class: center, middle ## IMSE 440 ## Applied Statistical Models in Engineering
## 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[![:scale 70%](images/msft.png)] -- 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)] ![:scale 90%](images/icecream_vs_temp.png) ] --- # What features to consider? --
.center[Distance vs. elevation gain for Fred's 25 bike rides] ![:scale 53%](images/dist_vs_elevation_1.png) -- ![:scale 44%](images/dist_vs_elevation_2.png)