The data on U.S. Trade in Goods and Services - Balance of Payments (BOP) Basis i

Question

The data on U.S. Trade in Goods and Services - Balance of Payments (BOP) Basis is given.

Compute the linear models for the ratio between Imports vs Exports in all three categories (Goods, Services, Total). Report all three models and decide which one of the linear models the best explains the data.  

Balance Exports Imports Period Total Goods BOP Services Total Goods BOP Services Total Goods BOP Services 1960 3508 4892 -1384 25940 19650 6290 22432 14758 7674 1961 4195 5571 -1376 26403 20108 6295 22208 14537 7671 1962 3370 4521 -1151 27722 20781 6941 24352 16260 8092 1963 4210 5224 -1014 29620 22272 7348 25410 17048 8362 1964 6022 6801 -779 33341 25501 7840 27319 18700 8619 1965 4664 4951 -287 35285 26461 8824 30621 21510 9111 1966 2939 3817 -878 38926 29310 9616 35987 25493 10494 1967 2604 3800 -1196 41333 30666 10667 38729 26866 11863 1968 250 635 -385 45543 33626 11917 45293 32991 12302 1969 91 607 -516 49220 36414 12806 49129 35807 13322 1970 2254 2603 -349 56640 42469 14171 54386 39866 14520 1971 -1302 -2260 958 59677 43319 16358 60979 45579 15400 1972 -5443 -6416 973 67222 49381 17841 72665 55797 16868 1973 1900 911 989 91242 71410 19832 89342 70499 18843 1974 -4293 -5505 1212 120897 98306 22591 125190 103811 21379 1975 12404 8903 3501 132585 107088 25497 120181 98185 21996 1976 -6082 -9483 3401 142716 114745 27971 148798 124228 24570 1977 -27246 -31091 3845 152301 120816 31485 179547 151907 27640 1978 -29763 -33927 4164 178428 142075 36353 208191 176002 32189 1979 -24565 -27568 3003 224131 184439 39692 248696 212007 36689 1980 -19407 -25500 6093 271834 224250 47584 291241 249750 41491 1981 -16172 -28023 11851 294398 237044 57354 310570 265067 45503 1982 -24156 -36485 12329 275236 211157 64079 299391 247642 51749 1983 -57767 -67102 9335 266106 201799 64307 323874 268901 54973 1984 -109072 -112492 3420 291094 219926 71168 400166 332418 67748 1985 -121880 -122173 294 289070 215915 73155 410950 338088 72862 1986 -138538 -145081 6543 310033 223344 86689 448572 368425 80147 1987 -151684 -159557 7874 348869 250208 98661 500552 409765 90787 1988 -114566 -126959 12393 431149 320230 110919 545715 447189 98526 1989 -93141 -117749 24607 487003 359916 127087 580144 477665 102479 1990 -80864 -111037 30173 535233 387401 147832 616097 498438 117659 1991 -31135 -76937 45802 578344 414083 164261 609479 491020 118459 1992 -39212 -96897 57685 616882 439631 177251 656094 536528 119566 1993 -70311 -132451 62141 642863 456943 185920 713174 589394 123780 1994 -98493 -165831 67338 703254 502859 200395 801747 668690 133057 1995 -96384 -174170 77786 794387 575204 219183 890771 749374 141397 1996 -104065 -191000 86935 851602 612113 239489 955667 803113 152554 1997 -108273 -198428 90155 934453 678366 256087 1042726 876794 165932 1998 -166140 -248221 82081 933174 670416 262758 1099314 918637 180677 1999 -258617 -337068 78450 969867 698524 271343 1228485 1035592 192893 2000 -372517 -446783 74266 1075321 784940 290381 1447837 1231722 216115 2001 -361511 -422370 60858 1005654 731331 274323 1367165 1153701 213465 2002 -418955 -475245 56290 978706 698036 280670 1397660 1173281 224379 2003 -493890 -541643 47754 1020418 730446 289972 1514308 1272089 242219 2004 -609883 -664766 54882 1161549 823584 337966 1771433 1488349 283083 2005 -714245 -782804 68558 1286022 913016 373006 2000267 1695820 304448 2006 -761716 -837289 75573 1457642 1040905 416738 2219358 1878194 341165 2007 -705375 -821196 115821 1653548 1165151 488396 2358922 1986347 372575 2008 -708726 -832492 123765 1841612 1308795 532817 2550339 2141287 409052 2009 -383774 -509694 125920 1583053 1070331 512722 1966827 1580025 386801 2010 -494658 -648678 154020 1853606 1290273 563333 2348263 1938950 409313 2011 -548625 -740646 192020 2127021 1499240 627781 2675646 2239886 435761 2012 -536773 -741171 204398 2218989 1562578 656411 2755762 2303749 452013 2013 -461876 -702244 240368 2293457 1592002 701455 2755334 2294247 461087 2014 -490176 -752169 261993 2376577 1633320 743257 2866754 2385489 481264 2015 -500361 -762565 262203 2261163 1510303 750860 2761525 2272868 488657 2016 -500560 -749926 249365 2212079 1459667 752412 2712639 2209592 503047

Explanation / Answer

The linear model for "Services vs Period" best fits the data because the correlation coefficient for this linear model is maximum out of the three.

Total SUMMARY OUTPUT Regression Statistics Multiple R 0.743354272 R Square 0.552575574 Adjusted R Square 0.544440584 Standard Error 0.130901642 Observations 57 ANOVA df SS MS F Significance F Regression 1 1.163924673 1.163924673 67.92578765 3.52703E-11 Residual 55 0.9424382 0.01713524 Total 56 2.106362873 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -16.10499431 2.095180926 -7.68668429 2.83142E-10 -20.30383069 -11.90615793 -20.30383069 -11.90615793 Period 0.008685756 0.001053878 8.241710238 3.52703E-11 0.006573738 0.010797774 0.006573738 0.010797774 Goods SUMMARY OUTPUT Regression Statistics Multiple R 0.854867761 R Square 0.730798888 Adjusted R Square 0.725904323 Standard Error 0.160579091 Observations 57 ANOVA df SS MS F Significance F Regression 1 3.850008696 3.850008696 149.3082202 2.64384E-17 Residual 55 1.418210451 0.025785645 Total 56 5.268219147 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -30.11976536 2.570191198 -11.71888122 1.40756E-16 -35.27054358 -24.96898713 -35.27054358 -24.96898713 Period 0.015797052 0.001292808 12.21917428 2.64384E-17 0.013206206 0.018387898 0.013206206 0.018387898 Services SUMMARY OUTPUT Regression Statistics Multiple R 0.8585127 R Square 0.737044055 Adjusted R Square 0.732263038 Standard Error 0.082600393 Observations 57 ANOVA df SS MS F Significance F Regression 1 1.051810178 1.051810178 154.1605119 1.38083E-17 Residual 55 0.375255369 0.006822825 Total 56 1.427065547 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 17.26898859 1.322082476 13.06196013 1.69982E-18 14.61947612 19.91850106 14.61947612 19.91850106 Period -0.00825684 0.000665009 -12.41613917 1.38083E-17 -0.009589547 -0.006924133 -0.009589547 -0.006924133

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