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The MASS package that comes with your R installed already, has the boxcox() function that you can use: After reading in the data, do:

library(MASS)
boxcox(y ~ x)

Then look at the graph this produces, which shows graphically a 95% confidence interval for the boxcox transformation parameter. But you do not really have enough data (n=10) to do this, the resulting confidence interval goes almost from -2 to 2!, with a maximum likelihood estimate of approximately 0 (a log-transform, as said before). If your real data have more observations, you should try this.

As others have said, this transformation is really trying to stabilize variances. This is not really obvious from theory, what it does, is to try to maximize a normal-distribution based likelihood function, which assumes constant variance. One could think that maximizing a normal-based likelihood would try to normalize the distribution of the residuals, but in practice the main contribution to maximizing the likelihood comes from stabilizing the variances. This is maybe not so surprising, given that the likelihood we maximizes is based on a constant variance normal distribution family!

I once wrote a slider-based demo in XLispStat, which demonstrated this clearly!

The MASS package that comes with your R installed already, has the boxcox() function that you can use: After reading in the data, do:

    library(MASS)
    boxcox(y ~ x)

Then look at the graph this produces, which shows graphically a 95% confidence interval for the boxcox transformation parameter. But you do not really have enough data (n=10) to do this, the resulting confidence interval goes almost from -2 to 2!, with a maximum likelihood estimate of approximately 0 (a log-transform, as said before). If your real data have more observations, you should try this.

As others have said, this transformation is really trying to stabilize variances. This is not really obvious from theory, what it does, is to try to maximize a normal-distribution based likelihood function, which assumes constant variance. One could think that maximizing a normal-based likelihood would try to normalize the distribution of the residuals, but in practice the main contribution to maximizing the likelihood comes from stabilizing the variances. This is maybe not so surprising, given that the likelihood we maximizes is based on a constant variance normal distribution family!

I once wrote a slider-based demo in XLispStat, which demonstrated this clearly!

The MASS package that comes with your R installed already, has the boxcox() function that you can use: After reading in the data, do:

library(MASS)
boxcox(y ~ x)

Then look at the graph this produces, which shows graphically a 95% confidence interval for the boxcox transformation parameter. But you do not really have enough data (n=10) to do this, the resulting confidence interval goes almost from -2 to 2!, with a maximum likelihood estimate of approximately 0 (a log-transform, as said before). If your real data have more observations, you should try this.

As others have said, this transformation is really trying to stabilize variances. This is not really obvious from theory, what it does, is to try to maximize a normal-distribution based likelihood function, which assumes constant variance. One could think that maximizing a normal-based likelihood would try to normalize the distribution of the residuals, but in practice the main contribution to maximizing the likelihood comes from stabilizing the variances.

I once wrote a slider-based demo in XLispStat, which demonstrated this clearly!

The MASS package that comes with your R installed already, has the boxcox() function that you can use: After reading in the data, do:

library(MASS)
boxcox(y ~ x)

Then look at the graph this produces, which shows graphically a 95% confidence interval for the boxcox transformation parameter. But you do not really have enough data (n=10) to do this, the resulting confidence interval goes almost from -2 to 2!, with a maximum likelihood estimate of approximately 0 (a log-transform, as said before). If your real data have more observations, you should try this.

As others have said, this transformation is really trying to stabilize variances. This is not really obvious from theory, what it does, is to try to maximize a normal-distribution based likelihood function, which assumes constant variance. One could think that maximizing a normal-based likelihood would try to normalize the distribution of the residuals, but in practice the main contribution to maximizing the likelihood comes from stabilizing the variances. This is maybe not so surprising, given that the likelihood we maximizes is based on a constant variance normal distribution family!

I once wrote a slider-based demo in XLispStat, which demonstrated this clearly!

The MASS package that comes with your R installed already, has the boxcox() function that you can use: After reading in the data, do:

library(MASS)
boxcox(y ~ x)

Then look at the graph this produces, which shows graphically a 95% confidence interval for the boxcox transformation parameter. But you do not really have enough data (n=10) to do this, the resulting confidence interval goes almost from -2 to 2!, with a maximum likelihood estimate of approximately 0 (a log-transform, as said before). If your real data have more observations, you should try this.

As others have said, this transformation is really trying to stabilize variances. This is not really obvoius from theory, what it does, is to try to maximize a normal-distribution based likelihood function, which assumes constant variance. One could think that maximizing a normal-based likelihood would try to normalize the distribution of the residuals, but in practice the main contribution to maximiznig the likelihood comes from stabilizing the variances.

I once wrote a slider-based demo in Xstatlisp, which demonstrated this clearly!

The MASS package that comes with your R installed already, has the boxcox() function that you can use: After reading in the data, do:

library(MASS)
boxcox(y ~ x)

Then look at the graph this produces, which shows graphically a 95% confidence interval for the boxcox transformation parameter. But you do not really have enough data (n=10) to do this, the resulting confidence interval goes almost from -2 to 2!, with a maximum likelihood estimate of approximately 0 (a log-transform, as said before). If your real data have more observations, you should try this.

As others have said, this transformation is really trying to stabilize variances. This is not really obvious from theory, what it does, is to try to maximize a normal-distribution based likelihood function, which assumes constant variance. One could think that maximizing a normal-based likelihood would try to normalize the distribution of the residuals, but in practice the main contribution to maximizing the likelihood comes from stabilizing the variances.

I once wrote a slider-based demo in XLispStat, which demonstrated this clearly!