# after normalize data, Using multiple regression analysis how to predict y?

I want to predict yield(y), I have independent variables are rain(x1) and Soil(x2)

yield(y) : 25000, 26000, 27000, 28000, 29000

Rain_mm (x1) : 1000, 875, 852, 1005, 1250

Soil ( x2) : 0, 0, 1, 1, 2,

Next, I was normalize this data to scale in same range using this code :

from sklearn.preprocessing import Normalizer
import pandas
import numpy
url = "data.csv"
dataframe = pandas.read_csv(url)
array = dataframe.values
# separate array into input and output components
X = array[:,0:3]
scaler = Normalizer().fit(X)
normalizedX = scaler.transform(X)


next, I have use regression formula ,using this normalizedX values ,

suppose now we have bo , b1 and b2 value . I want to predict yield using regression model.

yield = b0 + b1 * rain + b2 * soil

for example : bo = 1.25 , b1 =0.45 , b2 =-0.36

Now, I am confusing when I use this regression equation for predict yield(y), I get all value in the scale range data, (in normalize data), I want to convert this numbers in original yield.

for example : if I have plug value rain 1000, and soil 0 , then yield will be comes 25000 or any predicted number but not in 0 to 1 range.

Any one help me how to get that? or I am doing wrong something? any hints?

## 1 Answer

I'll begin by stating that normalization (scaling/shifting) of the data used in training a regression model isn't strictly necessary, and won't typically affect the accuracy of prediction for new input values. I say typically because in cases where the inputs or the predicted values approach the upper/lower limits of digital representation you may experience truncation errors or data type overflow, though with a dynamically typed language such as python, these worries should be mostly hidden from the user.

I would encourage you to perform the regression fitting on the unnormalized training data. If you insist on performing the normalization pre-processing then you can use a sklearn.preprocessing class that implements the inverse_transform() function (like the StandardNormalizer class). You can then fit the class to the training data and later apply the inverse_transform() function to the predicted output value(s).

The class you are using: "Normalizer" is performing L2-norm normalization on a per-sample basis by default, which is not recommended for the regression problem because the adapted weights in your model will be seeing different scales for a particular feature across the training sample. I don't expect your regression model to accurately predict the outcome of a new input vector when the "Normalizer" pre-processing class is employed.

• oh I see, thanks very much, can you tell me If I have use standardNormalizer class then can I get R^2 high? or it will be same ? – Kiran Prajapati Feb 10 '17 at 8:35
• So Normalizer is not help for regression , right? – Kiran Prajapati Feb 10 '17 at 8:40
• @KiranPrajapati, The normalization preprocessing technique that you employ (or don't employ) won't change the performance of your regression model. The way to improve the goodness of fit (of which R^2 is one of many indicators) of your model is to understand the type of relationship you expect to see between your input(s) and output(s) and give your model explicit expressiveness in describing that relationship. Fitting a linear model on data that follows an exponential relationship would be a flaw in your modeling of the problem for example, not in the handling of the input data. – Ryan Neph Feb 11 '17 at 8:23