\nimport matplotlib.pyplot as plt\nimport numpy as np\n\n# Create a scatter plot with demand as color\nplt.scatter(data['hour'], data['T2M'], c=data['Demand'], cmap='plasma', s=50)\n\n# Add colorbar\ncbar = plt.colorbar()\ncbar.set_label('Demand (MW)')\n\n# Set labels for axes\nplt.xlabel('Hour of the Day')\nplt.ylabel('Temperature (\u00b0C)')\n\nplt.title('Temperature vs Hour (Color-coded by Demand)')\n\nplt.show()\n\n<\/pre><\/div>\n\n![\"\"](\"http:\/\/savvaspanagi.com\/wp-content\/uploads\/2023\/11\/image-2.png\")
<\/figure>\n\n\nThe first analysis illustrates the fluctuation of demand in megawatts (MW) in response to variations in temperature and hour. In instances of low demand, the figure showcases a darker color, transitioning to brighter hues as demand increases.<\/p>\n\n\n\n
Data’s preparation<\/strong><\/p>\n\n\n\nPrior to normalizing the data, it’s crucial to recognize that the ‘hour’ feature is cyclical. A detailed analysis on handling cyclical features has been discussed in a previous post, accessible here<\/span><\/a>. Furthermore, the guidance on scaling data developed in other post here<\/span><\/a>, Normalisation and Standardisation method implemented. Moreover, the data’s was divided into test and training data.<\/p>\n\n\n\nfrom sklearn.preprocessing import StandardScaler\nsc=StandardScaler()\ndata.loc[:,['hour_sin','hour_cos','T2M_norm']]=sc.fit_transform(data.loc[:,['hour_sin','hour_cos','T2M']])\n\nfrom sklearn.model_selection import train_test_split\nX_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state = 0)\n<\/pre><\/div>\n\n\nAssessing Machine Learning Regression Models: RMSE and R-squared Evaluation<\/strong><\/p>\n\n\n\nWhen it comes to checking how well a machine learning regression model is doing, we use two important measures: RMSE and R-squared. RMSE looks at the average difference between the predicted values and the actual values. If the RMSE is low, it means the model is doing a good job. R-squared, on the other hand, tells us how much of the variability in the data our model can explain. A higher R-squared is better, showing that the model fits the data well. So, by looking at both RMSE and R-squared, we can figure out if our regression model is accurate and how well it explains the data.<\/p>\n\n\n
\nfrom sklearn.metrics import r2_score\nfrom sklearn.metrics import mean_squared_error\n# Calculate RMSE\nrmse = np.sqrt(mean_squared_error(y_test, X_test[:,5]))\n\n# Calculate R-squared\nr_squared = r2_score(y_test, X_test[:,5])\n\nprint(f'RMSE: {rmse}')\nprint("R-squared:", r_squared)\n<\/pre><\/div>\n\n\nCurrent TSO’s demand forecast accuracy: RMSE= 30.194821557544707 , R-squared= 0.9700502334373836<\/p>\n\n\n\n
1. Multiple Linear Regression<\/strong><\/p>\n\n\n\nMultiple Linear Regression is a statistical technique that helps us make predictions by analyzing the relationships between multiple variables. Imagine you have a dataset with one outcome you want to predict (let’s call it ‘Y’) and several factors that might influence it (let’s call them ‘X1,’ ‘X2,’ etc.).<\/p>\n\n\n
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<\/p>\n\n\n\nThe goal is to find the best values for b0,b1,\u2026,bk<\/em> that minimize the difference between our predicted Y<\/em> and the actual Y<\/em> in our dataset. Once we find these values, we can use them to make predictions. For example, if we want to predict someone’s weight (Y<\/em>), we’d use their height (X1), age (X2), and other relevant factors. The coefficients (b<\/em>0,b<\/em>1,\u2026,bk<\/em>) tell us how much Y<\/em> is expected to change for a one-unit change in each X<\/em> variable, holding other variables constant. A positive coefficient means an increase in Y<\/em> with an increase in the corresponding X<\/em>, and a negative coefficient means the opposite.