Question

An economic organization tracks summary statistics of various countries. These include GDP (gross domestic product per capita) and trade balances (measured as a percentage of GDP). Exporting countries tend to have large positive trade balances. Importers have negative balances. The data are shown in the accompanying table. Formulate the SRM with GDP as the response and Trade Balance as the explanatory variable. Complete parts (a) through (c) below. B: Click the icon to view the data table. (a) Country X reported the highest positive balance of trade, 23.7% of GDP and per capita GDP equal to $62,000. Fit the least squares equation both with and without country X and compare the results. Does the fitted slope change by very much? Find the least squares equation without country X. Complete the equation below. Estimated GDP ($ per cap) = + Trade Bal (% GDP) (Round to the nearest integer as needed.)

Trade Balance (% GDP) / GDP ($ per capita)

-1.4 20062

13.2 36807

0.2 27363

-6 33552

6.4 26059

9.4 37202

2.2 16518

15.9 56163

-0.3 15832

0.3 38259

13.2 36372

6.9 43251

1.2 8772

-7 18603

-2.2 39321

1.4 42305

-6.3 27453

10.4 59576

-2.5 23101

-5.9 3788

Answer 1

Solution:

The least square equation (or the regression model) for the given data can be found using Excel data analysis regression tool with GDP ($ per capita) as the dependent variable and trade balance (% of GDP) as the independent variable.

1. Excluding country X, following regression results are generated:

Then, without country X, we have the following equation:

SUMMARY OUTPUT Regression Statistics Multiple F 0.622876 R Square 0.387975 Adjustedi 0.353973 Standard E 11680.81 Observati 20 GDP ($ per capita) Trade Balance % of GDP) 20062 -1.4 36807 13.2 27363 0.2 33552 -6 26059 6.4 37202 9.4 16518 22 56163 15.9 15832 -0.3 38259 0.3 36372 13.20 43251 8772 18603 39321 -2.2 42305 1.4 27453 -6.3 59576 10.4 23101 -2.5 3788 -5.9 ANOVA of Regressio Residual Total SS MS F gnificance F 1 1.56E+09 1.56E+09 11.41055 0.003351 18 2.46E+09 1.36E+08 19 4.01E+09 Coefficientsandard Err Stat P-value Lower 95%upper 95%ower 95.0%pper 95.0% Intercept 27369.93 2773.185 9.869493 1.09E-08 21543.69 33196.18 21543.69 33196.18 X Variable 1282.288 379.6054 3.377951 0.003351 484.767 2079.809 484.767 2079.809

Estimated GDP ($ per capita) = 27369.93 + 1282.288*Trade Bal (% GDP)

With rounding to nearest integer, we get:

Estimated GDP ($ per capita) = 27370 + 1282*Trade Bal (% GDP)

2. Similarly, including country X, following regression results are generated:

SUMMARY OUTPUT 2.2 Regression Statistics Multiple F 0.708625 R Square 0.502149 Adjustedi 0.475946 Standard E 11396.48 Observati 21 GDP ($ per capita) Trade Balance (% of GDP) 20062 -1.4 36807 13.2 27363 0.2 33552 26059 37202 16518 56163 15.9 15832 -0.3 38259 0.3 36372 43251 6.9 8772 1.2 18603 39321 -2.2 42305 1.4 27453 -6.3 59576 10.4 23101 -2.5 3788 -5.9 62000 23.7 13.2 ANOVA of Regressio Residual Total SS MS F gnificance F 1 2.49E+09 2.49E+09 19.16401 0.000324 19 2.47E+09 1.3E+08 20 4.96E+09 Coefficientsandard Err Stat p-value Lower 95%upper 95%ower 95.0%pper 95.0% Intercept 27355.81 2705.277 10.11202 4.4E-09 21693.6 33018.02 21693.6 33018.02 X Variable 1344.601 307.1497 4.377672 0.000324 701.7289 1987.473 701.7289 1987.473

Then, with country X, we have the following equation:

Estimated GDP ($ per capita) = 27355.81 + 1344.601*Trade Bal (% GDP)

With rounding to nearest integer, we get:

Estimated GDP ($ per capita) = 27356 + 1345*Trade Bal (% GDP)

Clearly, the fitted slope changes by 1345 - 1282 = 63