Step-by-Step Code Explanation
Imports necessary libraries:
import statsmodels.api as sm
import numpy as np
statsmodels.api is used for statistical modeling.
numpy is used for numerical computations and array handling.
x = np.array([1, 2, 3, 4, 5])
y = np.array([2, 4, 6, 8, 10])
Defines input variables:
x = [1, 2, 3, 4, 5] (independent variable)
y = [2, 4, 6, 8, 10] (dependent variable)
The relationship is perfectly linear with y = 2x.
model = sm.OLS(y, sm.add_constant(x)).fit()
Creates and fits an Ordinary Least Squares (OLS) regression model:
sm.add_constant(x) adds a bias (intercept) term to x.
sm.OLS(y, X).fit() computes the best-fit line for y = 2x.
print(model.params[1])
Extracts and prints the slope (coefficient) of x
The slope represents how much y changes for each unit change in x.
Ideally, the output should be 2.0, but the actual printed value is:
1.9999999999999998
Why is the Output 1.9999999999999998 Instead of 2.0?
This happens due to floating-point precision errors in Python. Here’s why:
Floating-Point Representation
Computers store decimal numbers in binary floating-point format, which sometimes cannot exactly represent simple decimals.
Tiny rounding errors occur during calculations, leading to results like 1.9999999999999998 instead of 2.0.
Final Answer (Exact Value with Floating-Point Precision)
1.999
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