which python regression function to use for linear regression curve - regression

Question

Im trying to replicate a function in python and was able to code the following using multiple columns in a dataframe but was wondering if there is a python regression function that would do this more effectively. Here is the link to the description of the function. Sorry in advanced not really a stats guy. :)
http://tlc.thinkorswim.com/center/reference/thinkScript/Functions/Statistical/Inertia.html
It states that its the linear regression curve using the least-squares method to approximate data for each set of bars.
input y = close;
input n = 20;
def x = x[1] + 1; # previous value + 1
def a = (n * Sum(x * y, n) - Sum(x, n) * Sum(y, n) ) / ( n * Sum(Sqr(x), n) -Sqr(Sum(x, n)));
def b = (Sum(Sqr(x), n) * Sum(y, n) - Sum(x, n) * Sum(x * y, n) ) / ( n * Sum(Sqr(x), n) - Sqr(Sum(x, n)));
plot InertiaTS = a * x + b;
Thanks
Updated
here is the pandas columns and function. I first defined the xValue and yValue columns and then the following which is the raw calculation:
df['ind1']= ((10 * (df['xValue']*df['ysValue']).rolling(10, min_periods=10).sum() - df['xValue'].rolling(10, min_periods=10).sum()*df['ysValue'].rolling(10, min_periods=10).sum())/ (10 * (df['xValue'] ** 2).rolling(10, min_periods=10).sum() - (df['xValue'].rolling(10, min_periods=10).sum())**2)) * df['xValue'] + (((df['xValue'] ** 2).rolling(10, min_periods=10).sum()*df['ysValue'].rolling(10, min_periods=10).sum() - df['xValue'].rolling(10, min_periods=10).sum()*(df['xValue']*df['ysValue']).rolling(10, min_periods=10).sum())/(10 * (df['xValue'] ** 2).rolling(10, min_periods=10).sum() - (df['xValue'].rolling(10, min_periods=10).sum())**2))

Answer 1

It's not really clear whether you are just looking for a way to perform regression in python or you want to code the algorithm yourself.
if you want a package to do the regression, you can look at scikit-learn
Using,
from sklearn import linear_model
linear_model.LinearRegression()
If you want to code your own algorithm, you can look at gradient descent. you can look at a video by Andrew Ng on coursera - https://www.coursera.org/learn/machine-learning/lecture/GFFPB/gradient-descent-intuition. It's fairly intuitive to code the algorithm, the steps are as follows,
i. define a cost function - this is based on OLS(ordinary least squares) and looks like,
J = 1/2 (h(x) - y ) ^2
ii. take a partial derivative of cost function wrt each feature or j. Here X is the input vector comprised of n features one of which is j.
iii. Update the feature vector using gradient descent -
theta = theta - alpha * (partial derivative)
You can find the details here from Andrew Ng's papaper: http://cs229.stanford.edu/notes/cs229-notes1.pdf
sorry, it's difficult to put latex on SO