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5 Implementation

🎉 Tutorial Complete!

You've successfully specified a complete GLM. Here's how to fit it in practice.

Your Complete Model

MaxHeartRate ~ Normal(μ, σ²) where μ = β₀ + β₁·Age + β₂·ExAng + β₃·STDep
Response
Max Heart Rate
Link
Identity
Family
Gaussian
Method
Maximum Likelihood

1 Load the data

# Load the heart disease dataset
heart <- read.csv("heart.csv")

# Preview the data
head(heart)

2 Fit the GLM

# Fit the model using glm()
model <- glm(
  thalach ~ age + exang + oldpeak,
  data = heart,
  family = gaussian(link = "identity")
)
Note: For Gaussian + identity, you could also use lm() which gives identical results. Using glm() makes the GLM framework explicit and is easily adapted to other families.

3 View results

# Summary of fitted model
summary(model)

# Extract coefficients
coef(model)

# Confidence intervals
confint(model)

4 Check assumptions

# Diagnostic plots
par(mfrow = c(2, 2))
plot(model)

# Check for patterns in residuals
# - Residuals vs Fitted: look for constant spread
# - Q-Q plot: points should follow diagonal
# - Scale-Location: horizontal band = good
# - Residuals vs Leverage: no influential outliers

Expected Output

Call: glm(formula = thalach ~ age + exang + oldpeak, family = gaussian(link = "identity"), data = heart) Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 203.3660 6.7458 30.147 < 2e-16 *** age -0.8298 0.1247 -6.657 1.34e-10 *** exang -14.2542 2.4519 -5.813 1.57e-08 *** oldpeak -3.7805 1.0091 -3.746 0.000215 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 (Dispersion parameter for gaussian family taken to be 366.9819) Null deviance: 169344 on 302 degrees of freedom Residual deviance: 109727 on 299 degrees of freedom AIC: 2655.2

1 Import libraries and load data

import pandas as pd
import statsmodels.api as sm
import statsmodels.formula.api as smf

# Load the heart disease dataset
heart = pd.read_csv("heart.csv")

# Preview the data
print(heart.head())

2 Fit the GLM

# Fit the model using formula interface
model = smf.glm(
    formula="thalach ~ age + exang + oldpeak",
    data=heart,
    family=sm.families.Gaussian(
        link=sm.families.links.Identity()
    )
).fit()
Note: For Gaussian + identity, you could also use smf.ols() which gives identical results. Using glm() makes the GLM framework explicit and is easily adapted to other families.

3 View results

# Summary of fitted model
print(model.summary())

# Extract coefficients
print(model.params)

# Confidence intervals
print(model.conf_int())

4 Check assumptions

import matplotlib.pyplot as plt
import scipy.stats as stats

# Get residuals and fitted values
residuals = model.resid_pearson
fitted = model.fittedvalues

# Create diagnostic plots
fig, axes = plt.subplots(2, 2, figsize=(10, 8))

# Residuals vs Fitted
axes[0, 0].scatter(fitted, residuals, alpha=0.5)
axes[0, 0].axhline(y=0, color='red', linestyle='--')
axes[0, 0].set_xlabel('Fitted values')
axes[0, 0].set_ylabel('Residuals')
axes[0, 0].set_title('Residuals vs Fitted')

# Q-Q plot
stats.probplot(residuals, plot=axes[0, 1])
axes[0, 1].set_title('Q-Q Plot')

plt.tight_layout()
plt.show()

Expected Output

Generalized Linear Model Regression Results ============================================================================== Dep. Variable: thalach No. Observations: 303 Model: GLM Df Residuals: 299 Model Family: Gaussian Df Model: 3 Link Function: Identity Scale: 366.98 Method: IRLS Log-Likelihood: -1322.6 Date: Thu, 11 Dec 2025 Deviance: 1.0973e+05 Time: 15:31:43 Pearson chi2: 1.10e+05 No. Iterations: 3 Pseudo R-squ. (CS): 0.3524 Covariance Type: nonrobust ============================================================================== coef std err z P>|z| [0.025 0.975] ------------------------------------------------------------------------------ Intercept 203.3660 6.746 30.147 0.000 190.144 216.588 age -0.8298 0.125 -6.657 0.000 -1.074 -0.585 exang -14.2542 2.452 -5.813 0.000 -19.060 -9.448 oldpeak -3.7805 1.009 -3.746 0.000 -5.758 -1.803 ==============================================================================

What's Next?

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