In the data, there are 355 observations including one continuous dependent variable (Y: ranges from 15-55) and 12 independent variables (continuous, categorical, and ordinal). The X1 (2 levels) and X6 (3 levels) are considered as categorical variables. Here are some questions that I have:
Can I assume that all the coefficients (except X1 and X6 which are categorical) are linear with respect to Y?
Can I consider X5 as continuous variable; however, it is ordinal and ranges from (1-7)?
Can I get the X7 (year) as continuous variable; however, it’s ordinal and rages from 2002-2006 (In fact, year of data per se does not improve the response; it is the other factors occurring in the same time period which result in improvements and we don’t know those factors), does this approach seem logical?.
In general if I use different transformations on independent variables such as log, squared, square root, and inverse, do I need to standardize the data also?
Here is the scatter plot:
Any feedback and insights would be highly appreciated. Thank you