A statistical program is recommended. Consider the following data for two variables, x and y. x 135 110 130 145 175 160 120 Y₁ 145 100 120 115 135 130 110 (a) Compute the standardized residuals for these data. (Round your answers to two decimal places.) X; Y₁ Standardized Residuals 135 145 110 100 130 120 145 115 175 135 160 130 120 110 Do the data include any outliers? Explain. (Round your answers to two decimal places.) The standardized residual with the largest absolute value is , corresponding to y; = (b) Plot the standardized residuals against ŷ. Does this plot reveal any outliers? The plot shows no possible outliers. O The plot shows one possible outlier. The plot shows two possible outliers. The plot shows more than two possible outliers. (c) Develop a scatter diagram for these data. Does the scatter diagram indicate any outliers in the data? O The diagram indicates that there are no possible outliers. O The diagram indicates that there is one possible outlier. O The diagram indicates that there are two possible outliers. O The diagram indicates that there are more than two possible outliers. . Since this residual is --Select--- O, it --Select--- In general, what implications does this finding have for simple linear regression? O For simple linear regression, it is impossible to determine whether there is an outlier using standardized residuals, a standardized residual plot, or a scatter diagram. For simple linear regression, we must calculate standardized residuals, plot a standardized residual plot, and construct a scatter diagram to identify an outlier. O For simple linear regression, we can determine an outlier by looking at the scatter diagram. an outlier.
A statistical program is recommended. Consider the following data for two variables, x and y. x 135 110 130 145 175 160 120 Y₁ 145 100 120 115 135 130 110 (a) Compute the standardized residuals for these data. (Round your answers to two decimal places.) X; Y₁ Standardized Residuals 135 145 110 100 130 120 145 115 175 135 160 130 120 110 Do the data include any outliers? Explain. (Round your answers to two decimal places.) The standardized residual with the largest absolute value is , corresponding to y; = (b) Plot the standardized residuals against ŷ. Does this plot reveal any outliers? The plot shows no possible outliers. O The plot shows one possible outlier. The plot shows two possible outliers. The plot shows more than two possible outliers. (c) Develop a scatter diagram for these data. Does the scatter diagram indicate any outliers in the data? O The diagram indicates that there are no possible outliers. O The diagram indicates that there is one possible outlier. O The diagram indicates that there are two possible outliers. O The diagram indicates that there are more than two possible outliers. . Since this residual is --Select--- O, it --Select--- In general, what implications does this finding have for simple linear regression? O For simple linear regression, it is impossible to determine whether there is an outlier using standardized residuals, a standardized residual plot, or a scatter diagram. For simple linear regression, we must calculate standardized residuals, plot a standardized residual plot, and construct a scatter diagram to identify an outlier. O For simple linear regression, we can determine an outlier by looking at the scatter diagram. an outlier.
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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![**Title: Analyzing Statistical Data: Standardized Residuals and Outliers**
**Introduction:**
A statistical program is recommended for analyzing the data provided for two variables, \[x\] and \[y\]. The dataset is as follows:
\[x_i\]: 135, 110, 130, 145, 175, 160, 120
\[y_i\]: 145, 100, 120, 115, 135, 130, 110
**Task (a): Compute the Standardized Residuals**
You are required to compute the standardized residuals for the given data. The table provided below will display the standardized residuals once calculated:
| \[x_i\] | \[y_i\] | Standardized Residuals |
|---------|---------|------------------------|
| 135 | 145 | |
| 110 | 100 | |
| 130 | 120 | |
| 145 | 115 | |
| 175 | 135 | |
| 160 | 130 | |
| 120 | 110 | |
**Outlier Analysis:**
- Determine if the data include any outliers by examining the standardized residuals. Explain your findings rounded to two decimal places.
- Identify the standardized residual with the largest absolute value and the corresponding \[y_i\] value. Based on whether this residual is selected (over a certain threshold), determine if it is considered an outlier.
**Task (b): Plot Analysis**
- Plot the standardized residuals against \[\hat{y}\].
- Assess whether the plot reveals any outliers by selecting one of the options provided:
- The plot shows no possible outliers.
- The plot shows one possible outlier.
- The plot shows two possible outliers.
- The plot shows more than two possible outliers.
**Task (c): Scatter Diagram Development**
- Develop a scatter diagram for the data.
- Analyze the scatter diagram to determine if it indicates any outliers. Choose from the following statements:
- The diagram indicates no possible outliers.
- The diagram indicates one possible outlier.
- The diagram indicates two possible outliers.
- The diagram indicates more than two possible outliers.
**Conclusion: Implications for Simple Linear Regression**
Evaluate the implications of](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F840ac9d4-eb27-4280-b70d-21eed9a81895%2Fde502949-f277-4958-a14e-f88e4d379517%2Fzuyhang_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Analyzing Statistical Data: Standardized Residuals and Outliers**
**Introduction:**
A statistical program is recommended for analyzing the data provided for two variables, \[x\] and \[y\]. The dataset is as follows:
\[x_i\]: 135, 110, 130, 145, 175, 160, 120
\[y_i\]: 145, 100, 120, 115, 135, 130, 110
**Task (a): Compute the Standardized Residuals**
You are required to compute the standardized residuals for the given data. The table provided below will display the standardized residuals once calculated:
| \[x_i\] | \[y_i\] | Standardized Residuals |
|---------|---------|------------------------|
| 135 | 145 | |
| 110 | 100 | |
| 130 | 120 | |
| 145 | 115 | |
| 175 | 135 | |
| 160 | 130 | |
| 120 | 110 | |
**Outlier Analysis:**
- Determine if the data include any outliers by examining the standardized residuals. Explain your findings rounded to two decimal places.
- Identify the standardized residual with the largest absolute value and the corresponding \[y_i\] value. Based on whether this residual is selected (over a certain threshold), determine if it is considered an outlier.
**Task (b): Plot Analysis**
- Plot the standardized residuals against \[\hat{y}\].
- Assess whether the plot reveals any outliers by selecting one of the options provided:
- The plot shows no possible outliers.
- The plot shows one possible outlier.
- The plot shows two possible outliers.
- The plot shows more than two possible outliers.
**Task (c): Scatter Diagram Development**
- Develop a scatter diagram for the data.
- Analyze the scatter diagram to determine if it indicates any outliers. Choose from the following statements:
- The diagram indicates no possible outliers.
- The diagram indicates one possible outlier.
- The diagram indicates two possible outliers.
- The diagram indicates more than two possible outliers.
**Conclusion: Implications for Simple Linear Regression**
Evaluate the implications of
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VIEWStep 3: Determine the residuals and standard residual for the given data set.
VIEWStep 4: Plot standardized residual against predicted value of y.
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