CODEWITHSUNDEEP
pythonmachine-learninglinear-regression
rrz0
rrz0

Reputation: 2302

How to retrieve original coefficients after performing regression on normalised data without using Scikit-Learn?

I am reading data from a file using pandas which looks like this:

data.head()

   ldr1  ldr2  servo
0   971   956     -2
1   691   825   -105
2   841   963    -26
3   970   731     44
4   755   939    -69

I proceed to normalize this data to perform gradient descent:

my_data = (my_data - my_data.mean())/my_data.std()
my_data.head()

       ldr1      ldr2     servo
0  1.419949  1.289668  0.366482
1 -0.242834  0.591311 -1.580420
2  0.647943  1.326984 -0.087165
3  1.414011  0.090200  1.235972
4  0.137231  1.199041 -0.899949

I perform multivariate regression and end up with fitted parameters on the normalized data:

Thetas:  [[ 0.31973117  0.45401309 -0.12941108]]

I would like to plot the plane of best fit on the original data and not the normalized data using the normalized thetas.

I used scipy.optimize.curve_fit to perform multivariate linear regression and come up with the optimal fitted parameters. I know that the original thetas should be close to the following: 

[   0.26654135   -0.15218007 -107.79915373]

How can I get the 'original' thetas for the original data-set in order to plot, without using Scikit-Learn?

Any suggestions will be appreciated.

As per the answer below:

m
ldr1     731.891429
ldr2     714.080000
servo    -21.388571
dtype: float64
s
ldr1     168.392347
ldr2     187.583221
servo     52.904576
dtype: float64

I then proceed with:

original_thetas = np.dot(theta, s) + m

which yields:

original_thetas
ldr1     862.420572
ldr2     844.609144
servo    109.140572
dtype: float64

I am not sure if I am performing the calculation incorrectly or if the method presented does not work for the coefficients themselves.

Upvotes: 4

Views: 1435

Answers (1)

Ken Syme
Ken Syme

Reputation: 3632

I believe you just need to store the mean and standard deviations

m = data.mean()
s = data.std()

And then inverse the transformation

theta * s + m

Upvotes: 6

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