# The effect of scale of predictor variables in regression techniques

In polynomial regression, it is recommended to center predictor input variables to break multi colinear relationships of x to x^2.

From Wikipedia: The underlying monomials can be highly correlated "For example, x and x2 have correlation around 0.97 when x is uniformly distributed on the interval (0, 1). "

When a variable x is between -1 and 1, x^2 makes the magnitude smaller while when x is outside of that range, x^2 makes x's magnitude larger.

Making the variable into an integer variable could change the behavior.

E.g.

df$x=round((df$x - mean(df\$))*100)


Any opinions on the scale especially in regards to interval [-1,1] vs [-100,100]

It is common to normalize predictors subtracting the mean and dividing by the standard deviation when doing inference analysis but this question pertains to regression prediction.

Asking a similar question in regards to natural log, a variable that has a range (0,1] has a dramatically different transformed value than [1,100].

log(seq(0.1,1,.1)) #mostly negative
log(seq(0.1,1,.1)*100) #rather positive


If the predictor variable in the case of log happened to be sometimes less than 1 and others greater than 1, that could make the transformation act a little "wild". Would it be best to transform the variable to be within (0,1] or [1,] but not both?