Consider the following set of dependent and independent variables. Using technology, check for the presence of multicollinearity. If multicollinearity is present, take the necessary steps to eliminate it.  Select the correct choice and, if necessary, fill in the answer boxes to complete your choice.  A) Eliminate the variable x(__), which has a VIF of (__). No more variables need to be eliminated. B) Eliminate the variable x(__), which has a VIF of (__). Then eliminate the variable x(__), which has a VIF of (__).  C) No variables need to be eliminated.  y 33 31 38 37 40 46 48 54 47 58 x1 53 55 55 58 57 61 66 70 89 71 x2 24 17 20 17 9 15 14 11 15 12 x3 7 16 10 13 19 18 24 21 28 30

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Consider the following set of dependent and independent variables. Using technology, check for the presence of multicollinearity. If multicollinearity is present, take the necessary steps to eliminate it. 

Select the correct choice and, if necessary, fill in the answer boxes to complete your choice. 

A) Eliminate the variable x(__), which has a VIF of (__). No more variables need to be eliminated.

B) Eliminate the variable x(__), which has a VIF of (__). Then eliminate the variable x(__), which has a VIF of (__). 

C) No variables need to be eliminated. 

y 33 31 38 37 40 46 48 54 47 58
x1 53 55 55 58 57 61 66 70 89 71
x2 24 17 20 17 9 15 14 11 15 12
x3 7 16 10 13 19 18 24 21 28

30

**Analyzing Multicollinearity in a Set of Variables**

Consider the following set of dependent and independent variables. Using technology, check for the presence of multicollinearity. If multicollinearity is present, take the necessary steps to eliminate it.

|  y  | x₁ | x₂ | x₃ |
|----|----|----|----|
| 33 | 53 | 24  | 7   |
| 31 | 55 | 17  | 16 |
| 38 | 55 | 19  | 10 |
| 37 | 58 | 15  | 13 |
| 40 | 57 | 14  | 19 |
| 46 | 61 | 11  | 18 |
| 48 | 66 | 14  | 24 |
| 54 | 70 | 11  | 21 |
| 47 | 89 | 14  | 28 |
| 58 | 71 | 12  | 30 |

**Instructions:**

Select the correct choice and, if necessary, fill in the answer boxes to complete your choice. (Type integers or decimals. Round to one decimal place as needed.)

- **Option A:**
  - Eliminate the variable \( x \_\_\_\_ \) which has a VIF of \(\_\_\_\_\). No more variables need to be eliminated.

- **Option B:**
  - Eliminate the variable \( x \_\_\_\_ \) which has a VIF of \(\_\_\_\_\). Then, eliminate the variable \( x \_\_\_\_ \) which has a VIF of \(\_\_\_\_\).

Click to select and enter your answer(s) and then click Check Answer. 

**Explanation:**

The Variance Inflation Factor (VIF) is used to detect the presence of multicollinearity. If VIF is above a certain threshold (commonly 5 or 10), it indicates significant multicollinearity, suggesting the need to eliminate variables to improve model stability and interpretability.
Transcribed Image Text:**Analyzing Multicollinearity in a Set of Variables** Consider the following set of dependent and independent variables. Using technology, check for the presence of multicollinearity. If multicollinearity is present, take the necessary steps to eliminate it. | y | x₁ | x₂ | x₃ | |----|----|----|----| | 33 | 53 | 24 | 7 | | 31 | 55 | 17 | 16 | | 38 | 55 | 19 | 10 | | 37 | 58 | 15 | 13 | | 40 | 57 | 14 | 19 | | 46 | 61 | 11 | 18 | | 48 | 66 | 14 | 24 | | 54 | 70 | 11 | 21 | | 47 | 89 | 14 | 28 | | 58 | 71 | 12 | 30 | **Instructions:** Select the correct choice and, if necessary, fill in the answer boxes to complete your choice. (Type integers or decimals. Round to one decimal place as needed.) - **Option A:** - Eliminate the variable \( x \_\_\_\_ \) which has a VIF of \(\_\_\_\_\). No more variables need to be eliminated. - **Option B:** - Eliminate the variable \( x \_\_\_\_ \) which has a VIF of \(\_\_\_\_\). Then, eliminate the variable \( x \_\_\_\_ \) which has a VIF of \(\_\_\_\_\). Click to select and enter your answer(s) and then click Check Answer. **Explanation:** The Variance Inflation Factor (VIF) is used to detect the presence of multicollinearity. If VIF is above a certain threshold (commonly 5 or 10), it indicates significant multicollinearity, suggesting the need to eliminate variables to improve model stability and interpretability.
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