I wrote a vectorized Gradient descent implementation of the linear regression model. The Dataset looks something like:
It's Not Working properly as I am getting negative R Squared error I don't understand why ?? Should I decrease Alpha or No. of Iterations or is there any problem in my implementation what should I do?
My Regression plot looks something like below I don't know why I am getting such a line. 
My Cost Function Error plot with respect to the number of iterations in Gradient descent looks something like below 
R Squared Error is: -3.744682246118262
My Code Snippet:
import numpy as np from sklearn.model_selection import train_test_split import seaborn as sns import matplotlib.pyplot as plt import pandas as pd def CostFunction(Theta,DataMatrix): Size = DataMatrix.shape[0] Error = 0 for i in range(0,Size): Feature = np.vstack(([1],np.array(DataMatrix[i][:-1]).reshape(-1,1))) Error += (np.transpose(Theta).dot(Feature) - DataMatrix[i][-1]) ** 2 return (1/(2*Size))*Error def GradientDescent(Theta,Alpha,DataMatrix,Iterations): Progress = [] Iterate = 0 Size = DataMatrix.shape[0] Error = np.zeros((DataMatrix.shape[1],1)) while(Iterations): for i in range(0,Size): Feature = np.vstack(([1],np.array(DataMatrix[i][:-1]).reshape(-1,1))) #Last Entry is Label Thats Why Error += (np.transpose(Theta).dot(Feature) - DataMatrix[i][-1])*Feature Theta -= Alpha*(1/Size)*Error if(Iterations % 10 == 0): Progress.append([Iterate,CostFunction(Theta,DataMatrix)]) Iterate += 10 Iterations -= 1 return [Theta,Progress] def ProgressCurve(Progress): Progress = [[i[0],i[1].ravel()[0]] for i in Progress] sns.lineplot(x = np.array(Progress)[:,0],y = np.array(Progress)[:,1],marker = '*') plt.show() def Prediction(Theta,Test): Predicted = [] for i in range(0,Test.size): Feature = np.vstack(([1],np.array(Test[i]).reshape(-1,1))) Predicted.append(np.transpose(Theta).dot(Feature)) return Predicted def Error_Metric(Actual,Predicted): Actual = np.array(Actual,dtype = 'float64').reshape(-1,1) Predicted = np.array(Predicted,dtype = 'float64').reshape(-1,1) Error = (Actual - Predicted) ** 2 Variance = (Actual - np.mean(Actual)*np.ones((Actual.shape[0],1))) ** 2 return (1 - np.sum(Error)/np.sum(Variance)) def RegressionLine(X,Y,Orig_X,Orig_Y): Y = [i[0].ravel()[0] for i in Y] sns.scatterplot(x = Orig_X,y = Orig_Y,color = "blue") sns.lineplot(x = X,y = Y,color = "red") plt.show() X = 2*np.random.rand(1000) Y = 4 + 3*X + np.random.randn(1000) X_Train,X_Test,Y_Train,Y_Test = train_test_split(X,Y,test_size = 0.3,random_state = 0) DataFrame = pd.DataFrame() DataFrame['X'] = X_Train DataFrame['Y'] = Y_Train DataMatrix = DataFrame.as_matrix() ThetaParams = np.random.randn(2,1) Theta,Progress = GradientDescent(ThetaParams,0.001,DataMatrix,50) Prediction_Out = Prediction(Theta,np.array(X_Test)) Error = Error_Metric(Y_Test,Prediction_Out) ProgressCurve(Progress) RegressionLine(X_Test,Prediction_Out,X,Y) print(Error) 
