# Linear Regression Model

### 1. What is Regression?

One of the most often used regression methods is linear regression. Linear regression is a linear approach to modeling the relationship between a dependent variable and independent variables. Our goal here is to predict the output value based on the input features by multiplying the optimal coefficients. In the figure above, the red dots represent each samples. The straight blue line represents the line that best explains the samples, and is called a linear regression equation.

### 2. Examples of Regression

(1) Predict sales.
(2) Predict economic growth.
(3) Predict oil prices.
(4) Analyze impact of GPA on college admission.

### 3. Types of Linear Regression

1. Simple Linear Regression - Single explanatory variable
In simple linear regression, the dependent variable is predicted based on a single explanatory variable. A typical form of simple linear regression looks like:

$a$ is the intercept term of the regression equation, $b$ is the coefficient of the variable $X$ in the regression equation, and $e$ is the error between the regression and actual values.

2. Multiple Linear Regression - More than one explanatory In simple linear regression, only one explanatory variable was considered to predict the dependent variable. However, in a multiple linear regression, you can use more than one explanatory variable to predict the dependent variable. The following is how multiple linear regression looks like when there are K number of variables.

Like simple linear regression, $a$ is the intercept term of the regression equation, $b_{k}$ is the coefficient of the variable $X_{k}$ in the regression equation, and $e$ is the error between the regression and actual values.

### 4. Regression Prediction Example

Analyzing the relationship between weather and sales using linear regression
There are myriads factors that may have an impact on sales, and weather is one of them. The y-axis is sales (the dependent variable is always on the y-axis) and the x-axis is the total rainfall. The graph shows how much in rained and how much sales were made each month. Through this graph, the company is able to see that their "sales is higher when the rainfall is also high," and they could use this insight to develop new sales strategy and grow their company.

### 5. Linear Regression with CLICK AI

CLICK AI provides codeless artificial intelligence model development experience for users. With a just few clicks, users can develop machine learning models at a professional level through the automated process, and can build practical models to maximize business revenues.

Data is analyzed to gain market insights, and data analysis results are available for users to easily understand. Artificial intelligence could be trained with data sets to find out data patterns and make predictions based on it. You can automate the entire data process.

First, the explanatory variables consist of GRE score, TOEFL score, university ranking, statement of purpose, letter of recommendation, undergraduate GPA, and research experience, and the value you want to predict is the probability of admission. Each explanatory variable can be used to predict the probability of admission to graduate school.