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Difficulty interpreting coefficients after linear regression model training

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I've successfully trained a linear regression model in scikit-learn, but I'm having trouble interpreting the coefficients. Could someone help me understand what the coefficients represent and how to interpret them?

This topic was modified 6 months ago by Neuraldemy Support
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  1. Positive Coefficients:

    • If a coefficient is positive, it means that as the corresponding feature increases, the predicted outcome is expected to increase as well.
  2. Negative Coefficients:

    • Conversely, if a coefficient is negative, it means that as the corresponding feature increases, the predicted outcome is expected to decrease.
  3. Magnitude of Coefficients:

    • The magnitude of a coefficient indicates the strength of its impact. Larger magnitudes suggest a stronger influence on the predicted outcome.

Let's say you have a linear regression model predicting house prices based on two features: square footage (sqft) and the number of bedrooms (bedrooms). Your model might look something like this: 

from sklearn.linear_model import LinearRegression

# Assuming X contains 'sqft' and 'bedrooms', and y is the target variable ('price')
model = LinearRegression()
model.fit(X, y)

# Get the coefficients
coefficients = model.coef_


print(coefficients)
>> Output: [50, 20000]

So, what does this mean?

  • The coefficient for sqft is 50. This implies that, holding all other factors constant, for every additional square foot in the house, the predicted price increases by $50.

  • The coefficient for bedrooms is 20000. This suggests that, holding all other factors constant, each additional bedroom contributes $20,000 to the predicted price.

nterpreting the Intercept:

There's also an intercept term in your linear regression model. This is like the base price of the house when all other features are zero.

intercept = model.intercept_
print(intercept)
>> Output: 50000

So, in our example, even if the house has zero square footage and zero bedrooms, the base price would be $50,000.

Important Considerations:

  • Scale Matters:

    • The scale of your features affects the magnitude of the coefficients. If one feature is in square feet and another in the number of bedrooms, their coefficients won't be directly comparable.
  • Check for Units:

    • Always check the units of your features. If your sqft is in thousands, the coefficient of 50 means $50,000 per square foot.
  • Interaction Effects:

    • Sometimes, the true impact of a feature depends on the values of other features. For a more nuanced understanding, you might explore interaction terms.

Please close the topic if your issue has been resolved. Add comments to continue adding more context or to continue discussion and add answer only if it is the answer of the question.
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