Should I ever standardise/normalise the target data/ dependent variables in regression models? After standardising the explanatory variables the difference in magnitude between the explanatory variables and the target data is ~3 orders of magnitudes. I want to know if transformation of the target data will still give valid results.
Thanks a lot folks!
 A: Scaling or zeroing will will not change the regression or classification results. The only down side is lose of interpretability.
Here are working examples in R showing that any combination of scaling or zeroing produces the same regression line.
Coefficients can be different, and that is okay. Here are the coefficients calculated in the models below in order.
  (Intercept)         disp
1    29.59985  -0.04121512
2    20.09062  -0.04121512
3    26.66946 -16.52314159
4    26.66946 -16.52314159

No zeroing or scaling
# orginal data
df <- mtcars
png("mtcars_original.png")
plot(df$disp, df$mpg, main="MPG VS Displacment")
abline(lm(mpg ~ disp, df), col = 2)
dev.off()

 
Zeroed
# zeroed displacement
df <- mtcars
df$disp <- df$disp - mean(df$disp)
png("mtcars_zeroed.png")
plot(df$disp, df$mpg, main="MPG VS Zeroed  Displacement")
abline(lm(mpg ~ disp, df), col = 2)
dev.off()


Scaled
# scaled displacment
df <- mtcars
df$disp <- (df$disp - min(df$disp)) / ( max(df$disp) -  min(df$disp))
png("mtcars_scaled.png")
plot(df$disp, df$mpg, main="MPG VS Scaled Displacment")
abline(lm(mpg ~ disp, df), col = 2)
dev.off()

 
Zeroed & Scaled
# zeroed & scaled displacment
df <- mtcars
dt$disp <- df$disp - mean(df$disp)
df$disp <- (df$disp - min(df$disp)) / ( max(df$disp) -  min(df$disp))
png("mtcars_zeroed_scaled.png")
plot(df$disp, df$mpg, main="MPG VS Scaled & Zeroed Displacment")
abline(lm(mpg ~ disp, df), col = 2)
dev.off()


A: It will. Your measurements are coordinates. For every value on the explanatory variable, you have a coordinate measurement on the target variable. If you don't change the order of either, then the relation remains intact. Right?
