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Suppose that you have a dataset that you wish to analyse consisting of positive values only, and that a histogram shows that the dataset is very right-skew. In an attempt to impose symmetry on (a version of) your data, you decide to transform the data using a log transformation, log, but find, having drawn a histogram of the transformed data, that the data are still right-skew, albeit less so. One of your colleagues, Colleague A, say, suggests that you should have transformed the data using a square root transformation, y = Colleague B, suggests that you should have transformed the data using √; another colleague, aquision a reciprocal transformation, y = 1/x. Given the target of attaining symmetry, which of your colleagues is the more likely to be right, and why?

Suppose that you have a dataset that you wish to analyse consisting of positive values only, and that a histogram shows that the dataset is very right-skew. In an attempt to impose symmetry on (a version of) your data, you decide to transform the data using a log transformation, log, but find, having drawn a histogram of the transformed data, that the data are still right-skew, albeit less so. One of your colleagues, Colleague A, say, suggests that you should have transformed the data using a square root transformation, y = Colleague B, suggests that you should have transformed the data using √; another colleague, aquision a reciprocal transformation, y = 1/x. Given the target of attaining symmetry, which of your colleagues is the more likely to be right, and why?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Invisib a) Suppose that you have a dataset that you wish to analyse consisting of positive values only, and that a histogram shows that the dataset is very right-skew. In an attempt to impose symmetry on (a version of) your data, you decide to transform the data using a log transformation, y = log x, but find, having drawn a histogram of the transformed data, that the data are still right-skew, albeit less so. One of your colleagues, Colleague A, say, suggests that you should have transformed the data using a square root transformation, y = √; another colleague, Colleague B, suggests that you should have transformed the data using a reciprocal transformation, y = 1/r. Given the target of attaining symmetry, which of your colleagues is the more likely to be right, and ed why? (b) Suppose now that you have another dataset comprising a set of observations on a response variable and a single explanatory variable, which you had hoped to be able to analyse using linear regression. You make a first attempt and produce the residual plot shown in Figure 2. (1810 Residual -1 1 (C) 0.5 1 mit alebgyue elambient to aizylous issiqesis tadi eu list atrisitos doisongen ows adi to olsas of sus 979 911 lebon endjogad od dat Jes 1.5 2 Fitted value Figure 2 A residual plot You wonder whether a transformation might allow a better analysis using linear regression. Which variable might you transform, and why? odl 2.5 3
Transcribed Image Text:Invisib a) Suppose that you have a dataset that you wish to analyse consisting of positive values only, and that a histogram shows that the dataset is very right-skew. In an attempt to impose symmetry on (a version of) your data, you decide to transform the data using a log transformation, y = log x, but find, having drawn a histogram of the transformed data, that the data are still right-skew, albeit less so. One of your colleagues, Colleague A, say, suggests that you should have transformed the data using a square root transformation, y = √; another colleague, Colleague B, suggests that you should have transformed the data using a reciprocal transformation, y = 1/r. Given the target of attaining symmetry, which of your colleagues is the more likely to be right, and ed why? (b) Suppose now that you have another dataset comprising a set of observations on a response variable and a single explanatory variable, which you had hoped to be able to analyse using linear regression. You make a first attempt and produce the residual plot shown in Figure 2. (1810 Residual -1 1 (C) 0.5 1 mit alebgyue elambient to aizylous issiqesis tadi eu list atrisitos doisongen ows adi to olsas of sus 979 911 lebon endjogad od dat Jes 1.5 2 Fitted value Figure 2 A residual plot You wonder whether a transformation might allow a better analysis using linear regression. Which variable might you transform, and why? odl 2.5 3
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