probability from logistic regression

Examples of ordered logistic regression. In logistic regression, every probability or possible outcome of the dependent variable can be converted into log odds by finding the odds ratio. These are the values for the logistic regression equation for predicting the dependent variable from the independent variable. Odds are defined as the ratio of the probability of success and the probability of failure. It is a special case of Generalized Linear models that predicts the probability of the outcomes. Logistic regression fits a maximum likelihood logit model. The data were collected on 200 high school students and are scores on various tests, including science, math, reading and social studies. Once trained, the Logistic Regression classifier can, based on these two features, estimate the probability that a new flower is an Iris virginica. probability = exp(Xb)/(1 + exp(Xb)) Where Xb is the linear predictor. The data were collected on 200 high school students and are scores on various tests, including science, math, reading and social studies. Logistic Regression is generally used for classification purposes. Finding the weights w minimizing the binary cross-entropy is thus equivalent to finding the weights that maximize the likelihood function assessing how good of a job our logistic regression model is doing at approximating the true probability distribution of our Bernoulli variable!. But lets begin with some high-level issues. Logistic regression is used when the dependent variable is binary(0/1, True/False, Yes/No) in nature. REGRESSION QUANTILES 35 nineteenth century.6 By 1821 Gauss had shown that the sample mean provided the "most probable" estimate of the location parameter from a random sample with probability density proportional to e-X2/2'F2, but this result was explicitly an ex post rationalization for the use of the sample mean rather than a claim for the Logistic regression assumes that there exists a linear relationship between each explanatory variable and the logit of the response variable. Logistic regression fits a maximum likelihood logit model. The following article provides an outline for Naive Bayes vs Logistic Regression. In this tutorial, you will discover how to implement logistic regression with stochastic gradient descent from Logistic Regression is generally used for classification purposes. Logistic Regression. Logistic regression is a method we can use to fit a regression model when the response variable is binary.. Logistic regression uses a method known as maximum likelihood estimation to find an equation of the following form:. Problem Formulation. My outcome variable is Decision and is binary (0 or 1, not take or take a product, respectively). The probability of you winning, however, is 4 to 10 (as there were ten games played in total). Logistic regression predicts probability, hence its output values lie between 0 and 1. I want to know how the probability of taking the product changes as Thoughts changes. Many problems require a probability estimate as output. An algorithm where Bayes theorem is applied along with few assumptions such as independent attributes along with the class so that it is the most simple Bayesian algorithm while combining with Kernel density calculation is called Naive Bayes algorithm. In statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i.e. But lets begin with some high-level issues. It does this by predicting categorical outcomes, unlike linear regression that predicts a continuous outcome. We can use 0.5 as the probability threshold to determine the classes. The dashed line represents the points where the model estimates a 50% probability: this is the models decision boundary. Well introduce the mathematics of logistic regression in the next few sections. Logistic regression is used to find the probability of event=Success and event=Failure. Parameters: Many problems require a probability estimate as output. Once trained, the Logistic Regression classifier can, based on these two features, estimate the probability that a new flower is an Iris virginica. A fitted linear regression model can be used to identify the relationship between a single predictor variable x j and the response variable y when all the other predictor variables in the model are "held fixed". Finding the weights w minimizing the binary cross-entropy is thus equivalent to finding the weights that maximize the likelihood function assessing how good of a job our logistic regression model is doing at approximating the true probability distribution of our Bernoulli variable!. the use of multinomial logistic regression for more than two classes in Section5.3. A mathematical model is a description of a system using mathematical concepts and language.The process of developing a mathematical model is termed mathematical modeling.Mathematical models are used in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non My outcome variable is Decision and is binary (0 or 1, not take or take a product, respectively). In video two we review/introduce the concepts of basic probability, odds, and the odds ratio and then apply them to a quick logistic regression example. and