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11.38  Building a multiple linear regression model. Let’s now build a model to predict the life-satisfaction...

11.38  Building a multiple linear regression model. Let’s now build a model to predict the life-satisfaction score, LSI.

  1. (a) Consider a simple linear regression using GINI as the explanatory variable. Run the regression and summarize the results. Be sure to check assumptions.

  2. (b) Now consider a model using GINI and LIFE. Run the multiple regression and summarize the results. Again be sure to check assumptions.

  3. (c) Now consider a model using GINI, LIFE, and DEMOCRACY. Run the multiple regression and summarize the results. Again be sure to check assumptions.

  4. (d) Now consider a model using all four explanatory variables. Again summarize the results and check assumptions.

Data:

Country LSI GINI CORRUPT DEMOCRACY LIFE
Algeria 5.4 35.3 2.8 1.5 74.5
Argentina 7.3 44.5 2.8 5.5 76.95
Armenia 5 31.3 2.9 3 73.23
Australia 7.7 35.2 8.8 6 81.81
Austria 7.4 29.2 8.1 6 79.78
Azerbaijan 5.3 33.7 2.1 1.5 67.36
Bangladesh 5.3 32.1 1.7 3.5 69.75
Belarus 5.2 26.5 2.1 1 71.2
Belgium 7.3 33 7.1 5.5 79.51
Bolivia 6.3 56.3 2.5 5 67.57
Brazil 7.5 54.7 3.7 4 72.53
United Kingdom 7.2 36 8.6 5.5 78.54
Bulgaria 4.4 28.2 4.1 4.5 73.59
Canada 7.8 32.6 8.7 6 81.38
Chile 6.7 52.1 7.3 5 77.7
Colombia 7.7 55.9 4 3 74.55
Denmark 8.3 24.7 9.4 6 78.63
Dominican Republic 7.5 47.2 3 5 77.31
Egypt 5.7 30.8 3.4 1.5 72.66
El Salvador 6.7 48.3 4.2 4.5 73.44
Estonia 6 36 6.5 5.5 73.33
Finland 7.9 26.9 9.4 6 79.27
France 6.6 32.7 7.3 5.5 81.19
Germany 7.1 28.3 7.8 5.5 80.07
Ghana 5.2 42.8 3.5 4.5 61
Greece 6.4 34.3 4.6 5 79.92
Honduras 7 57 2.6 4 70.61
Hungary 5.5 31.2 5.3 5.5 74.79
Iceland 8.2 35.9 9.2 6 80.9
India 5.5 33.9 2.9 4.5 66.8
Indonesia 6.3 35.6 2.2 3.5 71.33
Iran 5.9 38.3 2.9 1 70.06
Ireland 7.6 34.3 7.5 6 80.19
Israel 7 39.2 6.3 5 80.96
Italy   6.7 36 5.2 5.5 81.77
Japan   6.5 24.9 7.3 5.5 82.25
Jordan 5.9 35.4 5.7 3 80.05
Kenya 3.7 47.7 2.1 1.5 59.48
Latvia   5.4 34.8 4.8 5.5 72.68
Lithuania 5.5 37.6 4.8 5.5 75.34
Mali 4.7 33 2.9 4.5 52.61
Mexico 7.9 47.2 3.5 4.5 76.47
Moldova 4.9 33 2.8 4 71.37
Morocco 5.4 40.9 3.2 2.5 75.9
Netherlands 7.6 30.9 9 6 79.68
New Zealand 7.5 36.2 9.6 6 80.59
Nigeria 5.7 42.9 1.9 3 47.56
Norway 7.9 25.8 8.7 6 80.2
Pakistan 5 30 2.1 1.5 65.99
Peru 6.2 48.1 3.5 3.5 72.47
Philippines 5.9 43 2.5 4.5 71.66
Poland 6.4 34 4.2 5.5 76.05
Portugal 5.7 38.5 6.5 6 78.54
Romania 5.7 27.4 3.7 5 73.98
Russia 5.5 40.1 2.3 2 66.29
Senegal 4.5 40.3 3.2 3.5 59.78
Slovakia 5.9 26 4.9 5.5 75.83
Slovenia 6.9 31.2 6.6 5.5 77.3
South-Africa 5.8 63.1 4.5 5.5 49.33
South-Korea 6 31.6 5 5 79.05
Spain 7.2 34.7 6.7 5.5 81.17
Sweden 7.8 25 9.3 6 81.07
Switzerland 8 33.7 9 6 81.07
Tanzania 2.8 37.6 2.9 3 52.85
Turkey 5.7 40 4.1 2.5 72.5
Uganda 4.8 44.3 2.5 1.5 53.24
Ukraine 5 25.6 2.7 3 68.58
Uruguay 6.7 45.3 5.9 6 76.21
USA 7.4 40.8 7.2 6 78.37
Uzbekistan 6 36.7 2.2 0.5 72.51
Vietnam 6.1 35.6 2.6 0.5 72.18
Zimbabwe 3 50.1 2.6 1.5 49.64
math   Statistics-And-Probability   
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Homework Answers

