Simple Linear Regression is a method used to model the relationship between two variables by fitting a linear equation to observed data.

• Independent Variable (X): The predictor or input variable

• Dependent Variable (Y): The outcome or response variable

• Goal: To find the best-fit line that minimizes the error in predicting Y based on X

• \(\beta_0\): Intercept

• \(\beta_1\): Slope of the line

• \(\epsilon\): Error term, representing unexplained variability

A scatter plot can visually illustrate the relationship between \(X\) and \(Y\).

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

Understanding Slope and Intercept - Intercept (\(\beta_0\)): The expected value of Y when X is zero. - Slope (\(\beta_1\)):The change in Y fora one-unit increase in X. For example, if \(\beta_1 = 2\), this means that for every increase of 1 unit in X, Y increases by 2 units.

# Fitting the model
model <- lm(y ~ x, data = data)

# Displaying a clean summary table
model_summary <- tidy(model)
kable(model_summary, caption = "Summary of Linear Model")

Simple linear regression is a fundamental statistical technique used to understand and predict relationships between two continuous variables. It provides insights into the strength and direction of the relationship.