Update 08.decision_tree.md

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+# Decision Tree Analysis
+
+This section is dedicated to decision tree analysis. Because the dependent variable is not categorical, the DecisionTreeRegressor from scikit-learn was employed. 
+After the first decision tree was created, using the original dataset (with Duration_hours and Duration_min combined into a single variable Total_Duration), the \( R^2 \) value was 0.999977. This value seemed suspuciously perfect. 
+The effect of the high correlation value can also be seen in the figure below, which is a plot of the actual vs predicted value, and as can be seen the predicted values fall almost perfectly along the actual values.
+
+<p align="center">
+  <img src="images/Actual_Predicted_Vals_Original_Data.png" alt="Actual vs predicted values for the original dataset" width="600px">
+  <br>
+  <strong>Figure 7:</strong> Correlation matrix created using the original dataset.
+</p>
+
+
+
+To understand the origins of this \( R^2 \) value, firstly a correlation plot was created. The first correlation plot is seen below in Figure 8:
+
+<p align="center">
+  <img src="images/Correlation_Mat_Original_Data.png" alt="Correlation matrix created using the original dataset" width="600px">
+  <br>
+  <strong>Figure 8:</strong> Correlation matrix created using the original dataset.
+</p>
+
+As can be seen from the figure above, the highest correlation appears between Total_Duration and CO2_Emitted (US Ton), the depenent variable. This makes sense, of course, because the longer the plane is in flight, the more \( CO_2 \) will be emitted.