict the current in kA given the wind speed if it differs from the regression equation. Plot the residuals vs. the fitted values.

Hand in a one-page sample of the Minitab Worksheet you constructed and used for this problem. Label your worksheet columns so the data they contain are intuitively identifiable.

(1) Current as a linear function of wind speed

(2) Current as a function of the natural logarithm of the wind speed

(3) Natural logarithm of the current as a function of the wind speed

(4) Square root of current vs. wind speed

(5) Clearly identify which of the four models is best for prediction? What criteria did you use to select the best model and explain?

(6) Using the best model construct a 95% prediction interval for the current when the wind speed is 6.1 mph. How does your prediction interval compare to the observed current at a speed of 6.1 mph? Show all relevant work/output.

(7) For your best model plot the residuals as a function of time and interpret.

(8) For your best model construct a plot of the predicted values of the current in kA vs. the observed values of current and compare to a 45 degree line (with slope =1) Use this plot and the results in (7) to write a brief paragraph to “your management” on the use of your best model in practice?

Data for this problem

Y is the current in kA

X is the wind speed in mph

Day |
X |
Y |

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 |
4.2 1.4 6.6 4.7 2.6 5.8 1.8 5.8 7.3 7.1 6.4 4.6 1.6 2.3 4.2 3.7 5.9 6 10.7 5.3 5.1 4.9 8.3 7.1 9.2 4.4 8 10.5 5.1 5.8 2.6 7.7 6.1 5.5 4.7 4 2.3 11.9 8.6 5.6 4.2 6.2 7.7 6.6 6.9 |
1.9 0.7 2.2 2 1.1 2.6 0.3 2.3 2.6 2.7 2.4 2.2 1.1 1.5 1.5 2.1 2.2 2.6 3.2 2.3 1.9 2.3 3.1 2.3 2.9 1.8 2.6 3 2.1 2.5 1.4 2.8 2.4 2.2 2.3 2 1.2 3 2.5 2.1 1.7 2.3 2.6 2.9 2.6 |

**Summary**

The question belongs to Statistics and it discusses about calculation of linear regression and examining the results.

**Total Word Count 1563**

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