Identify the conditions and assumption that must be satisfied before proceeding with the regression inference. Check whether the assumptions are satisfied.

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Answer 1

Question

Chapter 25, Problem 1E

To determine

Identify the conditions and assumption that must be satisfied before proceeding with the regression inference.

Check whether the assumptions are satisfied.

Expert Solution & Answer

Explanation of Solution

The given outputs show the regression model, the scatterplot for the data, the associated plots of residuals and histogram of residuals, for the graduate rates and acceptance rates in 2013.

Conditions of the regression analysis:

Straight line Condition: There should not be any bend in the original scatter plot of the data or in the plot of residuals against predicted values.
Independence assumption: The errors in the true regression model must be independent of each other.
Thickness Condition: The spread of the data around the generally straight relationship must be consistent for all values of x.
Nearly Normal Condition, Outlier Condition: The histogram must be symmetric and bell-shaped and the normal probability plot must be straight, with no outlier must be there.

Checking the condition of regression analysis:

Straight Enough Condition: There is no bend in the scatter plot of the data that is there is a linear relationship with equal spread about a regression line.
Independence assumption: The residual plot shows no pattern or structure and there are no striking outliers.
Thickness Condition: The spread of the residuals is consistent throughout the plot.
Nearly Normal Condition, Outlier Condition: The histogram of residual is symmetric and bell-shaped, with no outliers.

Thus, it can be concluded that the all the conditions for regression are satisfied.

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Answer 2

Question

Chapter 25, Problem 1E

To determine

Identify the conditions and assumption that must be satisfied before proceeding with the regression inference.

Check whether the assumptions are satisfied.

Expert Solution & Answer

Explanation of Solution

The given outputs show the regression model, the scatterplot for the data, the associated plots of residuals and histogram of residuals, for the graduate rates and acceptance rates in 2013.

Conditions of the regression analysis:

Straight line Condition: There should not be any bend in the original scatter plot of the data or in the plot of residuals against predicted values.
Independence assumption: The errors in the true regression model must be independent of each other.
Thickness Condition: The spread of the data around the generally straight relationship must be consistent for all values of x.
Nearly Normal Condition, Outlier Condition: The histogram must be symmetric and bell-shaped and the normal probability plot must be straight, with no outlier must be there.

Checking the condition of regression analysis:

Straight Enough Condition: There is no bend in the scatter plot of the data that is there is a linear relationship with equal spread about a regression line.
Independence assumption: The residual plot shows no pattern or structure and there are no striking outliers.
Thickness Condition: The spread of the residuals is consistent throughout the plot.
Nearly Normal Condition, Outlier Condition: The histogram of residual is symmetric and bell-shaped, with no outliers.

Thus, it can be concluded that the all the conditions for regression are satisfied.

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Answer 3

Question

Chapter 25, Problem 1E

To determine

Identify the conditions and assumption that must be satisfied before proceeding with the regression inference.

Check whether the assumptions are satisfied.

Expert Solution & Answer

Explanation of Solution

The given outputs show the regression model, the scatterplot for the data, the associated plots of residuals and histogram of residuals, for the graduate rates and acceptance rates in 2013.

Conditions of the regression analysis:

Straight line Condition: There should not be any bend in the original scatter plot of the data or in the plot of residuals against predicted values.
Independence assumption: The errors in the true regression model must be independent of each other.
Thickness Condition: The spread of the data around the generally straight relationship must be consistent for all values of x.
Nearly Normal Condition, Outlier Condition: The histogram must be symmetric and bell-shaped and the normal probability plot must be straight, with no outlier must be there.

Checking the condition of regression analysis:

Straight Enough Condition: There is no bend in the scatter plot of the data that is there is a linear relationship with equal spread about a regression line.
Independence assumption: The residual plot shows no pattern or structure and there are no striking outliers.
Thickness Condition: The spread of the residuals is consistent throughout the plot.
Nearly Normal Condition, Outlier Condition: The histogram of residual is symmetric and bell-shaped, with no outliers.

Thus, it can be concluded that the all the conditions for regression are satisfied.

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Answer 4

Question

Chapter 25, Problem 1E

To determine

Identify the conditions and assumption that must be satisfied before proceeding with the regression inference.

Check whether the assumptions are satisfied.

Expert Solution & Answer

Explanation of Solution

The given outputs show the regression model, the scatterplot for the data, the associated plots of residuals and histogram of residuals, for the graduate rates and acceptance rates in 2013.

