A table with the estimated standard errors, t- statistics, regression coefficients, and P- values of the different regression model.

Question

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Answer 1

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 11, Problem 39E

(a)

To determine

To find: A table with the estimated standard errors, t- statistics, regression coefficients, and P- values of the different regression model.

(a)

Expert Solution

Answer to Problem 39E

Solution: The required table is shown below:

Model	Explanatory variable	regression coefficients	standard errors	t- statistics	P values
Model.	Intercept	6.5269	0.6464	10.096	<0.001
	GINI	−0.0074	0.01689	−0.4285	0.675
Model II	Intercept	−3.8077	1.1211	−3.396	0.0011
	GINI	0.039116	0.01184	3.3034	0.0015
	LIFE	0.11788	0.01187	9.927	<0.05
Model-III	Intercept	−2.9671	1.07834	−2.7516	0.0076
	GINI	0.03662	0.01109	3.3016	0.0015
	LIFE	0.09530	0.01304	7.3074	<0.05
	DEMOCRACY	0.2077	0.0630	3.2956	0.0015
Model-IV	Intercept	−2.3139	1.01313	−2.2839	0.0255
	GINI	0.04470	0.010529	4.246	<0.001
	LIFE	0.07821	0.01287	6.0775	<0.05
	DEMOCRACY	0.05261	0.07390	0.71187	0.0949
	CORRUPT	0.19414	0.0571	3.4000	0.0011

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:

LSI=β0+β1GINI+β2LIFE+β3DEMOCRACY+β4CORRUPT+ε

The assumption of the error term is normally distributed with average 0 and a constant standard deviation, and it can be written as ε~N(0,σ).

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 determine

To test: The change of regression coefficients and P-values in the different models.

(b)

Expert Solution

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 t=−0.42(P=0.675) to t=4.25(P<0.005). The DEMOCRACY t-statistics drop from the third model to the fourth model as t=3.295(P<0.005) to t=0.712(P=0.095).

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:

LSI=β0+β1GINI+β2LIFE+β3DEMOCRACY+β4CORRUPT+ε

The assumption of the error term is normally distributed with average 0 and a constant standard deviation, and it can be written as ε~N(0,σ).

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 t=−0.42(P=0.675) to t=4.25(P<0.005). The DEMOCRACY t- statistics drops from the third model to the fourth model as t=3.295(P<0.005) to t=0.712(P=0.095).

(c)

To determine

To test: The choice of best model and summarize the results on the basis of four model.

(c)

Expert Solution

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 R2=0.70 and the estimated regression equation is y^=−2.354+0.04619GINI+0.22034LIFE+0.07934CORRUPT.

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 R2=0.70 and the estimated regression equation is y^=−2.354+0.04619GINI+0.22034LIFE+0.07934CORRUPT, where F=52.92 and P<0.005 with a high R2=0.70 value. So, the model is fit to predict LSI on the basis of the GINI, LIFE, and CORRUPT as explanatory variables. The assumption of the error term is normally distributed with average 0 and a constant standard deviation, and it can be written as ε~N(0,σ).

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Answer 2

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 11, Problem 39E

(a)

To determine

To find: A table with the estimated standard errors, t- statistics, regression coefficients, and P- values of the different regression model.

(a)

Expert Solution

Answer to Problem 39E

Solution: The required table is shown below:

Model	Explanatory variable	regression coefficients	standard errors	t- statistics	P values
Model.	Intercept	6.5269	0.6464	10.096	<0.001
	GINI	−0.0074	0.01689	−0.4285	0.675
Model II	Intercept	−3.8077	1.1211	−3.396	0.0011
	GINI	0.039116	0.01184	3.3034	0.0015
	LIFE	0.11788	0.01187	9.927	<0.05
Model-III	Intercept	−2.9671	1.07834	−2.7516	0.0076
	GINI	0.03662	0.01109	3.3016	0.0015
	LIFE	0.09530	0.01304	7.3074	<0.05
	DEMOCRACY	0.2077	0.0630	3.2956	0.0015
Model-IV	Intercept	−2.3139	1.01313	−2.2839	0.0255
	GINI	0.04470	0.010529	4.246	<0.001
	LIFE	0.07821	0.01287	6.0775	<0.05
	DEMOCRACY	0.05261	0.07390	0.71187	0.0949
	CORRUPT	0.19414	0.0571	3.4000	0.0011

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:

LSI=β0+β1GINI+β2LIFE+β3DEMOCRACY+β4CORRUPT+ε

The assumption of the error term is normally distributed with average 0 and a constant standard deviation, and it can be written as ε~N(0,σ).

