![]() ![]() for point in X_test: theta, pred = predict(X, y, point, tau) preds.append(pred) # Reshaping X_test and preds X_test = np.array(X_test).reshape(nval,1) preds = np.array(preds).reshape(nval,1) # Plotting plt.plot(X, y, 'b.') plt.plot(X_test, preds, 'r.') # Predictions in red color. preds = # Predicting for all nval values and storing them in preds. X_test = np.linspace(-3, 3, nval) # Empty list for storing predictions. # X_test includes nval evenly spaced values in the domain of X. # The values for which we are going to predict. # nval -> number of values/points for which we are going to # predict. See comments (#) def plot_predictions(X, y, tau, nval): # X -> Training data. Now, let’s plot our predictions for about 100 points( x) which are in the domain of x. pred = np.dot(point_, theta) # Returning the theta and predictions return theta, pred Plotting Predictions theta = np.linalg.pinv(X_.T*(w * X_))*(X_.T*(w * y)) # Calculating predictions. w = wm(point_, X_, tau) # Calculating parameter theta using the formula. point_ = np.array() # Calculating the weight matrix using the wm function we wrote # earlier. X_ = np.append(X, np.ones(m).reshape(m,1), axis=1) # point is the x where we want to make the prediction. # Just one parameter: theta, that's why adding a column of ones # to X and also adding a 1 for the point where we want to # predict. The slope of the line is m, and c is the intercept (the value of y when x0) Image of the linear model: our dataset: height-weight. m = X.shape # Appending a cloumn of ones in X to add the bias term. A linear regression line has an equation of the form ymx+c, where x is the explanatory variable and y is the dependent variable. See comments (#) def predict(X, y, point, tau): # m = number of training examples. Plt.xticks(()) plt.yticks(()) plt.The formula for prediction source: Plt.plot(X, regr.predict(X), color='yellow', linewidth=2, label='Weighted model - scaled', linestyle='dashed') Sample_weight = sample_weight / sample_weight.max() Plt.plot(X, regr.predict(X), color='red', linewidth=3, label='Weighted model') Plt.plot(X, regr.predict(X), color='blue', linewidth=3, label='Unweighted model') Plt.scatter(X, y, s=sample_weight, c='grey', edgecolor='black') # Create equal weights and then augment the last 2 ones X, y = datasets.load_diabetes(return_X_y=True) import matplotlib.pyplot as pltįrom sklearn.linear_model import LinearRegression And, scaling does not affect the outcome, as expected. In the weighted version, we emphasize the region around last two samples, and the model becomes more accurate there. (Hint: if it is right, what should the coefficients on the i. Another more common example is, if the client is struggling with a particular movement or exercise. Use the second model to test the hypothesis that the first model is right. A hard training session will inflict further stress on the body and could create a serious hormone imbalance, and if that client is wanting to lose weight or even bulk up, then this could be very detrimental to their success. Then regress price on weight, foreign and i.rep78. Uniform scaling would not change the outcome. Try regressing price on weight, foreign and rep78, ignoring the fact that rep78 is a categorical variable. N can be passed as is if it already reflects the priorities. Therefore, it is the relative scale of the weights that matters. Internally, weights w are multiplied by the residuals in the loss function : The weights enable training a model that is more accurate for certain values of the input (e.g., where the cost of error is higher). ![]()
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