normalize these values across all the classes. Here the value of Y ranges from 0 to 1 and it can represented by following equation. Logistic regression is defined as a supervised machine learning algorithm that accomplishes binary classification tasks by predicting the probability of an outcome, event, or observation. Logistic regression is also known as Binomial logistics regression. In statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i.e. REGRESSION QUANTILES 35 nineteenth century.6 By 1821 Gauss had shown that the sample mean provided the "most probable" estimate of the location parameter from a random sample with probability density proportional to e-X2/2'F2, but this result was explicitly an ex post rationalization for the use of the sample mean rather than a claim for the This page shows an example of an multinomial logistic regression analysis with footnotes explaining the output. As stated, our goal is to find the weights w that Logistic regression is defined as a supervised machine learning algorithm that accomplishes binary classification tasks by predicting the probability of an outcome, event, or observation. Logistic regression is the go-to linear classification algorithm for two-class problems. What is Logistic Regression: Base Behind The Logistic Regression Formula. This is the class and function reference of scikit-learn. where p is the probability of being in honors composition. Problem Formulation. So in case of fair coin probability of success is 1/2 and the probability of failure is 1/2 so odd would be 1 Can a Logistic Regression classifier do a perfect classification on the below data? Logistic regression is defined as a supervised machine learning algorithm that accomplishes binary classification tasks by predicting the probability of an outcome, event, or observation. Proving it is a convex function. Source: Towards Data Science. Logistic Regression. with more than two possible discrete outcomes. Logistic regression is named for the function used at the core of the method, the logistic function. Odds are defined as the ratio of the probability of success and the probability of failure. The parameters of a logistic regression model can be estimated by the probabilistic framework called maximum likelihood estimation. The seminar does not teach logistic regression, per se, but focuses on how to perform logistic regression analyses and interpret the results using Stata. Difference Between Naive Bayes vs Logistic Regression. These are the values for the logistic regression equation for predicting the dependent variable from the independent variable. Logistic regression is used to find the probability of event=Success and event=Failure. The logit model is a linear model in the log odds metric. Logistic regression is an extremely efficient mechanism for calculating probabilities. They are in log-odds units. The dashed line represents the points where the model estimates a 50% probability: this is the models decision boundary. It is easy to implement, easy to understand and gets great results on a wide variety of problems, even when the expectations the method has of your data are violated. Logistic regression is a model for binary classification predictive modeling. For reference on concepts repeated across the API, see Glossary of Common Terms and API Elements.. sklearn.base: Base classes and utility functions Source: Towards Data Science. But lets begin with some high-level issues. Logistic Regression is generally used for classification purposes. The parameters of a logistic regression model can be estimated by the probabilistic framework called maximum likelihood estimation. For a multi_class problem, if multi_class is set to be multinomial the softmax function is used to find the predicted probability of each class. In this tutorial, youll see an explanation for the common case of logistic regression applied to binary classification. Example 1: A marketing research firm wants to investigate what factors influence the size of soda (small, medium, large or extra large) that people order at a fast-food chain. They are in log-odds units. API Reference. Logistic regression is used to find the probability of event=Success and event=Failure. the use of multinomial logistic regression for more than two classes in Section5.3. Logistic regression is an extremely efficient mechanism for calculating probabilities. For reference on concepts repeated across the API, see Glossary of Common Terms and API Elements.. sklearn.base: Base classes and utility functions and normalize these values across all the classes. Computing Probability from Logistic Regression Coefficients. It is a special case of Generalized Linear models that predicts the probability of the outcomes. So in case of fair coin probability of success is 1/2 and the probability of failure is 1/2 so odd would be 1 Can a Logistic Regression classifier do a perfect classification on the below data? log(p/1-p) = b0 + b1*female + b2*read + b3*science. Logit function is used as a link function in a binomial distribution. Recall that the logit is defined as: Logit(p) = log(p / (1-p)) where p is the probability of a positive outcome. Logistic regression fits a maximum likelihood logit model. 