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 determine

To test: The change of regression coefficients and P-values in the different models.

(b)

Expert Solution

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 t=−0.42(P=0.675) to t=4.25(P<0.005). The DEMOCRACY t-statistics drop from the third model to the fourth model as t=3.295(P<0.005) to t=0.712(P=0.095).

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:

LSI=β0+β1GINI+β2LIFE+β3DEMOCRACY+β4CORRUPT+ε

The assumption of the error term is normally distributed with average 0 and a constant standard deviation, and it can be written as ε~N(0,σ).

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 t=−0.42(P=0.675) to t=4.25(P<0.005). The DEMOCRACY t- statistics drops from the third model to the fourth model as t=3.295(P<0.005) to t=0.712(P=0.095).

(c)

To determine

To test: The choice of best model and summarize the results on the basis of four model.

(c)

Expert Solution

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 R2=0.70 and the estimated regression equation is y^=−2.354+0.04619GINI+0.22034LIFE+0.07934CORRUPT.

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 R2=0.70 and the estimated regression equation is y^=−2.354+0.04619GINI+0.22034LIFE+0.07934CORRUPT, where F=52.92 and P<0.005 with a high R2=0.70 value. So, the model is fit to predict LSI on the basis of the GINI, LIFE, and CORRUPT as explanatory variables. The assumption of the error term is normally distributed with average 0 and a constant standard deviation, and it can be written as ε~N(0,σ).

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Answer 3

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 11, Problem 39E

(a)

To determine

To find: A table with the estimated standard errors, t- statistics, regression coefficients, and P- values of the different regression model.

(a)

Expert Solution

Answer to Problem 39E

Solution: The required table is shown below:

Model	Explanatory variable	regression coefficients	standard errors	t- statistics	P values
Model.	Intercept	6.5269	0.6464	10.096	<0.001
	GINI	−0.0074	0.01689	−0.4285	0.675
Model II	Intercept	−3.8077	1.1211	−3.396	0.0011
	GINI	0.039116	0.01184	3.3034	0.0015
	LIFE	0.11788	0.01187	9.927	<0.05
Model-III	Intercept	−2.9671	1.07834	−2.7516	0.0076
	GINI	0.03662	0.01109	3.3016	0.0015
	LIFE	0.09530	0.01304	7.3074	<0.05
	DEMOCRACY	0.2077	0.0630	3.2956	0.0015
Model-IV	Intercept	−2.3139	1.01313	−2.2839	0.0255
	GINI	0.04470	0.010529	4.246	<0.001
	LIFE	0.07821	0.01287	6.0775	<0.05
	DEMOCRACY	0.05261	0.07390	0.71187	0.0949
	CORRUPT	0.19414	0.0571	3.4000	0.0011

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:

LSI=β0+β1GINI+β2LIFE+β3DEMOCRACY+β4CORRUPT+ε

The assumption of the error term is normally distributed with average 0 and a constant standard deviation, and it can be written as ε~N(0,σ).

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 determine

To test: The change of regression coefficients and P-values in the different models.

(b)

Expert Solution

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 t=−0.42(P=0.675) to t=4.25(P<0.005). The DEMOCRACY t-statistics drop from the third model to the fourth model as t=3.295(P<0.005) to t=0.712(P=0.095).

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:

LSI=β0+β1GINI+β2LIFE+β3DEMOCRACY+β4CORRUPT+ε

The assumption of the error term is normally distributed with average 0 and a constant standard deviation, and it can be written as ε~N(0,σ).

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 t=−0.42(P=0.675) to t=4.25(P<0.005). The DEMOCRACY t- statistics drops from the third model to the fourth model as t=3.295(P<0.005) to t=0.712(P=0.095).

(c)

To determine

To test: The choice of best model and summarize the results on the basis of four model.

(c)

Expert Solution

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 R2=0.70 and the estimated regression equation is y^=−2.354+0.04619GINI+0.22034LIFE+0.07934CORRUPT.

