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Logistic Regression is derived from liner regression to deal with the problem of binary classification. Intuitively, the work of logistic regression is to apply a transformation on the figure of liner regression function so that it has a value range of 0 to +1 and being centrosymmetic on coordinate (0, 5). The shape of the decision boundary is determined by the value of parameter vector. The choice of a sigmoid function as the mapping function is to utilize its value range and (0, 0.5) point on it. With this magic 0.5 on y axis, the value of logistic function can be both use to make the prediction ( < 0.5, false, >=0.5, true) and to obtain a confidence about the prediction (0.5 = 50% confidence, 0.7 = 70% confidence). Confidence can be estimated by the distance of the prediction point on the figure to the other side of the upper bound line or lower bound line. 

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