How to find variance percentage given VIF

 ## **Step-by-Step Solution**

### **1. Understanding VIF Formula**

The Variance Inflation Factor is:

\[

\text{VIF} = \frac{\text{Actual variance of coefficient}}{\text{Variance with no multicollinearity}}

\]

Given: **VIF = 1.8**

### **2. Interpret the VIF Value**

\[

1.8 = \frac{\text{Actual variance}}{\text{Variance with no multicollinearity}}

\]

This means the actual variance is **1.8 times** what it would be with no multicollinearity.

### **3. Calculate Percentage Increase**

If variance with no multicollinearity = 1 (base), then:

- Actual variance = 1.8

- **Increase** = 1.8 - 1 = 0.8

- **Percentage increase** = \( \frac{0.8}{1} \times 100\% = 80\% \)

---

## **Final Answer**

\[

\boxed{80}

\]

The variance of the coefficient is **80% greater** than what it would be if there was no multicollinearity.

---

### **Verification**

- VIF = 1.0 → 0% increase (no multicollinearity)

- VIF = 2.0 → 100% increase (variance doubles)

- VIF = 1.8 → 80% increase ✓

This makes intuitive sense: moderate multicollinearity (VIF = 1.8) inflates the variance by 80% compared to the ideal case.