# Viability of log-log transformation for some data

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• RubinLicht
In summary, the conversation discusses the usage of logarithmic transformations in data analysis, specifically in relation to creating a scatter plot and working with non-linear relationships. The speakers consider the potential benefits and limitations of using logarithmic transformations in their project.
RubinLicht
I have taken AP Statistics, and this is for the final project. What we have learned consists of some simple significant tests (t test, z test for proportions, two sample tests, chi squared, and logarithmic transforms).

My partner and I are considering creating a scatter plot of distance between dominoes and the speed of the dominoes. If we applied a logarithmic transformation to the data (assuming there is some power relationship, which is most definitely not centered at the origin), would the data appear somewhat linear?

I would also like a clarification, do log log transformations work on, say, parabolas with vertexes not centered at (0,0)? (I just plotted a parabola with its vertex at 2,4 in mathematica, and the graph turned out strange for values to the left of the vertex, is there any way to amend for this?)Thanks

RubinLicht said:
If we applied a logarithmic transformation to the data (assuming there is some power relationship, which is most definitely not centered at the origin), would the data appear somewhat linear?
Test it? For some relations it can become linear.

RubinLicht said:
I would also like a clarification, do log log transformations work on, say, parabolas with vertexes not centered at (0,0)?
No, unless you take that offset into account separately (e. g. plot log(x-1) instead of log(x)).

## 1. What is a log-log transformation?

A log-log transformation is a mathematical technique used to transform data that is not normally distributed into a more linear pattern. It involves taking the logarithm of both the independent and dependent variables.

## 2. When is a log-log transformation necessary?

A log-log transformation is necessary when the data does not follow a normal distribution and there is a non-linear relationship between the independent and dependent variables. This transformation helps to create a more linear relationship between the variables, making it easier to analyze and interpret the data.

## 3. How does a log-log transformation affect the data?

A log-log transformation compresses the data, making extreme values less extreme and bringing all values closer together. This can help to reduce the influence of outliers and make the data more suitable for statistical analysis.

## 4. What are the benefits of using a log-log transformation?

The main benefit of using a log-log transformation is that it can help to improve the linear relationship between variables, making it easier to model and analyze the data. It can also help to reduce the influence of outliers and make the data more normally distributed.

## 5. Are there any limitations to using a log-log transformation?

While a log-log transformation can be useful in certain situations, it is not always appropriate for all types of data. It is important to carefully consider the characteristics of the data and the research question before deciding to use a log-log transformation. Additionally, the interpretation of the transformed data may be more complex than the original data, so it is important to communicate and explain the results carefully.

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