<\/p>\n\n\n\nImplementation of Multiple<\/em> Linear Regression<\/strong><\/p>\n\n\n\n# Training the Simple Linear Regression model on the Training set\nfrom sklearn.linear_model import LinearRegression\nMLR = LinearRegression()\nMLR.fit(X_train[:,:3], y_train)\n\n# Predicting the Test set results\ny_predMLR = MLR.predict(X_test[:,:3])\n\nfrom sklearn.metrics import r2_score\nfrom sklearn.metrics import mean_squared_error\n# Calculate RMSE\nrmse = np.sqrt(mean_squared_error(y_test, y_predMLR))\n\n# Calculate R-squared\nr_squared = r2_score(y_test, y_predMLR)\n\nprint(f'RMSE: {rmse}')\nprint("R-squared:", r_squared)\n\n<\/pre><\/div>\n\n\n2. Polyonimial Regression<\/strong><\/p>\n\n\n\nPolynomial regression focuses on capturing nonlinear patterns by introducing higher-degree polynomial terms of a single independent variable. Polynomial regression is particularly useful when the relationship between the variables is nonlinear, providing a more accurate fit to the data compared to the linear assumptions of multiple linear regression.<\/p>\n\n\n
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<\/p>\n\n\n\nImplementation of Polyonimial Regression<\/strong><\/p>\n\n\n\nfrom sklearn.preprocessing import PolynomialFeatures\nfrom sklearn.linear_model import LinearRegression\nfrom sklearn.pipeline import make_pipeline\n\n# Assuming X_train is your feature matrix with 3 columns, and y_train is your target variable\n\n# Create a polynomial regression model with degree 2 (you can change the degree as needed)\ndegree = 2\nPR = make_pipeline(PolynomialFeatures(degree), LinearRegression())\n\n# Train the model\nPR.fit(X_train[:,:3], y_train)\n\n# Make predictions\ny_predPR = PR.predict(X_test[:,:3])\n\nfrom sklearn.metrics import mean_squared_error\n# Calculate RMSE\nrmse = np.sqrt(mean_squared_error(y_test, y_predPR))\n\n# Calculate R-squared\nr_squared = r2_score(y_test, y_predPR)\n\nprint(f'RMSE: {rmse}')\nprint("R-squared:", r_squared)\n<\/pre><\/div>\n\n\nImplementation Support Vector Regression<\/strong><\/p>\n\n\n\n# Training the SVR model on the whole dataset\nfrom sklearn.svm import SVR\nSVR = SVR(kernel = 'rbf')\nSVR.fit(X_train[:,:3], y_train)\n\n# Predicting a new result\ny_predSVR=SVR.predict(X_test[:,:3])\n\nprint(np.concatenate((y_predSVR.reshape(len(y_predSVR),1), y_test.reshape(len(y_test),1)),1))\nfrom sklearn.metrics import mean_squared_error\n# Calculate RMSE\nrmse = np.sqrt(mean_squared_error(y_test, y_predSVR))\n# Calculate R-squared\nr_squared = r2_score(y_test, y_predSVR)\n\nprint(f'RMSE: {rmse}')\nprint("R-squared:", r_squared)\n<\/pre><\/div>\n\n\nImplementation Disicion Tree Regression<\/strong><\/p>\n\n\n\n# Training the Decision Tree Regression model on the whole dataset\nfrom sklearn.tree import DecisionTreeRegressor\nDTR = DecisionTreeRegressor(random_state = 0)\nDTR.fit(X_train[:,:3], y_train)\n# Predicting a new result\ny_predDTR=DTR.predict(X_test[:,:3])\nfrom sklearn.metrics import mean_squared_error\n# Calculate RMSE\nrmse = np.sqrt(mean_squared_error(y_test, y_predDTR))\n# Calculate R-squared\nr_squared = r2_score(y_test, y_predDTR)\nprint(f'RMSE: {rmse}')\nprint("R-squared:", r_squared)\n<\/pre><\/div>\n\n\nImplementation Random Forest Regression<\/strong><\/p>\n\n\n\n# Training the Random Forest Regression model on the whole dataset\nfrom sklearn.ensemble import RandomForestRegressor\nRFR = RandomForestRegressor(n_estimators = 10, random_state = 0)\nRFR.fit(X_train[:,:3], y_train)\n# Predicting a new result\ny_predRFR=RFR.predict(X_test[:,:3])\nfrom sklearn.metrics import mean_squared_error\n# Calculate RMSE\nrmse = np.sqrt(mean_squared_error(y_test, y_predRFR))\n# Calculate R-squared\nr_squared = r2_score(y_test, y_predRFR)\nprint(f'RMSE: {rmse}')\nprint("R-squared:", r_squared)\n<\/pre><\/div>\n\n\nResults<\/strong><\/p>\n\n\n\n\n