A Regression Model
Tags: Regression Analysis, Regression Modeling, Data Science, Regression

A Regression Model

What is Regression Analysis?

Regression analysis is a statistical method used for the elimination of a relationship between a dependent variable and an independent variable. It is useful in accessing the strength of the relationship between variables. It also helps in modeling the future relationship between the variables. Regression analysis consists of various types including linear, non-linear, and multiple linear. But the most useful ones are the simple linear and multiple linear. It can be utilized to assess the strength of the relationship between variables and for modeling, the future relationship between them. Regression analysis includes several variations, such as linear, multiple linear, and nonlinear. The most common models are simple linear and multiple linear. Nonlinear regression analysis is commonly used for more complicated data sets in which the dependent and independent variables show a nonlinear relationship.

Regression analysis is the method of using observations (data records) to quantify the relationship between a target variable (a field in the recordset), also referred to as a dependent variable, and a set of independent variables, also referred to as a covariate. For example, regression analysis can be used to determine whether the dollar value of grocery shopping baskets (the target variable) is different for male and female shoppers (gender is the independent variable). The regression equation estimates a coefficient for each gender that corresponds to the difference in value. The value of quantifying the relationship between a dependent variable and a set of independent variables is that the contribution of each independent variable to the value of the dependent variable becomes known. Once this is known, you need to know only the values of the independent variables in order to be able to make predictions about the value of the dependent variable. For example, when the coefficients for male and female shoppers are known, you can make precise revenue estimates for different distributions of shoppers. Specifically, you can predict the revenues for 80/20 females/males versus 60/40 females/males.

Regression Analysis Formula:

The formula is Y = MX + b

Where,

· Y is the dependent variable of the regression equation.

· M is the slope of the regression equation.

· X is the dependent variable of the regression equation.

· b is the constant of the equation.

What is the Purpose of Regression Analysis?

The purpose is to predict an outcome based on historical data. This historical data is understood with the help of regression analysis.

For example, you want to predict the data of what type of people buy the coffee. So, in this case, you will find the data of the person who buys coffee and collects information like their age, height, financial status, and other things.

Now after analyzing this data you will create a model to predict whether a person will buy the coffee or not. So, we can say regression analysis is used to predict the behavior of the dependent variable based on the large independent variables.

Why You Should Use Regression Analysis?

Regression analysis is useful in doing various things. Below we will discuss some primary reasons to consider regression analysis.

1. To Analyze a Wide Variety of Relationships

Regression analysis can help in handling various relationships between data sets. You can it in:

o Model multiple independent variables

o Continuous and categorical variables

o Polynomial terms to model curvatures

o Access interaction terms to determine the effect of one independent variable on the value of another independent variable

2. To Control Independent Variables

As noted, it helps in describing the change in each independent variable related to the dependent variable. We can say that it strategically controls all the variables within the model.

3. To Interpret Regression Output

In regression analysis, you must first fit and verify that you have a good model. After doing this, you must look at the regression coefficients and the p values. When you have a p-value less than 0.05 then the independent variable is statistically significant.

This p-value will help you to determine whether the relationship you observe in the sample also works with the larger population or not.

4. To Obtain Trustworthy Regression Results

When to use Regression Analysis?

When anyone says regression analysis, they often mean ordinary least square regressions. However, this is appropriate when there is one independent variable that is continuous when certain assumptions are met.

But in actuality, there are various types like count regressions, logistic regression, multinomial logistic, ordinal logistic, quantile, multivariate and other types.

Regression analysis is mainly used to estimate a target variable based on a set of features like predicting housing prices based on things like the number of rooms per house, the age of the house, etc.

Types of Regression

1. Linear Regression

This is used for predictive analysis. It is a linear approach is followed in this for modeling the relationship between the scalar response and explanatory variables.

This mainly focuses on the conditional probability distribution of the response given the value of predictors. However, in linear regression, there is a danger of overfitting.

The equation for Linear Regression is Y’ = bX + A.

2. Logistic Regression

This regression is used when the dependent variable is dichotomous. It estimates the parameters of the logistic model.

This regression helps in dealing with the data that has two possible criteria.

The equation for the Logistic Regression is l = β0 +β1X1 + β2X2

3. Polynomial Regression

This regression is used for curvilinear data. It is perfectly fitted with the method of least squares. This analysis aims to model the expected value of a dependent variable y in regard to the independent variable x.

The equation for Polynomial Regression is l =β0 +β0X1 +ε

4. Stepwise Regression

It is used for fitting the regression model with the predictive model. This regression is carried out automatically. However, with every step, the variable is added or subtracted from the set of explanatory variables.

In this, there is an approach of forwarding selection and backward elimination.

The formula for stepwise regression is bj.std = bj (Sx ­* SY-1)

5. Ridge Regression

This is a technique for analyzing multiple regression data. In this when multicollinearity occurs the least square estimates are unbiased.

A degree of bias is added to regression estimates and due to this the ridge regression reduces the standard errors.

The equation for the Ridge Regression is β = (XTX + λ * I)-1XT Y

6. Lasso Regression

In this, both variable selection and regularization methods are performed. It uses soft thresholding. Furthermore, it selects only a subset of the provided covariates to use in the final model.

The formula for Lasso Regression is N-1 ∑i=1NF (Xi, Yi, α, β)

7. Elastic Net Regression

It is a regularized regression method that linearly combines the penalties of the lasso and ridge methods. It is mainly used for support vector machines, portfolio optimization, and metric learning.

The equation for the Elastic Net Regression is ||β||1 = ∑pj=1 |βj|

Regression Analysis Examples

Now we will discuss four examples of regression analysis out of which two are related to finance and two are not related to finance.

Here are the examples related to Finance.