Update Part_15_Regression.md

Author: DragonflyStats

Part_15_Regression.md

@@ -1,13 +1,10 @@
 
 ### Fitting a line through data***
 
-Linear regression is the first, and therefore, probably the most fundamental
-model—a straight line through data.
+Linear regression is the first, and therefore, probably the most fundamental model—a straight line through data.
 
 #### Description
-The ***boston*** dataset is useful for learning about  linear regression. The \textit{boston*** dataset has the
-median home price of several areas in Boston. It also has other factors that might impact
-housing prices, for example, crime rate.
+The ***boston*** dataset is useful for learning about  linear regression. The ***boston*** dataset has the median home price of several areas in Boston. It also has other factors that might impact housing prices, for example, crime rate.
 
 #### Getting the data
 
@@ -16,16 +13,15 @@ Firstly, we import the datasets model, then we can load the dataset:
 <pre><code>
 from sklearn import datasets
 boston = datasets.load_boston()
-
 </code></pre>
 
 ### Implementation
 
 Using linear regression in scikit-learn is very simple. 
 
 First, import the ***LinearRegression*** object and create an object (lets call it ***lr***):
-<pre><code>
 
+<pre><code>
 from sklearn.linear_model import LinearRegression
 lr = LinearRegression()
 
@@ -35,16 +31,13 @@ To fit the model, supply the independent and dependent variables to the ***fit**
 <pre><code>
 
 lr.fit(boston.data, boston.target)
-	
-	LinearRegression(copy_X=True, fit_intercept=True, normalize=False)
-
+LinearRegression(copy_X=True, fit_intercept=True, normalize=False)
 </code></pre>
 
 Let's take a look at the regression coefficients:
 <pre><code>
-	
-	lr.coef_
-	array([ -1.07170557e-01,  4.63952195e-02, 2.08602395e-02,
+lr.coef_
+array([ -1.07170557e-01,  4.63952195e-02, 2.08602395e-02,
 	2.68856140e+00, -1.77957587e+01, 3.80475246e+00,
 	7.51061703e-04, -1.47575880e+00, 3.05655038e-01,
 	-1.23293463e-02, -9.53463555e-01, 9.39251272e-03,
@@ -53,43 +46,34 @@ Let's take a look at the regression coefficients:
 </code></pre>
 
 A common pattern to express the coefficients of the features and
-their names is ***zip(boston.feature\_names, lr.coef\_)***.
+their names is ***zip(boston.feature_names, lr.coef_)***.
 
 
-\item We can see which factors have a negative relationship with the
-outcome, and also the factors that have a positive relationship. 
-\item The per capita crime rate is the first coefficient in the regression. An increase in the per capita crime rate by town has a negative relationship with the price of a
-home in Boston. 
-\end{itemize***
+*  We can see which factors have a negative relationship with the outcome, and also the factors that have a positive relationship. 
+* The per capita crime rate is the first coefficient in the regression. An increase in the per capita crime rate by town has a negative relationship with the price of a home in Boston. 
 
+### Making Predictions
 
-
-### Making Predictions***
-Now, to get the predictions, use the ***predict*** method of
-***LinearRegression***:
+Now, to get the predictions, use the ***predict*** method of ***LinearRegression***:
 
 <pre><code>
-
 predictions = lr.predict(boston.data)
-
 </code></pre>
 
 
 ### Residuals***
-The next step is to look at how close the predicted values are to the actual data. These differences are known as \textbf{residuals***.
+The next step is to look at how close the predicted values are to the actual data. These differences are known as ***residuals***.
 We can use a histogram to look at these residuals.
 % % GRAPHIC 
 
 
-### Other Remarks***
+### Other Remarks
 The ***LinearRegression*** object can automatically normalize (or scale) the inputs:
-<pre><code>
 
+<pre><code>
 lr2 = LinearRegression(normalize=True)
 lr2.fit(boston.data, boston.target)
-
-	LinearRegression(copy_X=True, fit_intercept=True, normalize=True)
+LinearRegression(copy_X=True, fit_intercept=True, normalize=True)
 predictions2 = lr2.predict(boston.data)
 
 </code></pre>
-\end{document***