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# Key Insights on Computer Applications and Regression Analysis

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## INTRODUCTION

A computer application is based on the software program that runs the entire system such as email programs, web browsers, processors and utilise applications. Generally, the application is used in a group of programs that are designed for end users. The assignment will discuss the regression analysis technique and categorise it into different types. Furthermore, it will describe the different terminologies which are related to the regression and determine the correct regression model.

## 1. Define Regression Analysis

The regression analysis is based on the powerful statistical technique that allows to identification of the significant relationship between one or more variables. The primary regression is mainly used for conceptual distinct purposes that easily predict and forecast where it has substantial overlap with different field of machine learning. In different situations, regression analysis can be used to infer casual relationship among dependent and independent variables. In order to understand the concept of regression analysis for identifying variable that directly impacts on the overall software processing (Chen & et.al., 2019). It also maintained the statistical method that provides leverage across the organization to identify the degree to which particular independent variables influence dependent variables. For Example- Regression is often used to identify various types of factors such as commodity price and interest rates and other types of industries that influence the cost movement of assets. Through regression, it can easily utilise the project's expected return for various stocks and generate capital costs.

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The regression analysis consists of various terminologies that can be used during analysis which generate an accurate result or outcome.

• Regression Equation: it is based on the mathematical formula that is mainly applied to the explanatory variable. In this way, it is the best way to predict dependent variables and useful for modelling. For Example- â€œXâ€ and â€œYâ€ are two coordinates that represent the regression notation where â€œXâ€ as the dependent variable and â€œYâ€ for the independent variable.
• Dependent Variable: It is mainly representing the process that is trying to easily understand and predict actual outcomes. The dependent variable appears on the left side of the equation while used as a regression to predict the variable.
• P-Values: Most regression techniques can be performed by statistical tests which compute the actual probability. It is called a p-value that is associated with independent variables. This P-value reflects on the small probabilities and suggests that the coefficient is important to model with significant values (Gupta & et.al., 2019). The coefficient and variables do not help to predict the model in terms of dependent variables.
• Bias: It is based on the unbiased estimator that is expected to generate equal value in different parameters.
• T-test: It is the most common test in terms of null hypotheses that will perform specific functions in particular regression parameters.
• Multicollinearity: It is based on the situation where high degree of correlation among different independent variables in the particular regression model. X variable is close to a linear combination of another variable. Sometimes, it may include errors related to large standards and increase the inability to generate precise estimates.
• Interaction terms: It can be represented as pairwise items in the form of independent variables. This type of interaction is used on the regression which allows for the identification possibility of the degree to which the â€œXâ€ independent variable affects on â€œYâ€ variables.
• Omitted variable bias: This type of bias is based on the regression parameters that will arise from omitted independent variables from the regression model and also establishes the relation between one or more variables in a proper manner.
• Overfitting and Underfitting: when it has increased the unnecessary explanatory variables, which might to lead overfitting. It means that the algorithm works in properly on a specific set of training (KirjanÃ³w-BA & et.al., 2019). Sometimes, it is unable to perform the significant test sets also called high variance problems. On the other hand, if the algorithm works slowly that unable to fit a set of training.

## 3. Discuss Different Types of Regression.

There are different types of regression methods used for the purpose of analysis and to help identify the estimation result or outcome.

Linear Regression: It is one of the common techniques for the purpose of modelling. Usually, it is based on the dependent variables and independent variables that establish a relationship between them (Lawrence, 2019). It can be represented in the form of an equation such as Y=a+b*X+n. The linear regression method becomes sensitive which affects the regression line and also forecasts the values.

For Example:

Figure 1

It has shown the difference between multiple and single linear regression where multiple lines are independent variables.

Polynomial Regression:  It is based on the regression equation if the independent variables' power is more than one value. It can be represented in the form of an equation such as:

In polynomial regression, It is useful for temptation to fit in particular high degree polynomial that get low errors. As a result, it is generating over-fitting. It always polt the relationship to identify curves that fit in the particular nature of the problem.

