---
# System prepended metadata

title: multiple regression
tags: [exp_analysis, study_progress]

---

# multiple regression
參照: http://www.adart.myzen.co.uk/reporting-multiple-regressions-in-apa-format-part-one/
seven main assumptions
1. outliers
2. collinearity
3. independent errors
4. random normal distribution of errors
5. homoscedasticity 
6. linearity of data
7. non-zero variances
## Collinearity
**是指多變量線性回歸中，變量之間由於存在高度相關關係而使回歸估計不准確。在該情況下，多元回歸的係數可能會因為模型或數據的微小變化發生劇烈改變。**

greater than 10, or the Tolerance is less than 0.1, then you have concerns over multicollinearity.

## Independent Errors
**Xi =  mi + ei**
**where the ei are independently distributed and mi represent the averages at each point in time.**

Durbin-Watson values can be anywhere between 0 and 4.
Durbin-Watson value is **less than 1 or over 3** then it is counted as being significantly different from 2, and thus the assumption has not been met. 

## Homoscedasticity and Linearity
**Homoscedasticity: 異質變異數，又稱分散不均一性，指的是一系列的隨機變數間的變異數不相同**
**Heteroscedasticity: 異方差，又稱分散不均一性，指的是一系列的隨機變量間的方差不相同，相對於同質方差（Homoscedasticity）**

![](https://i.imgur.com/DPSYeJT.png)

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數據混合



