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I have a data set $N\times M$, which contains information about motorcycles: $N$ motorcycles have been sold during some time and for each bike there is $M$ parameters regarding the sale such as price, year it was built, where it was sold geographically etc.

I would like to investigate this data further and find out just which of these $M$ parameters best determine what price a bike is sold at.

I have previously heard about Principal Component Analysis and read some small notes about it. Can I use PCA for this, or are there other methods that suit this problem better?

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First, I suggest you make univariate descriptions of your $M$ variables, then bivariate statistics, such as the correlation matrix of numerical variables. You can also make plots price vs other variables. After this you'll know a little more about your data and the relationships between the variables.

Then, I think a PCA is actually a good idea but it won't be enough. With a PCA you'll be able to reduce the dimension of your data from $M$ to a much smaller dimension (except if your variables are uncorrelated, which I doubt) and to visualize your data. Interpreting the principal factors will probably be very useful. You may also detect several groups between your observations.

However, PCA won't do it if you want to be able to predict prices. In order to do this, you could just start by a linear regression, before using more sophisticated techniques if necessary.

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