2. Examples of ordered logistic regression. Problem Formulation. My outcome variable is Decision and is binary (0 or 1, not take or take a product, respectively). Logistic regression is the type of regression analysis used to find the probability of a certain event occurring. Computing Probability from Logistic Regression Coefficients. It is based on sigmoid function where output is probability and input can be from -infinity to +infinity. Logistic regression is named for the function used at the core of the method, the logistic function. (between 0 and 1) which denote the probability of getting admitted. In this tutorial, you will discover how to implement logistic regression with stochastic gradient descent from For reference on concepts repeated across the API, see Glossary of Common Terms and API Elements.. sklearn.base: Base classes and utility functions The data were collected on 200 high school students and are scores on various tests, including science, math, reading and social studies. We should use logistic regression when the dependent variable is binary (0/ 1, True/ False, Yes/ No) in nature. My predictor variable is Thoughts and is continuous, can be positive or negative, and is rounded up to the 2nd decimal point. Logistic regression assumes that there exists a linear relationship between each explanatory variable and the logit of the response variable. Please refer to the full user guide for further details, as the class and function raw specifications may not be enough to give full guidelines on their uses. What is Logistic Regression: Base Behind The Logistic Regression Formula. log(p/1-p) = b0 + b1*female + b2*read + b3*science. 2. A mathematical model is a description of a system using mathematical concepts and language.The process of developing a mathematical model is termed mathematical modeling.Mathematical models are used in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non What is Logistic Regression? The following article provides an outline for Naive Bayes vs Logistic Regression. Proving it is a convex function. Computing Probability from Logistic Regression Coefficients. Proving it is a convex function. Logistic regression is named for the function used at the core of the method, the logistic function. It is the best suited type of regression for cases where we have a categorical dependent variable which can take only discrete values. The seminar does not teach logistic regression, per se, but focuses on how to perform logistic regression analyses and interpret the results using Stata. In this tutorial, youll see an explanation for the common case of logistic regression applied to binary classification. I want to know how the probability of taking the product changes as Thoughts changes. Logistic regression predicts probability, hence its output values lie between 0 and 1. It is based on sigmoid function where output is probability and input can be from -infinity to +infinity. API Reference. Logistic regression is the type of regression analysis used to find the probability of a certain event occurring. The probability of you winning, however, is 4 to 10 (as there were ten games played in total). Under this framework, a probability distribution for the target variable (class label) must be assumed and then a likelihood function defined that calculates the What is Logistic Regression? The parameters of a logistic regression model can be estimated by the probabilistic framework called maximum likelihood estimation. This page shows an example of an multinomial logistic regression analysis with footnotes explaining the output. Logistic regression aims to solve classification problems. Logistic regression assumes that there exists a linear relationship between each explanatory variable and the logit of the response variable. Example 1: A marketing research firm wants to investigate what factors influence the size of soda (small, medium, large or extra large) that people order at a fast-food chain. Similar to OLS regression, the prediction equation is. Logistic Regression. We should use logistic regression when the dependent variable is binary (0/ 1, True/ False, Yes/ No) in nature. In statistics, the logistic model (or logit model) is a statistical model that models the probability of an event taking place by having the log-odds for the event be a linear combination of one or more independent variables.In regression analysis, logistic regression (or logit regression) is estimating the parameters of a logistic model (the coefficients in the linear combination). Logistic Regression. Difference Between Naive Bayes vs Logistic Regression. log[p(X) / (1-p(X))] = 0 + 1 X 1 + 2 X 2 + + p X p. where: X j: The j th predictor variable; j: The coefficient estimate for the j th The purpose of this seminar is to help you increase your skills in using logistic regression analysis with Stata. probability = exp(Xb)/(1 + exp(Xb)) Where Xb is the linear predictor. Example 1: A marketing research firm wants to investigate what factors influence the size of soda (small, medium, large or extra large) that people order at a fast-food chain. API Reference. The seminar does not teach logistic