Corrected typos, punctuation, and spacing issues (#21508)

guide/english/machine-learning/logistic-regression/index.md

@@ -3,12 +3,12 @@ title: Logistic Regression
 ---
 ## Logistic Regression
 ![Logistic Function](https://qph.fs.quoracdn.net/main-qimg-7c9b7670c90b286160a88cb599d1b733)<br>
-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 <a href='https://guide.freecodecamp.org/machine-learning/linear-regression' target='_blank'>Linear Regression</a> assumes that the response variable (Y) is quantitative or continuous, Logistic Regression is used specifically when the response variable is qualititative,or discrete.<br>
+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 <a href='https://guide.freecodecamp.org/machine-learning/linear-regression' target='_blank'>Linear Regression</a> assumes that the response variable (Y) is quantitative or continuous, Logistic Regression is used specifically when the response variable is qualititative, or discrete.<br>
 ![Linear vs Logistic](http://www.saedsayad.com/images/LogReg_1.png)
 
 #### 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) 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 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), 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.
 
 ![Cost Function](https://cdn-images-1.medium.com/max/800/1*wHtYmENzug_W6fIE9xY8aw.jpeg)
 <br>
@@ -24,28 +24,28 @@ Note: θ' is θ transpose.
 
 #### 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 :
+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 . 
+Where hθ(x) is = hypothetic value calculated in accordance with attributes and weights which are calculated and balanced via algorithm such as gradient descent. 
  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 
+Here cost function is not a proper sigmoid function in use but in place, two log functions which performs with greater efficiency 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 : 
+Logistic regression models the probability of the default class (i.e. the first class).
+You can classify results given by: 
 
 y = e^(b0 + b1*X) / (1 + e^(b0 + b1*X))
 
 into two classes.Like for sigmoid function 0.5 is set as the decision boundary all x for which y≥0.5 are classified as class A and for which y<0.5 are classified as class B.
 
 #### Multi class logistic regression:
-Although you will see logistic regression usually being used in case of binary classification but you can also use it in case of classification into multiple classes by:
+Although you will see logistic regression usually being used in case of binary classification, you can also use it in case of classification into multiple classes by:
 
 ##### one vs one method: 
 Here a classifier for each class is created separately and the classifier with the highest score is considered as output.
@@ -55,7 +55,7 @@ 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.<br>
-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.<br>
 3) Classify images based on pixel data.
 
@@ -70,7 +70,7 @@ Logistic regression requires quite large sample sizes.
 
 #### More Information:
 <!-- Please add any articles you think might be helpful to read before writing the article -->
-For further reading to build logistic regression step by step :
+For further reading to build logistic regression step by step:
 
 - Click <a href="https://medium.com/towards-data-science/building-a-logistic-regression-in-python-step-by-step-becd4d56c9c8"  target='_blank' rel='nofollow'>here</a> for an article about building a Logistic Regression in Python.
 - Click <a href="http://nbviewer.jupyter.org/gist/justmarkham/6d5c061ca5aee67c4316471f8c2ae976" target='_blank' rel='nofollow'>here</a> for another article on building a Logical Regression.