For Example-

Figure 2

Logistic Regression: this type of regression is mainly used to find out the probability of different events. It may be considered a failure and a success. The logistic regression uses dependent variables in terms of binary value Whereas the range of â€œYâ€ values exists between 0 to 1. For Example- We have worked with the other binomial distributions that needed to select specific link functions. It is the best suitable for distribution and performing logit functions. In logistic regression, it doesn't require any type of linear relationship between independent and dependent variables. It can handle multiple relationships because it applicable for non-linear transformation.

Ridge Regression: It is a type of technique or method that is mainly used for data that suffers from various multicollinearities. In the process, even though least square estimations are unbiased and raise large variances. In this way, it deviates to observe values that are far from other true values. It also adding bias to the regression estimates and eliminates standards of errors (Sahu, Bharimalla & Dash, 2020). The method decomposes the predicted errors into different ways: variances and biases. It may occur prediction errors because of these components. On the other hand, it can be identified that the Ridge regression method resolve the problem of multicollinearity by using shrinkage parameters.

Lasso Regression: This type of regression is similar to ridge regression where it can penalize the absolute size of the regression coefficient. It is also capable of reducing the variability and improving accuracy in the model. Lasso is mainly used to find out absolute values through the penalty function instead of any squares. It may lead to penalising the values which causes estimate parameters that turn into zero. This type of model is considered a regularization method in terms of high predication between correlations.

Elastic Net Regression: Elastic net regression is basically a hybrid of ridge and lasso regression methods which perform functions on the basis of L1 and L2. It is the most useful concept that considers multiple features and establishes a connection between them. Through the Lasso technique, it is likely to pick one value randomly while the elastic-net method picks both values. The elastic-net regression always encourages the effects between the correlated high variables because it has a limitation in selecting the particular variables.

Principal components Regression: it is the most widely technique used when it may apply independent variables that exist in the data or information. In this way, it is easily analysed through the statistical process to extract new features when highly correlated features are applied. Principal regression consists of multiple components with high variances and the purpose of predicting actual results or outcomes (Shafapour, Tehrany & et.al., 2019). It deals with the different situations and conditions by excluding the low variances in the regression process.

Quantile Regression: It is based on the statistical method that was intended to estimate and conduct the inference among different functions. In most cases, it can be reduced the total squared residuals which enables to calculation of the models by using conditional functions.  This type of quantile regression offers the overall mechanism for calculating the conditional median function and identifying its full range. It is the most suitable method in terms of application setting whereas predicting the parametric assumption on the relationship between line variance curves.

Support Vector Regression: this type of regression technique is useful for resolving both non-linear and linear models. It supports the overall process to minimize errors and individual hyper place which increases the margin. The support vector regression maintains and controls the features of the algorithm and uses the same principles as SVM for classifying into different manners (Tang & et.al., 2019). In Support vector regression, it can be determined the margin of tolerance will be used as a set of approximations and sent the request from different problems but it is a very complex process to handle errors. In this way, the Support vector regression method is helping to increase the margin and decrease errors.

Ordinal Regression: It is predicated on the ranked values. In other words, it is the simplest method in terms of regression that helps manage the ordinal nature of dependent variables.  In order to respond to the category of independent and dependent variables. it is a continuous process to test the failure and success events. The ordinal regression may contain one dependent variable and cannot use multiple types of dependent variables. In the context of predictive analysis, ordinal regression mainly describes the data or information which creates a relationship between one independent and dependent variable. For Example- it can be measured the regression line to express how change occurs in the independent variables and affects the independent variables.

Partial Least Squares Regression: It is a type of alternative technique or method of principal component when they have established the correlation between independent variables. it is becoming useful for managing a large number of independent variables. it always takes the variables into account and therefore often leads to models that are able to fit in the dependent variables.

