ei = 28, se = 8 (a-1) Calculate the standardized residual e*. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.) Standardized residual ei* (a-2) Determine whether or not it is unusual or an outlier. O Unusual O Outlier O Not unusual nor an outlier ei = -14, se = 6 (b-1) Calculate the standardized residual e;*. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.) Standardized residual ei*

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### Calculating and Evaluating Standardized Residuals

#### Given:

For the first case:
- \( e_i = 28 \)
- \( s_e = 8 \)

**(a-1)** *Calculate the standardized residual \( e_i^* \):*  
*(Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)*

- Input box for: "Standardized residual \( e_i^* \)"

**(a-2)** *Determine whether or not it is unusual or an outlier:*

- Options:
  - Unusual
  - Outlier
  - Not unusual nor an outlier

For the second case:
- \( e_i = -14 \)
- \( s_e = 6 \)

**(b-1)** *Calculate the standardized residual \( e_i^* \):*  
*(Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)*

- Input box for: "Standardized residual \( e_i^* \)"

### Explanation

Standardized residuals are used in statistics to assess how far away a data point is from the expected value. It is calculated as:

\[ e_i^* = \frac{e_i}{s_e} \]

where:
- \( e_i \) is the residual for data point \( i \).
- \( s_e \) is the standard error. 

The standardized residual helps in determining whether a data point is unusual or an outlier. Typically, residuals that fall beyond a certain range (e.g., >2 or <-2) may be considered as outliers. The user is prompted to input their calculated value and then determine its classification based on the options provided.
Transcribed Image Text:### Calculating and Evaluating Standardized Residuals #### Given: For the first case: - \( e_i = 28 \) - \( s_e = 8 \) **(a-1)** *Calculate the standardized residual \( e_i^* \):* *(Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)* - Input box for: "Standardized residual \( e_i^* \)" **(a-2)** *Determine whether or not it is unusual or an outlier:* - Options: - Unusual - Outlier - Not unusual nor an outlier For the second case: - \( e_i = -14 \) - \( s_e = 6 \) **(b-1)** *Calculate the standardized residual \( e_i^* \):* *(Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)* - Input box for: "Standardized residual \( e_i^* \)" ### Explanation Standardized residuals are used in statistics to assess how far away a data point is from the expected value. It is calculated as: \[ e_i^* = \frac{e_i}{s_e} \] where: - \( e_i \) is the residual for data point \( i \). - \( s_e \) is the standard error. The standardized residual helps in determining whether a data point is unusual or an outlier. Typically, residuals that fall beyond a certain range (e.g., >2 or <-2) may be considered as outliers. The user is prompted to input their calculated value and then determine its classification based on the options provided.
### Statistical Analysis Task

#### (b-2) Determine whether or not it is unusual or an outlier.
- Select one of the options:
  - ○ Unusual
  - ○ Outlier
  - ○ Not unusual nor an outlier

Given data:
- \( e_i = 123 \)
- \( s_e = 61 \)

#### (c-1) Calculate the standardized residual \( e_i^* \).
- The standardized residual should be calculated using the formula:
  \[ e_i^* = \frac{e_i}{s_e} \]
- **Instructions**: Negative values should be indicated with a minus sign. Round your answer to 3 decimal places.

Input field: 
- **Standardized residual \( e_i^* \)**: [ ]

#### (c-2) Determine whether or not it is unusual or an outlier.
- Select one of the options:
  - ○ Not unusual nor an outlier
  - ○ Outlier
  - ○ Unusual

#### Notes:
- A standardized residual that exceeds a certain threshold is generally used to determine if a data point is an outlier or unusual.
Transcribed Image Text:### Statistical Analysis Task #### (b-2) Determine whether or not it is unusual or an outlier. - Select one of the options: - ○ Unusual - ○ Outlier - ○ Not unusual nor an outlier Given data: - \( e_i = 123 \) - \( s_e = 61 \) #### (c-1) Calculate the standardized residual \( e_i^* \). - The standardized residual should be calculated using the formula: \[ e_i^* = \frac{e_i}{s_e} \] - **Instructions**: Negative values should be indicated with a minus sign. Round your answer to 3 decimal places. Input field: - **Standardized residual \( e_i^* \)**: [ ] #### (c-2) Determine whether or not it is unusual or an outlier. - Select one of the options: - ○ Not unusual nor an outlier - ○ Outlier - ○ Unusual #### Notes: - A standardized residual that exceeds a certain threshold is generally used to determine if a data point is an outlier or unusual.
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