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 R2=0.70 and the estimated regression equation is y^=−2.354+0.04619GINI+0.22034LIFE+0.07934CORRUPT, where F=52.92 and P<0.005 with a high R2=0.70 value. So, the model is fit to predict LSI on the basis of the GINI, LIFE, and CORRUPT as explanatory variables. The assumption of the error term is normally distributed with average 0 and a constant standard deviation, and it can be written as ε~N(0,σ).

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Answer 4

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 11, Problem 39E

(a)

To determine

To find: A table with the estimated standard errors, t- statistics, regression coefficients, and P- values of the different regression model.

(a)

Expert Solution

Answer to Problem 39E

Solution: The required table is shown below:

Model	Explanatory variable	regression coefficients	standard errors	t- statistics	P values
Model.	Intercept	6.5269	0.6464	10.096	<0.001
	GINI	−0.0074	0.01689	−0.4285	0.675
Model II	Intercept	−3.8077	1.1211	−3.396	0.0011
	GINI	0.039116	0.01184	3.3034	0.0015
	LIFE	0.11788	0.01187	9.927	<0.05
Model-III	Intercept	−2.9671	1.07834	−2.7516	0.0076
	GINI	0.03662	0.01109	3.3016	0.0015
	LIFE	0.09530	0.01304	7.3074	<0.05
	DEMOCRACY	0.2077	0.0630	3.2956	0.0015
Model-IV	Intercept	−2.3139	1.01313	−2.2839	0.0255
	GINI	0.04470	0.010529	4.246	<0.001
	LIFE	0.07821	0.01287	6.0775	<0.05
	DEMOCRACY	0.05261	0.07390	0.71187	0.0949
	CORRUPT	0.19414	0.0571	3.4000	0.0011

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:

LSI=β0+β1GINI+β2LIFE+β3DEMOCRACY+β4CORRUPT+ε

The assumption of the error term is normally distributed with average 0 and a constant standard deviation, and it can be written as ε~N(0,σ).

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 determine

To test: The change of regression coefficients and P-values in the different models.

(b)

Expert Solution

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 t=−0.42(P=0.675) to t=4.25(P<0.005). The DEMOCRACY t-statistics drop from the third model to the fourth model as t=3.295(P<0.005) to t=0.712(P=0.095).

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:

LSI=β0+β1GINI+β2LIFE+β3DEMOCRACY+β4CORRUPT+ε

The assumption of the error term is normally distributed with average 0 and a constant standard deviation, and it can be written as ε~N(0,σ).

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 t=−0.42(P=0.675) to t=4.25(P<0.005). The DEMOCRACY t- statistics drops from the third model to the fourth model as t=3.295(P<0.005) to t=0.712(P=0.095).

(c)

To determine

To test: The choice of best model and summarize the results on the basis of four model.

(c)

Expert Solution

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 R2=0.70 and the estimated regression equation is y^=−2.354+0.04619GINI+0.22034LIFE+0.07934CORRUPT.

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 R2=0.70 and the estimated regression equation is y^=−2.354+0.04619GINI+0.22034LIFE+0.07934CORRUPT, where F=52.92 and P<0.005 with a high R2=0.70 value. So, the model is fit to predict LSI on the basis of the GINI, LIFE, and CORRUPT as explanatory variables. The assumption of the error term is normally distributed with average 0 and a constant standard deviation, and it can be written as ε~N(0,σ).

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Answer 5

Chapter 11, Problem 39E

(a)

To determine

To find: A table with the estimated standard errors, t- statistics, regression coefficients, and P- values of the different regression model.

(a)

Expert Solution

Answer to Problem 39E

Solution: The required table is shown below:

Model	Explanatory variable	regression coefficients	standard errors	t- statistics	P values
Model.	Intercept	6.5269	0.6464	10.096	<0.001
	GINI	−0.0074	0.01689	−0.4285	0.675
Model II	Intercept	−3.8077	1.1211	−3.396	0.0011
	GINI	0.039116	0.01184	3.3034	0.0015
	LIFE	0.11788	0.01187	9.927	<0.05
Model-III	Intercept	−2.9671	1.07834	−2.7516	0.0076
	GINI	0.03662	0.01109	3.3016	0.0015
	LIFE	0.09530	0.01304	7.3074	<0.05
	DEMOCRACY	0.2077	0.0630	3.2956	0.0015
Model-IV	Intercept	−2.3139	1.01313	−2.2839	0.0255
	GINI	0.04470	0.010529	4.246	<0.001
	LIFE	0.07821	0.01287	6.0775	<0.05
	DEMOCRACY	0.05261	0.07390	0.71187	0.0949
	CORRUPT	0.19414	0.0571	3.4000	0.0011

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:

LSI=β0+β1GINI+β2LIFE+β3DEMOCRACY+β4CORRUPT+ε

The assumption of the error term is normally distributed with average 0 and a constant standard deviation, and it can be written as ε~N(0,σ).

