Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
9th Edition
ISBN: 9781319013387
Author: David S. Moore, George P. McCabe, Bruce A. Craig
Publisher: W. H. Freeman
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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
Check Mark

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
Check Mark

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
Check Mark

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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