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Python with Science Applicaitons/LabB/LabB1.py

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+# Lab B - Stephen Terrio, B00755443
+# Matrix Regression
+
+# Packages -
+import pandas as pd
+import matplotlib.pyplot as plt
+import numpy as np
+import math
+
+ # Reading excel sheet
+dataXY = pd.read_excel('IrisData_slr10.xls')
+dataXY.head()
+myDataArray=np.array(dataXY)
+
+# Filling arrays for later use
+x=myDataArray[:,0] # Pulling the first column to be used as X
+y=myDataArray[:,1] # Pulling the second column to be used as Y
+
+#Matrix Regression using 𝛽 =(𝑋𝑇*𝑋)−1 * (𝑋𝑇*𝑌)
+Xmatrix=np.vstack((np.ones(len(x)), x)).T
+# Using formula -> ((X-transpose * X)-inverse)*(X-transpose*Y)
+beta = np.linalg.inv(Xmatrix.T.dot(Xmatrix)).dot(Xmatrix.T).dot(y)
+print("Using Matrix Regression...")
+print(beta)
+
+# Using results from regression as intercept & coefficient for y hat
+# yHat = b0 + b1 + xi
+yHat = [beta[0] + beta[1] * i for i in x]
+
+# Residiuals -
+ei=[] # Using to store ei values
+for i in range(len(x)):
+# ei = yi - yhat
+    ei.append(y[i] - yHat[i])
+
+#Graph of predicted line vs values found in sheet
+plt.scatter(x, y) # Showing point values of x and y
+plt.plot(x, yHat, color='red') # Superposing line
+plt.show()
+
+# Ensuring they are NP arrays..
+ynp = np.array(y)
+xnp = np.array(x)
+ei_np = np.array(ei)
+
+#plotting ei vs y and ei vs x
+plt.plot(ei_np,ynp, color='red')
+plt.plot(ei_np ,xnp, color='blue')
+plt.show()