# SPSS linear regression - variables that are percentages

I have some data about music styles played at festivals. It looks like this:

Based on this (and other) data, I'd like to make a model to explain the price of a ticket for each festival. However I'm not sure how to handle this data in SPSS. Should I treat each style as a variable? And if I did, the styles aren't normal distributed. I can't take the natural logaritm to transform the data since there are zeros in every style.

How should I proceed?

Based on this description I might consider a model of the form (where $\text{group}_i$ refers to a music category):

$$\text{Price} = \beta_0 + \beta_1(\text{Total Number of Artists}) + \Sigma \lambda_i(\text{% of group}_i) + \Sigma \eta_i(\text{% of group}_i \cdot \text{Total Number of Artists}) + e$$

Where $\Sigma \lambda_i(\text{% of group}_i)$ represents a set of variables that is the percentage of each music style and $(\text{% of group}_i \cdot \text{Total Number of Artists})$ is the interaction between these values. Note that one of the groups needs to be ommitted in each of these steps to avoid perfect collinearity.

The fact that the independent variables are not normally distributed is not an issue (only the error term matters in OLS). This specification allows you to test the marginal impacts of adding additional acts or changing the composition of the current set of acts.

As always it might be the case that any of these explanatory variables have a non-linear relationship to Price, and each can be checked either in the marginal relationships or in partial residual plots to determine if non-linearity might exist.

• I'm not entirely sure how to do that in SPSS. Could you please elaborate on that? – user36860 Apr 16 '14 at 14:46
• @Tom - you will need to be more specific. This is just a linear regression equation with a set of variables. It should be pretty simple to estimate the equation in any software once you have your data. – Andy W Apr 16 '14 at 19:15
• I haven't seen a model of this form before. The ones I've seen were only with beta (and of course the error). I basically have no idea how a model with a lambda works nor what that part is called. That makes it hard for me to find any other resources so that I can find out how to work with it in SPSS. Are there any resources you can tell me off so that I can find out how this works? – user36860 Apr 17 '14 at 8:47
• I just used lambda and eta to signify a grouping of coefficients and the sigma means the sum of the coefficients. They go into the model one at a time - the same as any individual variable - it just doesn't make sense to test them individually since you can't make one go up without another going down. The SPSS tag wiki has various other resources listed. – Andy W Apr 17 '14 at 12:00