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## Analysis of Experiments

by: Blair Williamson

12

0

2

# Analysis of Experiments STAT 3115

Marketplace > University of Connecticut > Statistics > STAT 3115 > Analysis of Experiments
Blair Williamson
UCONN
GPA 3.87

Staff

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COURSE
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Staff
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Class Notes
PAGES
2
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KARMA
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## Popular in Statistics

This 2 page Class Notes was uploaded by Blair Williamson on Thursday September 17, 2015. The Class Notes belongs to STAT 3115 at University of Connecticut taught by Staff in Fall. Since its upload, it has received 12 views. For similar materials see /class/205906/stat-3115-university-of-connecticut in Statistics at University of Connecticut.

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Date Created: 09/17/15
Statistics 31155315 Handout 6 Sample Coef cient of Variation For a random sample of observations from a population with mean M and variance 0392 Y1Y2Yn we de ne the sample coe icient of variation as S 011 100 Y where S is the sample standard deviation The cv measures the precision of estimation the population mean u Example Suppose we have collected data on the monthly gains in for two mutual funds for a period of 12 month The summary is presented in the table below Fund Sample Mean for Gain Standard Deviation for Gain 11 22 mutual fund A 60 mutual fund B 12 Therefore the cv for mutual fund A is 20 and for mutual fund B is 50 What does it mean Let us look at the con dence intervals for the mean gain assuming the data is normal For mutual fund A a 95 Cl for the mean gain is 11i220122 12 which is 96124 For mutual fund B a 95 Cl for the mean gain is 12i 220160 12 which is 82 158 ln regression analysis the cv of variation measures the accuracy of our model in prediction We would like to have a cv of less than 10 if possible Transformation of Variables in Regression lf the simple or multiple linear regression model is not appropriate for a data set there are two basic choices 1 Abandon the regression model and search for a more appropriate model 2 Use some transformations on the data so that the regression model is appropriate for the transformed data The following transformations on the response variable can be helpful for some data sets 0 Y xY or Y Y a is useful when we have count type data Poisson model or MSE Y 0 Y arcsin Y7 or Y arcsinxY 110 is useful for data of propor tions or percentages or binomial model The variable Y has to be expressed in terms of a proportion 0 Y log Y or Y logY a is useful for data with m x Y 0 Y lY or Y lY a is useful for data with xMSE Y2 Transformation on the independent variable are used to correct for non linearity of the model 0 X logX or X logXa7 and X xX or X xXa increasing convex downward trend 0 X expX or X expX a and X X2 or X X a2 increasing convex upward trend 0 X exp7X or X exp7Xa7 and X lX or X lX a decreasing convex upward trend 0 UseY6061X62X2EorY6061X62X263X3E for all of the above and other trends

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