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 determine

To test: The change of regression coefficients and P-values in the different models.

(b)

Expert Solution

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 t=−0.42(P=0.675) to t=4.25(P<0.005). The DEMOCRACY t-statistics drop from the third model to the fourth model as t=3.295(P<0.005) to t=0.712(P=0.095).

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:

LSI=β0+β1GINI+β2LIFE+β3DEMOCRACY+β4CORRUPT+ε

The assumption of the error term is normally distributed with average 0 and a constant standard deviation, and it can be written as ε~N(0,σ).

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 t=−0.42(P=0.675) to t=4.25(P<0.005). The DEMOCRACY t- statistics drops from the third model to the fourth model as t=3.295(P<0.005) to t=0.712(P=0.095).

(c)

To determine

To test: The choice of best model and summarize the results on the basis of four model.

(c)

Expert Solution

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 R2=0.70 and the estimated regression equation is y^=−2.354+0.04619GINI+0.22034LIFE+0.07934CORRUPT.

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 R2=0.70 and the estimated regression equation is y^=−2.354+0.04619GINI+0.22034LIFE+0.07934CORRUPT, where F=52.92 and P<0.005 with a high R2=0.70 value. So, the model is fit to predict LSI on the basis of the GINI, LIFE, and CORRUPT as explanatory variables. The assumption of the error term is normally distributed with average 0 and a constant standard deviation, and it can be written as ε~N(0,σ).

Answer 6

Chapter 11, Problem 39E

(a)

To determine

To find: A table with the estimated standard errors, t- statistics, regression coefficients, and P- values of the different regression model.

(a)

Expert Solution

Answer to Problem 39E

Solution: The required table is shown below:

Model	Explanatory variable	regression coefficients	standard errors	t- statistics	P values
Model.	Intercept	6.5269	0.6464	10.096	<0.001
	GINI	−0.0074	0.01689	−0.4285	0.675
Model II	Intercept	−3.8077	1.1211	−3.396	0.0011
	GINI	0.039116	0.01184	3.3034	0.0015
	LIFE	0.11788	0.01187	9.927	<0.05
Model-III	Intercept	−2.9671	1.07834	−2.7516	0.0076
	GINI	0.03662	0.01109	3.3016	0.0015
	LIFE	0.09530	0.01304	7.3074	<0.05
	DEMOCRACY	0.2077	0.0630	3.2956	0.0015
Model-IV	Intercept	−2.3139	1.01313	−2.2839	0.0255
	GINI	0.04470	0.010529	4.246	<0.001
	LIFE	0.07821	0.01287	6.0775	<0.05
	DEMOCRACY	0.05261	0.07390	0.71187	0.0949
	CORRUPT	0.19414	0.0571	3.4000	0.0011

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:

LSI=β0+β1GINI+β2LIFE+β3DEMOCRACY+β4CORRUPT+ε

The assumption of the error term is normally distributed with average 0 and a constant standard deviation, and it can be written as ε~N(0,σ).

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.

Answer 7

Chapter 11, Problem 39E

(a)

To determine

To find: A table with the estimated standard errors, t- statistics, regression coefficients, and P- values of the different regression model.

