Update app.py

app.py

@@ -52,6 +52,14 @@ def plot_and_predict(zip, start_year, start_month, prediction_months):
     future_months = np.array([last_month_index + i for i in range(1, prediction_months + 1)]).reshape(-1, 1)
     predicted_prices = model.predict(future_months)
 
+    # Calculate standard error and prediction intervals
+    se = np.sqrt(np.sum((model.predict(X) - y) ** 2) / (len(y) - 2))
+    t = stats.t.ppf(0.975, len(y) - 2)  # 95% prediction interval
+    prediction_interval = t * se * np.sqrt(1 + 1/len(y) + (future_months - np.mean(X))**2 / np.sum((X - np.mean(X))**2))
+
+    upper_bound = predicted_prices + prediction_interval
+    lower_bound = predicted_prices - prediction_interval
+
     # Prepare data for plotting
     historical_prices_trace = go.Scatter(
         x=df['Date'],
@@ -67,6 +75,12 @@ def plot_and_predict(zip, start_year, start_month, prediction_months):
         name="Predicted Prices"
     )
 
+    # Plot prediction intervals
+    fig.add_traces([
+        go.Scatter(x=future_dates, y=upper_bound.flatten(), mode='lines', name='Upper Bound', line=dict(width=0)),
+        go.Scatter(x=future_dates, y=lower_bound.flatten(), mode='lines', name='Lower Bound', line=dict(width=0), fill='tonexty')
+    ])
+    
     # Plot data
     fig = go.Figure()
     fig.add_trace(historical_prices_trace)