Introduction

The statistical method to model the relationship between one dependent variable(target) and one or more independent variables(predictor) is considered as regression analysis. It basically deals with predictive modelling problems that involve predicting a numeric value. Getting the accuracy of the regression metrics is slightly harder, as we cannot predict the exact value, rather we can refer to the closest prediction against the real value.

  1. Regression Predictive Modeling
  2. Evaluating Regression Models
  3. Metrics for Regression

1. Regression Predictive Modeling

The predictive modelling that analyzes the relation between the target or dependent variable and independent variable in a dataset is referred to as regression analysis. The main goal of regression is the construction of an efficient model to predict the dependent attributes from a bunch of attribute variables. A regression metrics problem is when the output variable is either real or a continuous variable, for example, weight, area, salary, etc.

Regression model evaluation metrics mainly deals with two types of regression analysis techniques  :

1. Linear Regression            2. Logistic Regression

1. Linear Regression: A linear regression is a regression technique where the independent variable has a linear relationship with the dependent variable. It is used in cases where we want to predict some continuous quantity. For example, a linear regression metrics can be used to quantify the relative impacts of gender, age, and diet on height. The linear regression evaluation metric is based on the least square estimation, which states that the regression co-efficient should be chosen in such a way that it minimizes the sum of the squared distance of each observed response and aims at finding the best fitting straight line, known as the regression line.

2. Logistic Regression: Logistic regression is basically a special case of linear regression where we predict the output in a categorical behaviour. It predicts the probability of an event using the law of function. Logistic regression metric is based on the maximum likelihood estimation, which states that the co-efficient should be chosen in such a way that it maximizes the probability of Y,  with a given value of X. In the logistic regression evaluation metric, the relation between the dependent and independent variable is represented in a curve called the sigmoid curve. Log loss or Binary Crossentropy is an example of a logistic regression metric.

Keras may be a deep learning API written in Python, running on top of the machine learning platform TensorFlow developed with attention on sanctioning quick experimentation. The core information structures of Keras metrics for regression are layers and models, and also, the simplest form of the model is that it follows a sequence.

2. Evaluating Regression Models

Selecting the appropriate evaluation metric is one of the vital tasks for us when we are going to work on a learning model which is based on regression. The top evaluation metrics for regression are also known as loss functions. Usually, more than one metric is required to evaluate a machine learning model, and hence there are different data and projects; we have to select an appropriate regression performance metric. We cannot calculate accuracy for a regression model as accuracy is not a measure for regression.

3. Metrics for Regression

There are different evaluation metrics for regression used in machine learning. Some of the important types of regression metrics are:

1. Mean Absolute Error(MAE): The addition of all the positive and absolute values is referred to as the mean absolute error. While calculation, the positive value is taken despite the difference between the predicted and the actual value is negative. For example, if the actual value is 200, and the predicted value is 250, then the error difference that comes is negative. But the value taken is positive, and that is the actual value of error. Hence -50 will become 50. Now we can get the mean absolute error by dividing the sum of all absolute errors by the total number of absolute errors.

2. Mean Square Error(MSE): Mean square error is often positive on calculation. We can calculate it by square rooting the error difference of actual and predictive value and calculating its mean. If a model with completely different parameters is run by us, then the model that has lower MSE is deemed to be a better option.

3. Root Mean Square Error(RMSE): The root mean square error is calculated by square rooting MSE. The formula used in RMSE is very similar to MSE, but the only difference is we need to square root it.

4. Root Mean Square Log Error(RMSLE): RMSE that is calculated at logarithmic scale is known as the root mean square error. The log of 0 cannot be defined, so during the calculation of RMSLE, 1 is added to the predicted as well as the actual values as a constant because they can be 0. Hence the whole formula remains the same as RMSE, both for linear as well as logistic regression performance metrics.

Conclusion

Hence, we can conclude that regression is a set of statistical processes for estimating the relationships between the outcome variable and the features, and there are various regression metrics. We always have to calculate and compare the evaluation metrics for both testing and training data set, as a huge difference between both datasets means that there is a problem with our model. 

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