## Simple and multiple linear regression

Regression is one of the basic statistics models with a diversified application in fields such as finance and economics. It's the first model that introduces you into the world of modeling, such as the generalized linear regression models and financial models such as the Black-Scholes model. It might sound a bit simpler, but there are cases when assignments can be challenging. In such a case, do not hesitate to contact our online simple and multiple linear regression tutors who will help you with any queries that you might have.

### Simple and multiple regression

Linear regression is more common in data analysis model assignments that we handle, probably because of its simplicity of application. It seeks to identify the linear relationship between the variables. The most common forms of regression are simple and multiple linear regression. Like in any other model, linear regression models also have assumptions wherein they perfectly work.

### Assumptions of linear regressions

- Linearity exists between the variables.
- The residual error value is zero.
- The independent variable does not show any characteristics of randomness.
- The residual error has a constant value and is normally distributed.
- Non-collinearity- this assumption is only applicable to multiple linear regression because of the number of explanatory variables. The assumption means that the independent variables should indicate low levels of correlation.

### Simple linear regression

The simple linear regression is a model that shows linearity between a Y variable and an X variable. Their general equation is shown below.

Y = A + mX + ϵ

Where, A= x- intercept, m = the gradient or slope, and **ϵ**** =error term.**

Multiple linear regression.

They are similar to linear regression, the main between the two is the number of X variables. The general equation of multiple linear regression is given below.

Y = A ∑K_{i}X_{i} + ϵ

Where

K_{i} = the gradients of the explanatory variables.

ϵ= the residuals error

A = the intercept

Generally, a simple regression is a multiple regression with a single explanatory variable. The number of explanatory variables in a multiple regression could increase to infinity. Sometimes calculations involving multiple regressions are only possible by using statistical software such as STATA and R because they could be very cumbersome and time-consuming.

### Applications of simple and multiple regressions in real-life

The capital asset pricing model, which is abbreviated as CAPM, is a statistical model that shows the linearity between the expected property portfolio return and the market returns. CAPM is a linear model of the expected return and the market returns. A component of interest that shows the volatility of the market is the beta. The beta in the CAPM formula is the gradient. Investors make a decision depending on their risk preferences on whether or not to invest in the asset. The beta can be derived using the ordinary least square method.

Other applications of linear regression include modeling the impact of a product's price on the average sales, the impact of rain or the application of a certain pesticide on the agricultural produce, and predicting the sales of a firm.

### Linear regression in STATA

There are three steps that are needed to carry out linear regression in STATA. First, you open the program and navigate to the Statistics tab and click it. On the dropdown menu that appears, Click on the linear models and related menu. Then click on the linear models for the dropdown menu that appears again. It will immediately load a dialogue box in which you will fill your independent and dependent variables to perform linear regression.

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