Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables. It assumes a linear relationship between the variables. That can be explained by the change in the dependent variable is directly proportionnal to the change in the indepedent variable.

Here is an example to illustrate simple linear regression

set.seed(12345)

x <- 1:200
y <- 2* x + rnorm(200, mean = 0, sd = 10)

model <- lm(y~x)

library(ggplot2)

## Warning: package 'ggplot2' was built under R version 4.3.2

ggplot(data.frame(x,y), aes(x,y)) + geom_point() + geom_smooth(method = "lm", se = FALSE)

## `geom_smooth()` using formula = 'y ~ x'

Equation model

This is a simple linear regression model represented by the equation:

[y = _0 + _1x + ]

 ( y ) is the response variable  ( x ) is the predictor variable  ( beta_0 ) is the intercept  ( beta_1 ) is the slope  ( epsilon ) is the error term

install.packages(ggplot2)

• (y ) is the response variable
• (x ) is the predictor variable
• (beta_0 ) is the intercept
• (beta_1 ) is the slope
• (epsilon ) is the error term

1. Linearity: The relationship between X and Y is linear.
2. Independence: The observations are independent of each other.
3. Homoscedasticity: The variance of the error term is constant across all levels of X.
4. Normality: The error term follows a normal distribution with mean 0.
5. No multicollinearity: The predictor variable X is not highly correlated with other predictor variables.

To evaluate the fit of the model, we can look at:

1. R-squared: The proportion of variance in the response variable explained by the predictor variable.
2. Residuals: The differences between the observed and predicted values of the response variable.

In this concept, I introduced the concept of a simple linear regression and provide an example using simulated data. A linear regression model and plot the data along the regression line.Additionally I mentioned the model equation and evaluation.Linear regression assumes a linear relationship between the variables and that other factors not included in the model may influence the result of a study.