# Regression

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Regression

## 1. Model Validity

### 1.1. X vs Y

1.1.1. How best does it fit the straight line

### 1.2. SR vs Fit & X's

1.2.1. Constant variance

1.2.2. Random/No discernible patters

1.2.2.1. Smiley/Grumpy Face

### 1.3. Multicollinearity

1.3.1. Correlation table

1.3.1.1. +/- 0.70 cutoff

1.3.2. Signs of coefficients contradict signs of correlation between Y and X's

### 1.4. Outliers

1.4.1. Look for large S.D outside +/- 2 in the SR plot

1.4.2. Investigate if there are special circumstances

1.4.2.1. Dummy Variables

### 1.5. No value in these if the model is invalid

1.5.1. R^2

1.5.2. Significant p-values

## 3. Transformation

3.1.1. Log Y

3.3.1. Log Y

### 3.5. Non Linear/Curvilinerar

3.5.1. Quandratic

### 3.6. User Forced => Elasticity

3.6.1. LogY, LogX

### 3.7. Why - Log Tx

3.7.1. Normalises skewness

3.7.1.1. spread the small values out + squeeze the large values together.

## 5. Tips

5.1.1. use y-hat

### 5.2. Hypothesis testing

5.2.1. One / Two tailed => use biz logic

## 6. Interpretation

### 6.1. y = bo + b1x

6.1.1. If x increases by 1, then y increases by b1

### 6.2. y = bo + b1 Log(x)

6.2.1. A 1% increase in x, gives 0.01 x b1 increase in y

### 6.3. Log (y) = bo + b1x

6.3.1. A 1 unit increase in x gives a (b1 x 100)% increase in Y (Including when x is a 0-1 dummy variable)

### 6.4. Log (y) = bo + b1 Log (x)

6.4.1. A 1% increase in x gives a b1 % increase in Y

## 7. ANOVA

### 7.1. WHY:

7.1.1. test significance of linear Rx b/n Y and subset / all X's

### 7.2. F:

7.2.1. Similar T Statistic