Answer 8

(a)

Expert Solution

Answer to Problem 39E

Solution: The required table is shown below:

Model	Explanatory variable	regression coefficients	standard errors	t- statistics	P values
Model.	Intercept	6.5269	0.6464	10.096	<0.001
	GINI	−0.0074	0.01689	−0.4285	0.675
Model II	Intercept	−3.8077	1.1211	−3.396	0.0011
	GINI	0.039116	0.01184	3.3034	0.0015
	LIFE	0.11788	0.01187	9.927	<0.05
Model-III	Intercept	−2.9671	1.07834	−2.7516	0.0076
	GINI	0.03662	0.01109	3.3016	0.0015
	LIFE	0.09530	0.01304	7.3074	<0.05
	DEMOCRACY	0.2077	0.0630	3.2956	0.0015
Model-IV	Intercept	−2.3139	1.01313	−2.2839	0.0255
	GINI	0.04470	0.010529	4.246	<0.001
	LIFE	0.07821	0.01287	6.0775	<0.05
	DEMOCRACY	0.05261	0.07390	0.71187	0.0949
	CORRUPT	0.19414	0.0571	3.4000	0.0011

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

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:

LSI=β0+β1GINI+β2LIFE+β3DEMOCRACY+β4CORRUPT+ε

The assumption of the error term is normally distributed with average 0 and a constant standard deviation, and it can be written as ε~N(0,σ).

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.

Answer 13

(b)

To determine

To test: The change of regression coefficients and P-values in the different models.

(b)

Expert Solution

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 t=−0.42(P=0.675) to t=4.25(P<0.005). The DEMOCRACY t-statistics drop from the third model to the fourth model as t=3.295(P<0.005) to t=0.712(P=0.095).

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:

LSI=β0+β1GINI+β2LIFE+β3DEMOCRACY+β4CORRUPT+ε

The assumption of the error term is normally distributed with average 0 and a constant standard deviation, and it can be written as ε~N(0,σ).

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 t=−0.42(P=0.675) to t=4.25(P<0.005). The DEMOCRACY t- statistics drops from the third model to the fourth model as t=3.295(P<0.005) to t=0.712(P=0.095).

Answer 14

(b)

To determine

To test: The change of regression coefficients and P-values in the different models.

Answer 15

(b)

Expert Solution

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 t=−0.42(P=0.675) to t=4.25(P<0.005). The DEMOCRACY t-statistics drop from the third model to the fourth model as t=3.295(P<0.005) to t=0.712(P=0.095).

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

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:

LSI=β0+β1GINI+β2LIFE+β3DEMOCRACY+β4CORRUPT+ε

The assumption of the error term is normally distributed with average 0 and a constant standard deviation, and it can be written as ε~N(0,σ).

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 t=−0.42(P=0.675) to t=4.25(P<0.005). The DEMOCRACY t- statistics drops from the third model to the fourth model as t=3.295(P<0.005) to t=0.712(P=0.095).

Answer 20

(c)

To determine

To test: The choice of best model and summarize the results on the basis of four model.

(c)

Expert Solution

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 R2=0.70 and the estimated regression equation is y^=−2.354+0.04619GINI+0.22034LIFE+0.07934CORRUPT.

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 R2=0.70 and the estimated regression equation is y^=−2.354+0.04619GINI+0.22034LIFE+0.07934CORRUPT, where F=52.92 and P<0.005 with a high R2=0.70 value. So, the model is fit to predict LSI on the basis of the GINI, LIFE, and CORRUPT as explanatory variables. The assumption of the error term is normally distributed with average 0 and a constant standard deviation, and it can be written as ε~N(0,σ).

Answer 21

(c)

To determine

To test: The choice of best model and summarize the results on the basis of four model.

Answer 22

(c)

Expert Solution

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 R2=0.70 and the estimated regression equation is y^=−2.354+0.04619GINI+0.22034LIFE+0.07934CORRUPT.

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

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 R2=0.70 and the estimated regression equation is y^=−2.354+0.04619GINI+0.22034LIFE+0.07934CORRUPT, where F=52.92 and P<0.005 with a high R2=0.70 value. So, the model is fit to predict LSI on the basis of the GINI, LIFE, and CORRUPT as explanatory variables. The assumption of the error term is normally distributed with average 0 and a constant standard deviation, and it can be written as ε~N(0,σ).

Answer 27

Ch. 11.1 - Prob. 1UYK Ch. 11.1 - Prob. 2UYK Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

A table with the estimated standard errors, t- statistics, regression coefficients, and P- values of the different regression model.

Concept explainers

Videos

To find: A table with the estimated standard errors, t- statistics, regression coefficients, and P- values of the different regression model.

Answer to Problem 39E

Explanation of Solution

To test: The change of regression coefficients and P-values in the different models.

Answer to Problem 39E

Explanation of Solution

To test: The choice of best model and summarize the results on the basis of four model.

Answer to Problem 39E

Explanation of Solution

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