Oppiskele Interpreting Regression Results | Economic Modeling and Regression

Regression analysis is a powerful tool in economics for understanding relationships between variables. When you run a regression, the output typically includes coefficients for each predictor, an intercept, and a statistic called R-squared. Each of these elements provides important information about the economic relationship you are studying.

Coefficients show how much the dependent variable changes when the predictor changes by one unit, holding other factors constant;
The intercept is the expected value of the dependent variable when all predictors are zero;
R-squared measures how well the model explains the variation in the dependent variable.

Understanding these outputs is key to making meaningful economic interpretations.


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import pandas as pd
import numpy as np
from sklearn.linear_model import LinearRegression

# Simulated data: GDP growth (%) and unemployment rate (%)
data = {
    "GDP_Growth": [2.5, 3.0, 1.8, 2.2, 2.9, 1.5, 2.7, 3.2, 2.0, 2.4],
    "Unemployment": [5.1, 4.8, 5.5, 5.3, 4.9, 5.7, 5.0, 4.6, 5.4, 5.2]
}
df = pd.DataFrame(data)

X = df[["GDP_Growth"]]
y = df["Unemployment"]

model = LinearRegression()
model.fit(X, y)

print("Intercept:", round(model.intercept_, 3))
print("Coefficient for GDP_Growth:", round(model.coef_[0], 3))

When interpreting regression coefficients, you should focus on both the sign and the magnitude. In the unemployment and GDP growth model above, the coefficient for GDP growth indicates how much the unemployment rate is expected to change for each one percentage point increase in GDP growth. A negative coefficient means that as GDP growth increases, unemployment tends to decrease, which aligns with economic theory suggesting that stronger economic growth leads to lower unemployment. The size of the coefficient tells you how strong this relationship is: a larger absolute value means a bigger impact per unit change in GDP growth. The intercept represents the predicted unemployment rate when GDP growth is zero, which can also have economic meaning depending on the context.


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from sklearn.metrics import r2_score

# Predict unemployment using the model
y_pred = model.predict(X)

# Calculate R-squared
r2 = r2_score(y, y_pred)
print("R-squared:", round(r2, 3))

1. What does a negative coefficient for GDP growth imply in a regression predicting unemployment?

2. What does R-squared tell you about your regression model?

3. Fill in the blank: The intercept in a regression model represents _ _ _.

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Coefficients show how much the dependent variable changes when the predictor changes by one unit, holding other factors constant;
The intercept is the expected value of the dependent variable when all predictors are zero;
R-squared measures how well the model explains the variation in the dependent variable.