3.2 Simple Linear Regression: Definition

Simple linear regression: Very straightforward approach to predicting response $Y$ on predictor $X$.

$$Y \approx \beta_{0} + \beta_{1}X$$

• Read “$\approx$” as “is approximately modeled by.”
• $\beta_{0}$ = intercept
• $\beta_{1}$ = slope

$$\hat{y} = \hat{\beta}_{0} + \hat{\beta}_{1}x$$

• $\hat{\beta}_{0}$ = our approximation of intercept

• $\hat{\beta}_{1}$ = our approximation of slope

• $x$ = sample of $X$

• $\hat{y}$ = our prediction of $Y$ from $x$

• hat symbol denotes “estimated value”

• Linear regression is a simple approach to supervised learning