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