class: center, middle ## IMSE 440 ## Applied Statistical Models in Engineering <br> ## More on linear regression --- class: center, middle # When .red[not] to use linear regression? --- $$Y=\beta_0+\beta_1x_1+\cdots+\beta_px_p+\epsilon$$ $$\text{where }\;\epsilon \sim \text{N}(0, \sigma^2)$$ One of the assumptions: the errors are i.i.d. -- For some data, the variable values are not independent. - Time series data (or called longitudinal data) .center[] -- Regression is typically used for [cross-sectional data](https://en.wikipedia.org/wiki/Cross-sectional_data). --- # Nonlinear relationship -- .center[Ice cream sales vs. outside temperature] -- .center[ .gray[(hypothetical data)]  ] --- # What features to consider? -- <br> .center[Distance vs. elevation gain for Fred's 25 bike rides]  --     <!-- ------------------------------------------ -->