You must be familiar with several terms of statistics and simple linear regression is one of them. This blog talks about the concept of simple linear regression. Simple linear regression is a statistical strategy that permits us to sum up and study connections between two continuous or quantitative variables: One variable, meant A, is viewed as the predictor, explanatory, or independent variable. The other variable, meant B, is viewed as the response, outcome, or dependent variable.
In statistics, a simple linear regression model uses a single variable to predict the result of the other variable. You may confuse it with linear regression but let us make it clear through this blog that they both are different.
This blog carries the basics concept of simple linear regression such as the definition of linear regression, types of linear regression, the definition of simple linear regression, its assumptions, how to perform linear regression, limits of linear regression, examples of simple linear regression, and many more. Let’s begin with the basics of linear regression.
In layman terms, we can define linear regression as it is used for learning the linear relationship between the target and one or more forecasters, and it is probably one of the most popular and well inferential algorithms in statistics. Linear regression endeavours to demonstrate the connection between two variables by fitting a linear equation to observed information. One variable is viewed as an explanatory variable, and the other is viewed as a dependent variable.
For instance, a modeller should relate loads of people to their heights utilizing a linear regression model. Thus, it is a crucial and generally used type of foreseeing examination.
Normally, linear regression is divided into two types: Multiple linear regression and Simple linear regression. So, for better clearance, we will discuss these types in detail.
In this type of linear regression, we always attempt to discover the relationship between two or more independent variables or inputs and the corresponding dependent variable or output and the independent variables can be either continuous or categorical.
This linear regression analysis is very helpful in several ways like it helps in foreseeing trends, future values, and moreover predict the impacts of changes.
In simple linear regression, we aim to reveal the relationship between a single independent variable or you can say input, and a corresponding dependent variable or output. We can discuss this in a simple line as y = β0 +β1x+ε
Here, Y speaks to the output or dependent variable, β0 and β1 are two obscure constants that speak to the intercept and coefficient that is slope separately, and the error term is ε Epsilon.
We can also discuss this in the form of a graph and here is a sample simple linear regression model graph. Thus, in this whole blog, you will get to learn so many new things about simple linear regression in detail.
Simple Linear Regression graph, Image Source
It can be described as a method of statistical analysis that can be used to study the relationship between two quantitative variables. (Read also: Statistical Data Analysis)
Primarily, there are two things which can be found out by using the method of simple linear regression:
Regression models are used for the elaborated explanation of the relationship between two given variables. There are certain types of regression models like logistic regression models, nonlinear regression models, and linear regression models. The linear regression model fits a straight line into the summarized data to establish the relationship between two variables.
(Also read: What is Statistics? Types, Variance, and Bayesian Statistics)
To conduct a simple linear regression, one has to make certain assumptions about the data. This is because it is a parametric test. The assumptions used while performing a simple linear regression are as follows:
These three are the assumptions of regression methods.
(Must read: Types of Regression Techniques in Machine Learning)
However, there is one additional assumption that has to be taken into consideration while specifically conducting a linear regression.
Example of data that fails to meet the assumptions: One may think that cured meat consumption and the incidence of colorectal cancer in the U.S have a linear relationship. But later on, it comes to the knowledge that there is a very high range difference between the collection of data of both the variables. Since the homoscedasticity assumption is being violated here, there can be no linear regression test. However, a Spearman rank test can be performed to know about the relationship between the given variables.
Indeed, even the best information doesn't recount a total story. Regression investigation is ordinarily utilized in examination to set up that a relationship exists between variables. However, correlation isn't equivalent to causation: a connection between two variables doesn't mean one causes the other to occur. Indeed, even a line in a simple linear regression that fits the information focuses well may not ensure a circumstances and logical results relationship.
Utilizing a linear regression model will permit you to find whether a connection between variables exists by any means. To see precisely what that relationship is and whether one variable causes another, you will require extra examination and statistical analysis.
Now, let’s move towards understanding simple linear regression with the help of an example. We will take an example of teen birth rate and poverty level data.
This dataset of size n = 51 is for the 50 states and the District of Columbia in the United States (poverty.txt). The variables are y = year 2002 birth rate for each 1000 females 15 to 17 years of age and x = destitution rate, which is the percent of the state's populace living in families with wages underneath the governmentally characterized neediness level. (Information source: Mind On Statistics, 3rd version, Utts and Heckard).
Below is the graph (right image) in which you can see the (birth rate on the vertical) is indicating a normally linear relationship, on average, with a positive slope. As the poverty level builds, the birth rate for 15 to 17-year-old females will in general increment too.
Example graph of simple linear regression
Here is another graph (left graph) which is showing a regression line superimposed on the data.
The condition of the fitted regression line is given close to the highest point of the plot. The condition should express that it is for the "average" birth rate (or "anticipated" birth rate would be alright as well) as a regression condition portrays the normal estimation of y as a component of at least one x-variables. In statistical documentation, the condition could be composed y^=4.267+1.373x.
The R2 (adj) value (52.4%) is a change in accordance with R2 dependent on the number of x-variables in the model (just one here) and the example size. With just a single x-variable, the charged R2 isn't significant.
Simple linear regression is a regression model that figures out the relationship between one independent variable and one dependent variable using a straight line.
Hence, the simple linear regression model is represented by: y = β0 +β1x+ε. This blog carries all the basic facts related to simple linear regression, hope so this blog helps you in finding all your answers to your queries. Stay tuned with us to learn more about topics of statistics and many more.(Must read: XGBoost Algorithm for Classification and Regression)
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