Concept explainers
(a)
To find: A table with the estimated standard errors, t- statistics, regression coefficients, and P- values of the different regression model.
(a)
Answer to Problem 39E
Solution: The required table is shown below:
Model |
Explanatory variable |
regression coefficients |
standard errors |
t- statistics |
P values |
Model. |
Intercept |
||||
GINI |
|||||
Model II |
Intercept |
||||
GINI |
|||||
LIFE |
|||||
Model-III |
Intercept |
||||
GINI |
|||||
LIFE |
|||||
DEMOCRACY |
|||||
Model-IV |
Intercept |
||||
GINI |
|||||
LIFE |
|||||
DEMOCRACY |
|||||
CORRUPT |
Explanation of Solution
Calculation: On the basis of the GINI, LIFE, CORRUPT, and DEMOCRACY explanatory variables, one can estimate the multiple regression coefficient, standard error, t- statistics, and corresponding P- values by using excel.
The regression equation is written as:
The assumption of the error term is
The multiple regression analysis Model I can be obtained by using Minitab and following the steps given below:
Step 1: Open the Minitab worksheet.
Step 2: Go to Stat > Regression > Regression
Step 3: Select “LSI” in Response and select “GINI” in Predictors.
Step 4: Click “OK.”
The multiple regression analysis Model II can be obtained by using Minitab and following the steps given below:
Step 1: Open the Minitab worksheet.
Step 2: Go to Stat > Regression > Regression
Step 3: Select “LSI” in Response and select “GINI and LIFE” in Predictors.
Step 4: Click “OK.”
The multiple regression analysis Model III can be obtained by using Minitab and following the steps given below:
Step 1: Open the Minitab worksheet.
Step 2: Go to Stat > Regression > Regression
Step 3: Select “LSI” in Response and select “GINI, LIFE, and DEMOCRACY” in Predictors.
Step 4: Click “OK.”
The multiple regression analysis Model IV can be obtained by using Minitab and following the steps given below:
Step 1: Open the Minitab worksheet.
Step 2: Go to Stat > Regression > Regression
Step 3: Select “LSI” in Response and select “GINI, LIFE, DEMOCRACY, and CORRUPT” in Predictors.
Step 4: Click “OK.”
Interpretation: Hence, the estimated regression coefficients, t-statistics, standard errors, and P-values vary from the different regression model and its significant level changes according to the model.
(b)
To test: The change of regression coefficients and P-values in the different models.
(b)
Answer to Problem 39E
Solution: Some t-statistics are significant and some are not significant depends on the model, for example, t- statistics for the GINI coefficient grows from
Explanation of Solution
Calculation: On the basis of the GINI, LIFE, CORRUPT, and DEMOCRACY explanatory variables, one can estimate the multiple regression coefficients, standard error, t-statistics, and corresponding P-values by using excel. The regression equation is written as:
The assumption of the error term is normally distributed with average 0 and a constant standard deviation, and it can be written as
Conclusion: Hence, some t-statistics are significant and some are not significant depends on the model, for example, t-statistics for the GINI coefficient grows from
(c)
To test: The choice of best model and summarize the results on the basis of four model.
(c)
Answer to Problem 39E
Solution: A best model to predict the LSI is GINI, LIFE, and CORRUPT as explanatory variables due to the high value of
Explanation of Solution
Calculation: The multiple regression analysis can be obtained by using Minitab, follow the steps below:
Step 1: Open the Minitab worksheet.
Step 2: Go to Stat > Regression > Regression
Step 3: Select “LSI” in Response and select “GINI, LIFE, and CORRUPT” in Predictors.
Step 4: Click “OK.”
Conclusion: Therefore, best model to predict the LSI is GINI, LIFE, and CORRUPT as explanatory variables due to the high value of
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Chapter 11 Solutions
Introduction to the Practice of Statistics
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