Data normalization or not I have one data set with several variables and some of them have wide range. I want to predict sales from historical data.
Sales from 0 to 6000000,   epoch time like 1419656400  in seconds   but I also have  temperatures   from 0-100 degrees. 
I think if I want to compare different statistical effects of different features, normalization of data might have a fair comparison. 
What else advantage or disadvantage of data normalization?
Should I use same normalization method for  all the variables?
Thank you.
 A: Why rescaling/normalizing would not matter:
At a mathematics level, rescaling your data will not affect a regression in the sense that the estimated coefficients would also be rescaled.
In a sample of humans, if I regressed height in feet on:


*

*Arm length in feet 

*Arm length in inches


Either (1) or (2) would be the same in the sense that the estimated coefficient in case (1) would be 12 times the estimated coefficient in case (2).
More broadly, you can also apply an affine transformation to a variable if a constant is included in a regression. Imagine two regressions:
$$ y_i = a_1 + b_1 f_i + \epsilon_i  \quad \quad f = \text{temp in Fahrenheit} $$
$$ y_i = a_2 + b_2 c_i + \epsilon_i  \quad \quad c = \text{temp in Celsius} $$
We would have the coefficients linked by the conversion factor ($f = \frac{9}{5}c + 32$) between Celsius and Fahrenheit: $b_2 =  \frac{9}{5} b_1 $  and $a_2 = a_1 + 32 b_1$.
At a mathematical level, normalization doesn't really matter. But there are reasons to rescale/normalize!
Some reasons to rescale, standardize, normalize, etc...


*

*Easier interpretation!


Often times it can be easier to interpret whether a variable is big or small relative to its standard deviation. Standardizing a variable (i.e. subtract mean and divide by standard deviation) may have more interpretable coefficients. For example, it may be easier to interpret a one standard deviation increase in blood pressure rather than an increase of 10mmHg.


*Numerical properties


Including very large and very small numbers in a regression can lead to computational problems. In technical terms, you may have a design matrix with a very high condition number leading to imprecise calculations when multiplying matrices and solving linear systems. In plain English, sh*# can hit the fan.
Eg. If you're doing some corporate finance regression on big companies, maybe you want to measure revenue in units of millions of US dollars. 