Answer #1

a)

a simple linear regression using GINI as the explanatory variable

Regression Equation

LSI   =   6.503 - 0.0071 GINI

Coefficients

Term   Coef   SE Coef   T-Value   P-Value   VIF
Constant   6.503   0.643   10.11   0.000     
GINI   -0.0071   0.0168   -0.42   0.675   1.00

Model Summary

S   R-sq   R-sq(adj)   R-sq(pred)
1.21649   0.25%   0.00%   0.00%

Analysis of Variance

Source   DF   Adj SS   Adj MS   F-Value   P-Value
Regression   1   0.262   0.2622   0.18   0.675
GINI   1   0.262   0.2622   0.18   0.675
Error   70   103.589   1.4798        
Lack-of-Fit   60   89.586   1.4931   1.07   0.494
Pure Error   10   14.003   1.4003        
Total   71   103.851           


Assumption

1) From above graph data follows normality assumption.

2) residulals versus fitted value shows homoscedasticity assumption get satisfied.

b)  a model using GINI and LIFE

Regression Equation

LSI   =   -3.82 + 0.0394 GINI + 0.1177 LIFE

Coefficients

Term   Coef   SE Coef   T-Value   P-Value   VIF
Constant   -3.82   1.12   -3.40   0.001     
GINI   0.0394   0.0119   3.32   0.001   1.19
LIFE   0.1177   0.0119   9.88   0.000   1.19

Model Summary

S   R-sq   R-sq(adj)   R-sq(pred)
0.788438   58.70%   57.50%   52.94%

Analysis of Variance

Source   DF   Adj SS   Adj MS   F-Value   P-Value
Regression   2   60.958   30.4791   49.03   0.000
GINI   1   6.844   6.8437   11.01   0.001
LIFE   1   60.696   60.6961   97.64   0.000
Error   69   42.893   0.6216        
Total   71   103.851           

Assumptions

1) From above graph data follows normality assumption.

2) residulals versus fitted value shows homoscedasticity assumption get satisfied.

c) model using GINI, LIFE, and DEMOCRACY

Regression Equation

LSI   =   -2.94 + 0.0366 GINI + 0.0945 LIFE + 0.2146 DEMOCRACY

Coefficients

Term   Coef   SE Coef   T-Value   P-Value   VIF
Constant   -2.94   1.07   -2.75   0.008     
GINI   0.0366   0.0110   3.32   0.001   1.19
LIFE   0.0945   0.0128   7.36   0.000   1.61
DEMOCRACY   0.2146   0.0607   3.53   0.001   1.39

Model Summary

S   R-sq   R-sq(adj)   R-sq(pred)
0.730038   65.10%   63.56%   59.68%

Analysis of Variance

Source   DF   Adj SS   Adj MS   F-Value   P-Value
Regression   3   67.610   22.5367   42.29   0.000
GINI   1   5.884   5.8841   11.04   0.001
LIFE   1   28.873   28.8733   54.18   0.000
DEMOCRACY   1   6.652   6.6519   12.48   0.001
Error   68   36.241   0.5330        
Total   71   103.851           

Assumptions

1) From above graph data follows normality assumption.

2) residulals versus fitted value shows homoscedasticity assumption get satisfied.

d) model using GINI, LIFE, DEMOCRACY and corrupt

Regression Equation

LSI   =   -2.31 + 0.0447 GINI + 0.0782 LIFE + 0.0526 DEMOCRACY + 0.1941 CORRUPT

Coefficients

Term   Coef   SE Coef   T-Value   P-Value   VIF
Constant   -2.31   1.01   -2.28   0.026     
GINI   0.0447   0.0105   4.25   0.000   1.26
LIFE   0.0782   0.0129   6.08   0.000   1.87
DEMOCRACY   0.0526   0.0739   0.71   0.479   2.37
CORRUPT   0.1941   0.0571   3.40   0.001   3.02

Model Summary

S   R-sq   R-sq(adj)   R-sq(pred)
0.679202   70.24%   68.46%   64.07%

Analysis of Variance

Source   DF   Adj SS   Adj MS   F-Value   P-Value
Regression   4   72.943   18.2357   39.53   0.000
GINI   1   8.317   8.3169   18.03   0.000
LIFE   1   17.040   17.0396   36.94   0.000
DEMOCRACY   1   0.234   0.2338   0.51   0.479
CORRUPT   1   5.333   5.3328   11.56   0.001
Error   67   30.908   0.4613        
Total   71   103.851           

Assumptions

1) From above graph data follows normality assumption.

2) residulals versus fitted value shows homoscedasticity assumption get satisfied.

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