# Polynomial regression python kaggle

Hi, today we are going to learn about Logistic Regression in Python. It is strongly recommended that you should have knowledge about regression and linear regression. So, Logistic regression is another type of regression.

Regression used for predictive analysis. It is used for building a predictive model. Regression creates a relationship equation between the dependent variable and independent variable. In logistic regression, the outcome will be in Binary format like 0 or 1, High or Low, True or False, etc.

Polynomial Regression Vs. Linear Regression Explained In-depth With Python Implementation

The regression line will be an S Curve or Sigmoid Curve. So we can say logistic regression is used to get classified output. In Logistic Regression : Example: car purchasing prediction, rain prediction, etc.

The basic theoretical part of Logistic Regression is almost covered. It is unnecessary for the prediction. Here we check if any null value is present or not. And we found a lot of Null values are present in our data set. We check the shape of the current dataset. Which is enough to make a small predictive model.

Here we check which column has which data type. It is necessary to make all column to numeric for fitting any model. Here all are in Numeric data type, which is good for us. We make an X variable and put all columns, except the last one. And we make y variable and put only last column.

Into ratio. And we check the shape of them. Then we check the accuracy score. We got accuracy score as 0. Thank you. The whole program is available here: Logistics regression Download from here. Sorry Purnendu Das, but actually the performance of the model is mostly bad. The accuracy score wont help this time due to the fact that the dataset is actually unbalanaced. Your email address will not be published.

Logistics Regression in python By Purnendu Das. Linear regression graph.Hi, today we will learn how to extract useful data from a large dataset and how to fit datasets into a linear regression model. We will do various types of operations to perform regression.

Our main task to create a regression model that can predict our output.

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We will plot a graph of the best fit line regression will be shown. We will also find the Mean squared error, R2score. Finally, we will predict one sample.

At first, we should know about what is Regression? Basically, regression is a statistical term, regression is a statistical process to determine an estimated relationship of two variable sets.

In this diagram, we can fin red dots. They represent the price according to the weight. The blue line is the regression line. Then we import the car dataset.

### Linear Regression on Boston Housing Dataset

And print 5 sample dataset values. At first, we imported our necessary libraries. Here we print the shape of the dataset and print the different car companies with their total cars. Because different types of cars have different brand value and higher or lower price. So we take only one car company for better prediction. Then we view the shape and check if any null cell present or not.

We found there are many null cells present. We delete those rows which have null cells. It is very important when you make a dataset for fitting any data model. Then we cross check if any null cells present or not. No null cell found then we print 5 sample dataset values. It is very important to select only those columns which could be helpful for prediction. It depends on your common sense to select those columns.

After select only 2 columns, we view our new dataset. Then check the shape of the array. After viewing this graph we ensured that we can perform a linear regression for prediction. We create regressor. Here we can clearly understand the regression line. Here we create a function with the help of our trained regressor model. And we get our desired output. Note: The whole code is available into jupyter notebook format.In my previous blog, I covered the basics of linear regression and gradient descent.

To get hands-on linear regression we will take an original dataset and apply the concepts that we have learned. We will take the Housing dataset which contains information about d i fferent houses in Boston. We can also access this data from the scikit-learn library. There are samples and 13 feature variables in this dataset. The objective is to predict the value of prices of the house using the given features.

First, we will import the required libraries. Next, we will load the housing data from the scikit-learn library and understand it. The prices of the house indicated by the variable MEDV is our target variable and the remaining are the feature variables based on which we will predict the value of a house.

We will now load the data into a pandas dataframe using pd. We then print the first 5 rows of the data using head. We can see that the target value MEDV is missing from the data.

We create a new column of target values and add it to the dataframe. We count the number of missing values for each feature using isnull. However, there are no missing values in this dataset as shown below. Exploratory Data Analysis is a very important step before training the model. In this section, we will use some visualizations to understand the relationship of the target variable with other features.

We will use the distplot function from the seaborn library. We see that the values of MEDV are distributed normally with few outliers.

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Next, we create a correlation matrix that measures the linear relationships between the variables.This is my third blog in the Machine Learning series. This blog requires prior knowledge of Linear Regression. Linear regression requires the relation between the dependent variable and the independent variable to be linear. What if the distribution of the data was more complex as shown in the below figure?

Can linear models be used to fit non-linear data? How can we generate a curve that best captures the data as shown below? Well, we will answer these questions in this blog. The data generated looks like. The plot of the best fit line is. We can see that the straigh t line is unable to capture the patterns in the data. This is an example of under-fitting.

To overcome under-fitting, we need to increase the complexity of the model. To generate a higher order equation we can add powers of the original features as new features. The linear model. However the curve that we are fitting is quadratic in nature. To convert the original features into their higher order terms we will use the PolynomialFeatures class provided by scikit-learn.

Next, we train the model using Linear Regression. Fitting a linear regression model on the transformed features gives the below plot. It is quite clear from the plot that the quadratic curve is able to fit the data better than the linear line. The metrics of the cubic curve is. Below is a comparison of fitting linear, quadratic and cubic curves on the dataset. If we further increase the degree to 20, we can see that the curve passes through more data points.

Below is a comparison of curves for degree 3 and This is an example of over-fitting. Even though this model passes through most of the data, it will fail to generalize on unseen data. Note: adding more data can be an issue if the data is itself noise.

