Finding a linear model such as this one can be handled with OpenTURNS.
In OpenTURNS this is done with the LinearModelAlgorithmclass which creates a linear model from numerical samples. To be more specific, it builds the following linear model :
Y = a0 + a1.X1 + ... + an.Xn + epsilon,
where the error epsilon is gaussian with zero mean and unit variance. Assuming your data is in a csv file, here is a simple script to get the regression coefficients ai :
from __future__ import print_function
import pandas as pd
import openturns as ot
# Assuming the data is a csv file with the given structure
# Y X1 X2 .. X7
df = pd.read_csv("./data.csv", sep="\s+")
# Build a sample from the pandas dataframe
sample = ot.Sample(df.values)
# The observation points are in the first column (dimension 1)
Y = sample[:, 0]
# The input vector (X1,..,X7) of dimension 7
X = sample[:, 1::]
# Build a Linear model approximation
result = ot.LinearModelAlgorithm(X, Y).getResult()
# Get the coefficients ai
print("coefficients of the linear regression model = ", result.getCoefficients())
You can then easily get the confidence intervals with the following call :
# Get the confidence intervals at 90% of the ai coefficients
print(
"confidence intervals of the coefficients = ",
ot.LinearModelAnalysis(result).getCoefficientsConfidenceInterval(0.9),
)
You may find a more detailed example in the OpenTURNS examples.