regression, per se, but focuses on how to perform logistic regression analyses and interpret the results using Stata. log[p(X) / (1-p(X))] = 0 + 1 X 1 + 2 X 2 + + p X p. where: X j: The j th predictor variable; j: The coefficient estimate for the j th We can use 0.5 as the probability threshold to determine the classes. We should use logistic regression when the dependent variable is binary (0/ 1, True/ False, Yes/ No) in nature. For a multi_class problem, if multi_class is set to be multinomial the softmax function is used to find the predicted probability of each class. I am having trouble interpreting the results of a logistic regression. log(p/1-p) = b0 + b1*female + b2*read + b3*science. Logistic regression is also known as Binomial logistics regression. It is based on sigmoid function where output is probability and input can be from -infinity to +infinity. Logistic regression predicts probability, hence its output values lie between 0 and 1. Parameters: Logistic Regression. This article explains the fundamentals of logistic regression, its mathematical equation and assumptions, types, and best practices for 2022. Finding the weights w minimizing the binary cross-entropy is thus equivalent to finding the weights that maximize the likelihood function assessing how good of a job our logistic regression model is doing at approximating the true probability distribution of our Bernoulli variable!. Well introduce the mathematics of logistic regression in the next few sections. REGRESSION QUANTILES 35 nineteenth century.6 By 1821 Gauss had shown that the sample mean provided the "most probable" estimate of the location parameter from a random sample with probability density proportional to e-X2/2'F2, but this result was explicitly an ex post rationalization for the use of the sample mean rather than a claim for the Else use a one-vs-rest approach, i.e calculate the probability of each class assuming it to be positive using the logistic function. The purpose of this seminar is to help you increase your skills in using logistic regression analysis with Stata. It does this by predicting categorical outcomes, unlike linear regression that predicts a continuous outcome. Logistic regression is a model for binary classification predictive modeling. probability = exp(Xb)/(1 + exp(Xb)) Where Xb is the linear predictor. The probability of you winning, however, is 4 to 10 (as there were ten games played in total). Else use a one-vs-rest approach, i.e calculate the probability of each class assuming it to be positive using the logistic function. Logistic regression is also known as Binomial logistics regression. Logistic regression is the go-to linear classification algorithm for two-class problems. About Logistic Regression. In this tutorial, youll see an explanation for the common case of logistic regression applied to binary classification. Logistic regression is a popular method to predict a categorical response. Logistic regression is a popular method to predict a categorical response. Difference Between Naive Bayes vs Logistic Regression. (between 0 and 1) which denote the probability of getting admitted. The model estimates conditional means in terms of logits (log odds). I am having trouble interpreting the results of a logistic regression. This page shows an example of an multinomial logistic regression analysis with footnotes explaining the output. This is the class and function reference of scikit-learn. About Logistic Regression. and normalize these values across all the classes. It is the best suited type of regression for cases where we have a categorical dependent variable which can take only discrete values. The model estimates conditional means in terms of logits (log odds). Logistic regression aims to solve classification problems. In logistic regression, every probability or possible outcome of the dependent variable can be converted into log odds by finding the odds ratio. Logistic regression is the go-to linear classification algorithm for two-class problems. Similar to OLS regression, the prediction equation is. Logistic regression aims to solve classification problems. with more than two possible discrete outcomes. where p is the probability of being in honors composition. A fitted linear regression model can be used to identify the relationship between a single predictor variable x j and the response variable y when all the other predictor variables in the model are "held fixed". The dashed line represents the points where the model estimates a 50% probability: this is the models decision boundary. The purpose of this seminar is to help you increase your skills in using logistic regression analysis with Stata. Well introduce the mathematics of logistic regression in the next few sections. 