More on linear regression

class: center, middle

## IMSE 586 
## Big Data Analytics and Visualization
<br/>

### More on linear regression
<br/>
### Instructor: Fred Feng

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$$Y=\beta_0+\beta_1x_1+\cdots+\beta_px_p+\epsilon$$

$$\text{where }\;\epsilon \sim \text{N}(0, \sigma^2)$$

One of the assumptions is that the errors are [i.i.d.](https://en.wikipedia.org/wiki/Independent_and_identically_distributed_random_variables).

For some data, the values are *not* independent.

- Time series data (or [longitudinal](https://en.wikipedia.org/wiki/Longitudinal_study) data)

.center[![:scale 70%](images/msft.png)]

Regression is typically used for [cross-sectional data](https://en.wikipedia.org/wiki/Cross-sectional_data).

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# Nonlinear relationship

.center[Ice cream sales vs. outside temperature]

.center[.gray[(hypothetical data)]
![:scale 90%](images/icecream_vs_temp.png)
]

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### Knowing .red[what variables to consider] is crucial.

.center[Distance vs. elevation gain for Fred's 25 bike rides]

![:scale 53%](images/dist_vs_elevation_1.png)
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   ![:scale 44%](images/dist_vs_elevation_2.png)

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- X: Ice cream sales

- Y: Number of people drowning in swimming pools

Are X and Y correlated?

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class: middle, center

# .red[Correlation does not equal causation.]

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# Spurious correlation

https://www.tylervigen.com/spurious-correlations