Conditions of the regression analysis:

Straight line Condition: There should not be any bend in the original scatter plot of the data or in the plot of residuals against predicted values.
Independence assumption: The errors in the true regression model must be independent of each other.
Thickness Condition: The spread of the data around the generally straight relationship must be consistent for all values of x.
Nearly Normal Condition, Outlier Condition: The histogram must be symmetric and bell-shaped and the normal probability plot must be straight, with no outlier must be there.

Checking the condition of regression analysis:

Straight Enough Condition: There is no bend in the scatter plot of the data that is there is a linear relationship with equal spread about a regression line.
Independence assumption: The residual plot shows no pattern or structure and there are no striking outliers.
Thickness Condition: The spread of the residuals is consistent throughout the plot.
Nearly Normal Condition, Outlier Condition: The histogram of residual is symmetric and bell-shaped, with no outliers.

Thus, it can be concluded that the all the conditions for regression are satisfied.

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Answer 5

Chapter 25, Problem 1E

To determine

Identify the conditions and assumption that must be satisfied before proceeding with the regression inference.

Check whether the assumptions are satisfied.

Expert Solution & Answer

Explanation of Solution

The given outputs show the regression model, the scatterplot for the data, the associated plots of residuals and histogram of residuals, for the graduate rates and acceptance rates in 2013.

Conditions of the regression analysis:

Straight line Condition: There should not be any bend in the original scatter plot of the data or in the plot of residuals against predicted values.
Independence assumption: The errors in the true regression model must be independent of each other.
Thickness Condition: The spread of the data around the generally straight relationship must be consistent for all values of x.
Nearly Normal Condition, Outlier Condition: The histogram must be symmetric and bell-shaped and the normal probability plot must be straight, with no outlier must be there.

Checking the condition of regression analysis:

Straight Enough Condition: There is no bend in the scatter plot of the data that is there is a linear relationship with equal spread about a regression line.
Independence assumption: The residual plot shows no pattern or structure and there are no striking outliers.
Thickness Condition: The spread of the residuals is consistent throughout the plot.
Nearly Normal Condition, Outlier Condition: The histogram of residual is symmetric and bell-shaped, with no outliers.

Thus, it can be concluded that the all the conditions for regression are satisfied.

Answer 6

Chapter 25, Problem 1E

To determine

Identify the conditions and assumption that must be satisfied before proceeding with the regression inference.

Check whether the assumptions are satisfied.

Expert Solution & Answer

Explanation of Solution

The given outputs show the regression model, the scatterplot for the data, the associated plots of residuals and histogram of residuals, for the graduate rates and acceptance rates in 2013.

Conditions of the regression analysis:

Straight line Condition: There should not be any bend in the original scatter plot of the data or in the plot of residuals against predicted values.
Independence assumption: The errors in the true regression model must be independent of each other.
Thickness Condition: The spread of the data around the generally straight relationship must be consistent for all values of x.
Nearly Normal Condition, Outlier Condition: The histogram must be symmetric and bell-shaped and the normal probability plot must be straight, with no outlier must be there.

Checking the condition of regression analysis:

Straight Enough Condition: There is no bend in the scatter plot of the data that is there is a linear relationship with equal spread about a regression line.
Independence assumption: The residual plot shows no pattern or structure and there are no striking outliers.
Thickness Condition: The spread of the residuals is consistent throughout the plot.
Nearly Normal Condition, Outlier Condition: The histogram of residual is symmetric and bell-shaped, with no outliers.

Thus, it can be concluded that the all the conditions for regression are satisfied.

Answer 7

Chapter 25, Problem 1E

To determine

Identify the conditions and assumption that must be satisfied before proceeding with the regression inference.

Check whether the assumptions are satisfied.

Answer 8

Expert Solution & Answer

Explanation of Solution

The given outputs show the regression model, the scatterplot for the data, the associated plots of residuals and histogram of residuals, for the graduate rates and acceptance rates in 2013.

Conditions of the regression analysis:

Straight line Condition: There should not be any bend in the original scatter plot of the data or in the plot of residuals against predicted values.
Independence assumption: The errors in the true regression model must be independent of each other.
Thickness Condition: The spread of the data around the generally straight relationship must be consistent for all values of x.
Nearly Normal Condition, Outlier Condition: The histogram must be symmetric and bell-shaped and the normal probability plot must be straight, with no outlier must be there.

Checking the condition of regression analysis:

Straight Enough Condition: There is no bend in the scatter plot of the data that is there is a linear relationship with equal spread about a regression line.
Independence assumption: The residual plot shows no pattern or structure and there are no striking outliers.
Thickness Condition: The spread of the residuals is consistent throughout the plot.
Nearly Normal Condition, Outlier Condition: The histogram of residual is symmetric and bell-shaped, with no outliers.

Thus, it can be concluded that the all the conditions for regression are satisfied.