Coefficients of Categorical P-Values in Regression - Condense or Apply 0? This analysis is part of a much larger research project, but I've extracted a simple example that will fit the question I have.
Y = B0 + B1 * [Day of Week] + E
Day of Week is coded as 1 (Sunday)-7 (Saturday). I'm using R, so I used day.of.week = factor(day.of.week) for the regression.
The P-Values Associated with each are as follows:


*

*day.of.week2 0.76

*day.of.week3 0.11

*day.of.week4 0.03

*day.of.week5 0.32

*day.of.week6 0.44

*day.of.week7 0.00009


Cleary, Wednesday and Saturday are significant and I would apply the appropriate coefficient. My question is what about the other days? 


*

*Do I apply a 0 for the coefficient since they are not significant?

*Do I apply the given coefficient since I am choosing to use the coefficient for Wednesday/Friday?

*Do I recode my day.of.week variables to have 1,2,3,5,6 all be 1 and rerun the analysis? Therefore, my categorical interpretation for Day of Week would be Wednesday, Saturday, and All Other Days?


Thank you for any help you can offer, it is much appreciated.
 A: To clear up categorical variables, you can create k-1 contrasts among the categories, where k is the number of categories. For instance, you may want to know if weekends are different from weekdays. You assign the same value to Sat. And Sun. (let's say -2.5) and the same value to all weekdays (let's say 1). That is 1 contrast. Dummy coding assigns 1 to one category, and 0 to the rest. And the category that get the 1 changes for each contrast. Because you can have a max of k-1 contrasts, one category always receives 0. If you look at the coefficients of your model, you'll notice that the intercept is the mean ticket sales for Sunday (the category that always received 0). The significance of the other coefficients asks if the mean for that day is greater or less than the intercept (I.e. Sunday). You don't need to create 6 contrasts, also (though no real reason not to). You could just assign 1-7 to the days of the week. This variable will tell you if there is a linear trend in the data as you move from Sunday to Saturday. Again though, if your data can support a more complex model, and you are more interested in $R^2$ or prediction, then go with the more complex model. With k-1 contrasts, your model will perfectly predict the means of each day of the week within your data. With anything less than that, your model will only approximate the means.
Now, your comment tells me you don't care about individual coefficients. Coefficients and p values tell you if relationships you found in your data could have arisen by chance. You aren't interested in the relationships between days of the week, nor do you care how reliable that pattern is. As I said before, using k-1 contrasts on your categorical variable will perfectly predict the means of each day within your data. If you are trying to predict outside your data, then things get fuzzy. The standard in most areas I am familiar with is cross-validation. Ideally you would have multiple data sets or split your data to create multiple data sets. You would use one data set to create a good fitting model, and then tests how accurate it's predictions are in the second data set.  