How do we choose an optimal model? To answer this question we need to understand the bias vs variance trade-off. A high bias means that the model is unable to capture the patterns in the data and this results in under-fitting.

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Variance refers to the error due to the complex model trying to fit the data. High variance means the model passes through most of the data points and it results in over-fitting the data. The below picture summarizes our learning. From the below picture we can observe that as the model complexity increases, the bias decreases and the variance increases and vice-versa.

Ideally, a machine learning model should have low variance and low bias. Therefore to achieve a good model that performs well both on the train and unseen data, a trade-off is made.

## Implementation of Polynomial Regression:

Till now, we have covered most of the theory behind Polynomial Regression. We will transform the original features into higher degree polynomials before training the model.Please cite us if you use the software.

Generate a new feature matrix consisting of all polynomial combinations of the features with degree less than or equal to the specified degree. If True defaultthen include a bias column, the feature in which all polynomial powers are zero i. Order of output array in the dense case.

The total number of polynomial output features. The number of output features is computed by iterating over all suitably sized combinations of input features. Be aware that the number of features in the output array scales polynomially in the number of features of the input array, and exponentially in the degree. High degrees can cause overfitting.

If True, will return the parameters for this estimator and contained subobjects that are estimators. The method works on simple estimators as well as on nested objects such as Pipeline. The matrix of features, where NP is the number of polynomial features generated from the combination of inputs. Release Highlights for scikit-learn 0. Underfitting vs. Toggle Menu. Prev Up Next. PolynomialFeatures Examples using sklearn. New in version 0. Examples using sklearn.In this tutorial, we are going to understand the Multiple Linear Regression algorithm and implement the algorithm with Python.

In the equation, y is the single dependent variable value of which depends on more than one independent variable i. For example, you can predict the performance of students in an exam based on their revision time, class attendance, previous results, test anxiety, and gender. Here the dependent variable Exam performance can be calculated by using more than one independent variable.

So, this the kind of task where you can use a Multiple Linear Regression model.

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Now, let's do it together. We have a dataset Startups.

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Les have a glimpse of some of the values of that dataset. Note: this is not the whole dataset. You can download the dataset from here. Clearly, we can understand that it is a multiple linear regression problem, as the independent variables are more than one.

Let's take Profit as a dependent variable and put it in the equation as y and put other attributes as the independent variables. Now, let's jump to build the model, first the data preprocessing step. Here we will take Profit as in the dependent variable vector y, and other independent variables in feature matrix X. The dataset contains one categorical variable. So we need to encode or make dummy variables for that.

The above code will make two dummy variables as the categorical variable has two variations. And obviously, our linear equation will use both dummy variables.

But this will make a problem.

When multicollinearity exists, the model cannot distinguish the variables properly, therefore predicts improper outcomes. This problem is identified as the Dummy Variable Trap. To solve this problem, you should always take all dummy variables except one form the dummy variable set. Now, check how our model performed. The mean absolute error says our model has performed really bad on the test set. But we can improve the quality of the prediction by building Multiple Linear Regression model with methods such as Backward Elimination, Forward Selection etc.

In the tutorial, We are going to apply the backward elimination technique to improve our model.Polynomial Regression is a form of linear regression in which the relationship between the independent variable x and dependent variable y is modeled as an nth degree polynomial.

Polynomial regression fits a nonlinear relationship between the value of x and the corresponding conditional mean of y, denoted E y x.

Uses of Polynomial Regression: These are basically used to define or describe non-linear phenomenon such as:. The basic goal of regression analysis is to model the expected value of a dependent variable y in terms of the value of an independent variable x. In simple regression, we used following equation —. In many cases, this linear model will not work out For example if we analyzing the production of chemical synthesis in terms of temperature at which the synthesis take place in such cases we use quadratic model.

Since regression function is linear in terms of unknown variables, hence these models are linear from the point of estimation. Step 1: Import libraries and dataset Import the important libraries and the dataset we are using to perform Polynomial Regression.

Divide dataset into two components that is X and y. X will contain the Column between 1 and 2. Step 5: In this step we are Visualising the Linear Regression results using scatter plot. Step 6: Visualising the Polynomial Regression results using scatter plot. Step 7: Predicting new result with both Linear and Polynomial Regression. Writing code in comment? Please use ide. Related Articles. Polynomial regression fits a nonlinear relationship between the value of x and the corresponding conditional mean of y, denoted E y x Why Polynomial Regression: There are some relationships that a researcher will hypothesize is curvilinear.

Clearly, such type of cases will include a polynomial term. Inspection of residuals. If we try to fit a linear model to curved data, a scatter plot of residuals Y axis on the predictor X axis will have patches of many positive residuals in the middle.

Hence in such situation it is not appropriate.

An assumption in usual multiple linear regression analysis is that all the independent variables are independent. In polynomial regression model, this assumption is not satisfied.

Uses of Polynomial Regression: These are basically used to define or describe non-linear phenomenon such as: Growth rate of tissues. Progression of disease epidemics Distribution of carbon isotopes in lake sediments The basic goal of regression analysis is to model the expected value of a dependent variable y in terms of the value of an independent variable x.

Importing the libraries.