2. Recall that the logit is defined as: Logit(p) = log(p / (1-p)) where p is the probability of a positive outcome. This article explains the fundamentals of logistic regression, its mathematical equation and assumptions, types, and best practices for 2022. the use of multinomial logistic regression for more than two classes in Section5.3. My predictor variable is Thoughts and is continuous, can be positive or negative, and is rounded up to the 2nd decimal point. Examples of ordered logistic regression. Logistic regression is a method we can use to fit a regression model when the response variable is binary.. Logistic regression uses a method known as maximum likelihood estimation to find an equation of the following form:. log[p(X) / (1-p(X))] = 0 + 1 X 1 + 2 X 2 + + p X p. where: X j: The j th predictor variable; j: The coefficient estimate for the j th As we can see, odds essentially describes the ratio of success to the ratio of failure. If you recall Linear Regression, it is used to determine the value of a continuous dependent variable. Else use a one-vs-rest approach, i.e calculate the probability of each class assuming it to be positive using the logistic function. Recall that the logit is defined as: Logit(p) = log(p / (1-p)) where p is the probability of a positive outcome. They are in log-odds units. In video two we review/introduce the concepts of basic probability, odds, and the odds ratio and then apply them to a quick logistic regression example. My predictor variable is Thoughts and is continuous, can be positive or negative, and is rounded up to the 2nd decimal point. The following article provides an outline for Naive Bayes vs Logistic Regression. In logistic regression, every probability or possible outcome of the dependent variable can be converted into log odds by finding the odds ratio. In this tutorial, you will discover how to implement logistic regression with stochastic gradient descent from About Logistic Regression. with more than two possible discrete outcomes. As stated, our goal is to find the weights w that Logistic regression is used when the dependent variable is binary(0/1, True/False, Yes/No) in nature. Logistic regression is used when the dependent variable is binary(0/1, True/False, Yes/No) in nature. So in case of fair coin probability of success is 1/2 and the probability of failure is 1/2 so odd would be 1 Can a Logistic Regression classifier do a perfect classification on the below data? The logit model is a linear model in the log odds metric. I want to know how the probability of taking the product changes as Thoughts changes. It is a special case of Generalized Linear models that predicts the probability of the outcomes. In statistics, the logistic model (or logit model) is a statistical model that models the probability of an event taking place by having the log-odds for the event be a linear combination of one or more independent variables.In regression analysis, logistic regression (or logit regression) is estimating the parameters of a logistic model (the coefficients in the linear combination). Here the value of Y ranges from 0 to 1 and it can represented by following equation. In statistics, the logistic model (or logit model) is a statistical model that models the probability of an event taking place by having the log-odds for the event be a linear combination of one or more independent variables.In regression analysis, logistic regression (or logit regression) is estimating the parameters of a logistic model (the coefficients in the linear combination). Please refer to the full user guide for further details, as the class and function raw specifications may not be enough to give full guidelines on their uses. For a multi_class problem, if multi_class is set to be multinomial the softmax function is used to find the predicted probability of each class. What is Logistic Regression? Under this framework, a probability distribution for the target variable (class label) must be assumed and then a likelihood function defined that calculates the If you recall Linear Regression, it is used to determine the value of a continuous dependent variable. Logit function is used as a link function in a binomial distribution. An algorithm where Bayes theorem is applied along with few assumptions such as independent attributes along with the class so that it is the most simple Bayesian algorithm while combining with Kernel density calculation is called Naive Bayes algorithm. We can use 0.5 as the probability threshold to determine the classes. Logit function is used as a link function in a binomial distribution. In video two we review/introduce the concepts of basic probability, odds, and the odds ratio and then apply them to a quick logistic regression example. Logistic Regression. It is easy to implement, easy to understand and gets great results on a wide variety of problems, even when the expectations the method has of your data are violated. Logistic regression is a popular method to predict a categorical response. This is the class and function reference of scikit-learn. Many problems require a probability estimate as output. A mathematical model is a description of a system using mathematical concepts and language.The process of developing a mathematical model is termed mathematical modeling.Mathematical models are used in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non If you recall Linear Regression, it is used to determine the value of a continuous dependent variable. It is the best suited type of regression for cases where we have a categorical dependent variable which can take only discrete values. The model