diff --git a/guide/english/machine-learning/logistic-regression/index.md b/guide/english/machine-learning/logistic-regression/index.md
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@@ -3,30 +3,39 @@ title: Logistic Regression
---
## Logistic Regression
-Logistic regression is very similar to linear regression in that it attempts to predict a response variable Y given a set of X input variables. It's a form of supervised learning, which tries to predict the responses of unlabeled, unseen data by first training with labeled data, a set of observations of both independent (X) and dependent (Y) variables. But while Linear Regression assumes that the response variable (Y) is quantitative or continuous, Logistic Regression is used specifically when the response variable is qualititative,or discrete.
+Logistic regression is very similar to linear regression As in both algorithms ,models are trained to find a regression line to define function for futher prediction.Therefore, It's a form of supervised learning, which tries to predict the responses of unlabeled, unseen data by first training with labeled data,on a set of observations which consists of both independent (X) and dependent (Y) variables. But while Linear Regression assumes that the response variable (Y) is quantitative or continuous, Logistic Regression is used specifically when the response variable is qualititative,or discrete.
#### How it Works
Logistic regression models the probability that Y, the response variable, belongs to a certain category. In many cases, the response variable will be a binary one, so logistic regression will want to model a function y = f(x) that outputs a normalized value that ranges from, say, 0 to 1 for all values of X, corresponding to the two possible values of Y. It does this by using the logistic function:
-Logistic regression is the appropriate regression analysis to conduct when the dependent variable is dichotomous (binary). Like all regression analyses, the logistic regression is a predictive analysis. Logistic regression is used to describe data and to explain the relationship between one dependent binary variable and one or more nominal, ordinal, interval or ratio-level independent variables.
+Logistic regression is the appropriate regression analysis to conduct when the dependent variable is dichotomous (binary) But it has another form such as : mutivalued logistic regression which is used to classify for more than two classes. Like all regression analyses, the logistic regression is a predictive analysis. Logistic regression is used to describe data and to explain the relationship between one dependent binary variable and one or more nominal, ordinal, interval or ratio-level independent variables.
Logistic regression is used to solve classification problems, where the output is of the form y∈{0,1}. Here, 0 is a negative class and 1 is a positive class. Let's say we have a hypothesis hθ(x), where x is our dataset(a matrix) of length m. θ is the parameteric matrix. We have : 0 < hθ(x) < 1
In Logistic regression, hθ(x) is a sigmoid function, thus hθ(x) = g(θ'x).
+A Sigmoid function is an appropriate function developed by statician to classify which always result between 0 or 1 depending on its
+input attributes and weights(which is theta **θ** here)
g(θ'x) = 1/ 1 + e^(-θ'x)
Note: θ' is θ transpose.
-
-#### Cost function
+**Transpose is used to multiply here it with attribute array It will be easily understoodable once you get in a bit depth with Linear algebra.**
+#### Cost function
+Cost Function is a measure of How much our, Hypothetic function is farther to the observed one .
The cost function used for Logistic regression is :
J(θ)=(1/m)∑Cost(hθ(x(i)),y(i)) , where summation is from i=1 to m.
+Where hθ(x) is = hypothetic value calculated in accordance with attributes and wieghts which are calculated and balanced via algorithm such as gradient decent .
+ y = is the corresponding value from observation data set
+
+Here cost function is not a proper sigmoid function in use but in place ,two log functions which performs with greater efficieny without
+penalizing the learning algorithms are used.
Cost(hθ(x),y)=−log(hθ(x)) if y = 1
Cost(hθ(x),y)=−log(1−hθ(x)) if y = 0
+
#### Predictions using logistic regression:
Logistic regression models the probability of the default class(i.e. the first class).
You can classify results given by :
@@ -46,7 +55,8 @@ Here multiple(N*N(N-1)/2 where N=no. of classes) binary classifiers are made and
#### Applications of logistic regression:
1) To classify mail as spam or not spam.
-2) To determine presence or absence of certain disease like cancer based on symptoms and other medical data.
+2) To determine presence or absence of certain disease like cancer based on symptoms and other medical data
+Like- benign or malignant.
3) Classify images based on pixel data.
#### Logistic Regression Assumptions