For Example-

Poisson Regression: It is a generalized linear model that will be used in the regression analysis. The model is used to count data and contingency tables. This type of Poisson regression method assumes the actual response of â€œYâ€ variables and distributes the Poisson. In most of cases, the expected value can be modified through a linear combination of multiple parameters. Poisson regression is the most appropriate method for data rate because it easily counts each event and divides it into smaller units (Wu & et.al., 2019). The Poisson regression method is mainly used when it has counted the data of dependent variables. For Example- It will predict the number of calls in consumer care regarding a specific item. It will be an estimation of emergency numbers in particular services at the time of the event.

Negative Binomial Regression: The negative binomial regression is similar to the various regression techniques except that dependent variable can be observed to count to follow a negative binomial distribution. It is possible to consider the values of non-negative integers. It is a generalization of Poisson regression whereas formulation is popular because it allows modelling the Heterogeneity with the help of gamma distribution. This type of regression computes both categorical variables and numeric values.

Tobit Regression: it is mainly used to estimate the linear relationship among the multiple variables when observation exists in the dependent variable. It is important to identify true values which restrict the wide range of observations. In most of cases, The Dependent values are included in a certain range as a single value and describe the entire observation. Furthermore, it makes the same type of assumption which causes error distribution and is much more vulnerable to violation.

Cox Regression: The regression method is mainly used for the time-to-event data because it easily estimates the time it takes to reach a certain level of event. It is a survival analysis that compares time-to-event for different groups. Through Cox regression, it has been targeted the set of survival models which continuously represent variables on multiple event times. For Example- customers have opened their accounts on time until it happens attrition.

Quasi-Poisson Regression: It is an alternative method to negative binomial regression that is mainly used to overdispersed the count data or information. In this way, it can be measured the difference in the estimation effect of multiple covariates (Sahu, Bharimalla & Dash, 2020). There are some variances in quasi Poisson model in terms of linear function. A quasi-Poisson model is necessary to count the variables and display them in a better data format. It always contained the positive integer variables. in this method, it has estimated the magnitude of the coefficient that indicated a change in independent variable sizes and established direct relationship between them. This will help in measuring the accuracy and reliability through estimation.

## 4. Understand How to Choose the Correct Regression Model

It is the simplest way to understand different techniques and find out their overall working activities. In this way, it helps to identify the continuous result or outcome. Within various types of regression models, it is important to select the best technique in terms of dependent and independent variables (Sahu, Bharimalla & Dash, 2020). In dimensionally, it has needed to understand the data or information that shows characteristics of data.  It may consider multiple factors that should practised to choose the right regression model for the purpose of analysis.

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• Data exploration is based on the inevitable part of predicting the structure model and should be the initial step before choosing the right model. It is likely to determine the significant relationship between independent and dependent variables.
• It is the comparison between the different models that would analyse various metrics such as adjusted r-square, statistical parameters, BIC, r-square and AIC. On the other hand, it is one of Mallow's criteria that will check the bias possibility in the model and help of comparison between sub-models.
• Cross-validation is a type of model that can evaluate the prediction and divide data sets into smaller groups. In the simplest form, it squares the difference between predictable and observed values which generate an accuracy in result or outcome (Sahu, Bharimalla & Dash, 2020).
• In case, if set of data has been found in the multiple confounding variables. It should not select the automatic model because they do not want to put these models at the same time intervals.
• The regression regularization technique of the method works well if it increases the high level of dimensionality as well as multicollinearity among variables in a large number of data sets.

These are different factors that help in identifying the most suitable regression technique for representing the flow of data effectively and efficiently. In the above discussion, it can be analysed the different types of regression techniques and functionality and how they can interpret data or information. Furthermore, it will generate a specific result or outcome.

## CONCLUSION

In the above discussion, it concluded that a computer application is used as a software program that automatically runs systems through email programs, web browsers, and processors and utilises applications. It has designed a group of programs for end users. it has summarised the regression analysis technique and categorise into different types. There are various types of terminology used in the system, which are related to the regression and identify the correct regress

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