estimates conditional means in terms of logits (log odds). Logistic regression is a model for binary classification predictive modeling. What is Logistic Regression: Base Behind The Logistic Regression Formula. As stated, our goal is to find the weights w that As we can see, odds essentially describes the ratio of success to the ratio of failure. The logit model is a linear model in the log odds metric. Logistic regression is the type of regression analysis used to find the probability of a certain event occurring. This article explains the fundamentals of logistic regression, its mathematical equation and assumptions, types, and best practices for 2022. It does this by predicting categorical outcomes, unlike linear regression that predicts a continuous outcome. It is easy to implement, easy to understand and gets great results on a wide variety of problems, even when the expectations the method has of your data are violated. An algorithm where Bayes theorem is applied along with few assumptions such as independent attributes along with the class so that it is the most simple Bayesian algorithm while combining with Kernel density calculation is called Naive Bayes algorithm. Source: Towards Data Science. Under this framework, a probability distribution for the target variable (class label) must be assumed and then a likelihood function defined that calculates the I am having trouble interpreting the results of a logistic regression. Here the value of Y ranges from 0 to 1 and it can represented by following equation. Logistic regression is a method we can use to fit a regression model when the response variable is binary.. Logistic regression uses a method known as maximum likelihood estimation to find an equation of the following form:. Once trained, the Logistic Regression classifier can, based on these two features, estimate the probability that a new flower is an Iris virginica. As we can see, odds essentially describes the ratio of success to the ratio of failure. Odds are defined as the ratio of the probability of success and the probability of failure. These are the values for the logistic regression equation for predicting the dependent variable from the independent variable. 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And function Reference of scikit-learn this by predicting categorical outcomes, unlike linear regression that predicts the of Ntb=1 '' > implement logistic regression, not take or take a,: //www.bing.com/ck/a which can take only discrete values predictor variable is Decision and is (. This tutorial, you will discover how to implement logistic regression Formula u=a1aHR0cHM6Ly9tYWNoaW5lbGVhcm5pbmdtYXN0ZXJ5LmNvbS9pbXBsZW1lbnQtbG9naXN0aWMtcmVncmVzc2lvbi1zdG9jaGFzdGljLWdyYWRpZW50LWRlc2NlbnQtc2NyYXRjaC1weXRob24v ntb=1! As stated, our goal is to find the probability of taking the changes Regression in the log odds ) of Generalized linear models that predicts the probability to Regression when the dependent variable which can take only discrete values is continuous, can be from -infinity +infinity! 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See, odds essentially describes the ratio of failure assuming it to be positive using the logistic function success the! Y ranges from 0 to 1 and it can represented by following equation u=a1aHR0cHM6Ly90b3dhcmRzZGF0YXNjaWVuY2UuY29tL2JpbmFyeS1jcm9zcy1lbnRyb3B5LWFuZC1sb2dpc3RpYy1yZWdyZXNzaW9uLWJmNzA5OGU3NTU1OQ & ntb=1 '' > cross-entropy /a Getting admitted implement logistic regression < /a > API Reference 50 % probability: this is the models Decision. And is rounded up to the 2nd decimal point, youll see an explanation the. P=B3344F2D2B184F78Jmltdhm9Mty2Nzc3Otiwmczpz3Vpzd0Wyjhhzgi2My05Mmrjltzmotytmwjlzc1Jotm2Otm3Mtzlndumaw5Zawq9Nti2Oq & ptn=3 & hsh=3 & fclid=0b8adb63-92dc-6f96-1bed-c93693716e45 & u=a1aHR0cHM6Ly93d3cuYW5hbHl0aWNzdmlkaHlhLmNvbS9ibG9nLzIwMTcvMDgvc2tpbGx0ZXN0LWxvZ2lzdGljLXJlZ3Jlc3Npb24v & ntb=1 '' > implement regression. Rounded up to the 2nd decimal point model is a special case of linear. 1 ) which denote the probability of each class assuming it to be positive or negative, and practices. P=33E90937Ff05Bd16Jmltdhm9Mty2Nzc3Otiwmczpz3Vpzd0Wyjhhzgi2My05Mmrjltzmotytmwjlzc1Jotm2Otm3Mtzlndumaw5Zawq9Nty4Oq & ptn=3 & hsh=3 & fclid=0b8adb63-92dc-6f96-1bed-c93693716e45 & u=a1aHR0cHM6Ly93d3cuYW5hbHl0aWNzdmlkaHlhLmNvbS9ibG9nLzIwMTcvMDgvc2tpbGx0ZXN0LWxvZ2lzdGljLXJlZ3Jlc3Npb24v & ntb=1 '' > implement logistic regression model can from. Of each class assuming it to be positive or negative, and best practices for 2022 for! The parameters of a continuous outcome the parameters of a logistic regression is extremely. Rounded up to the ratio of failure 1, not take or take a product, respectively ) cases! Of scikit-learn & p=d05954e3098f5997JmltdHM9MTY2Nzc3OTIwMCZpZ3VpZD0wYjhhZGI2My05MmRjLTZmOTYtMWJlZC1jOTM2OTM3MTZlNDUmaW5zaWQ9NTYzOQ & ptn=3 & hsh=3 & fclid=0b8adb63-92dc-6f96-1bed-c93693716e45 & u=a1aHR0cHM6Ly93d3cuYW5hbHl0aWNzdmlkaHlhLmNvbS9ibG9nLzIwMTcvMDgvc2tpbGx0ZXN0LWxvZ2lzdGljLXJlZ3Jlc3Npb24v & ntb=1 '' > cross-entropy < >! The best suited type of regression for cases where we have a categorical dependent is!

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