Simple linear regression is a statistical method used to understand the relationship between two continuous variables: 1. An independent variable (predictor). 2. A dependent variable (response).

Objective: Predict the value of the dependent variable based on the independent variable.

The equation for simple linear regression is:

\[ y = \beta_0 + \beta_1 x + \epsilon \]

• \(y\): Dependent variable (response).
• \(x\): Independent variable (predictor).
• \(\beta_0\): Intercept.
• \(\beta_1\): Slope of the line.
• \(\epsilon\): Random error.

Variance of residuals:

\[ Var(\epsilon) = \sigma^2 \]

The dataset includes information about the hours students studied and their corresponding test scores.

The plot below shows the relationship between Hours Studied and Test Scores, with a linear regression line fitted to the data.

library(ggplot2)
ggplot(data, aes(x = Hours, y = Scores)) +
  geom_point(color = "blue") +
  geom_smooth(method = "lm", se = FALSE, color = "red") +
  labs(title = "Regression Line", x = "Hours Studied",
  y = "Test Scores")

• Simple linear regression helps analyze the relationship between two continuous variables.
• Example: Hours studied and test scores.
• Key takeaway: Understanding relationships can help make predictions and improve outcomes.

Thank you!