• What is Simple Linear Regression?
• Model & Interpretation
• Example Dataset
• Model Fit in R
• Visualization (ggplot + plotly)
• Inference (P-values, CI, Prediction)
• Takeaways

\[ Y = \beta_0 + \beta_1 X + \varepsilon \]

Where:
- \(\beta_0\) = intercept
- \(\beta_1\) = slope
- \(\varepsilon\) = error term (noise)

\[ \text{Assumptions: Linearity,Independence,Normality,Equal Variance} \]

• Linearity: Relationship between X and Y is linear
  
• Independence: Observations are independent
  
• Normality: Errors are normally distributed
  
• Equal Variance: Spread of errors is similar across X values

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

# Fit simple linear regression model
fit <- lm(mpg ~ wt, data = df)
#Display Summary
summary(fit)

## 
## Call:
## lm(formula = mpg ~ wt, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.5432 -2.3647 -0.1252  1.4096  6.8727 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  37.2851     1.8776  19.858  < 2e-16 ***
## wt           -5.3445     0.5591  -9.559 1.29e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.046 on 30 degrees of freedom
## Multiple R-squared:  0.7528, Adjusted R-squared:  0.7446 
## F-statistic: 91.38 on 1 and 30 DF,  p-value: 1.294e-10

• Weight is negatively related to MPG.
• The model suggests heavier cars burn more fuel.
• Visual diagnostics indicate the regression is reasonable.
• This method can be extended to multiple predictors.