Windmill Output. Where we considered the relationship between a windmill’s direct current (DC) output and wind speed. a. Obtain a scatterplot of DC output versus speed. In view of your scatterplot, what power transformations of DC output and/or speed would you suggest in order to straighten the scatterplot? b. Obtain a draftsman plot of appropriate power transformations of DC output versus appropriate transformations of speed. What transformations would you suggest be used in an attempt to straighten the scatterplot? c. Based on your analysis in part (b), select a power transformation of DC output and/or of speed. Perform a regression analysis for these transformed variables. Obtain a plot of residuals versus fitted values and a normal probability plot of residuals. Perform a residual analysis to assess the assumptions of linearity of the regression equation, constancy of the conditional standard deviations, and normality of the conditional distributions. Check for outliers and influential observations. d. Does your analysis in part (c) reveal any violations of the assumptions for regression inferences? Explain your answer. e. For the regression equation of the transformed variables obtained in part (c), write the regression equation relating DC output to wind speed.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Windmill Output. Where we considered the relationship between a windmill’s direct current (DC) output and wind speed.
a. Obtain a
b. Obtain a draftsman plot of appropriate power transformations of DC output versus appropriate transformations of speed. What transformations would you suggest be used in an attempt to straighten the scatterplot?
c. Based on your analysis in part (b), select a power transformation of DC output and/or of speed. Perform a
d. Does your analysis in part (c) reveal any violations of the assumptions for regression inferences? Explain your answer.
e. For the regression equation of the transformed variables obtained in part (c), write the regression equation relating DC output to wind speed.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 11 images
