GNP = b _{0} + b _{1} MILMOB
where GNP is the % change in GNP and MILMOB is the change in military mobilization is fitted below: (Note: One did not need to transform the given data.)
============================================================ LS // Dependent Variable is GNP Date: 02/28/98 Time: 17:54 Sample: 1915 1988 Included observations: 74 ============================================================ Variable CoefficienStd. Errort-Statistic Prob. ============================================================ C 3.025348 0.547696 5.523772 0.0000 MILMOB 3.697863 0.547363 6.755782 0.0000 ============================================================ R-squared 0.387966 Mean dependent var 3.061841 Adjusted R-squared 0.379466 S.D. dependent var 5.980692 S.E. of regression 4.711230 Akaike info criter 3.126553 Sum squared resid 1598.089 Schwarz criterion 3.188825 Log likelihood -218.6839 F-statistic 45.64060 Durbin-Watson stat 1.266900 Prob(F-statistic) 0.000000 ============================================================
The residuals of a regression are saved in the variable name by the reserved word RESID after every regression. The EVIEWS command GENR (generate) can be used to save the residuals into a variable called RES, say, as follows:
GENR RES=RESID
We can then look at the residuals by typing
SHOW RES
in EVIEWS. This display is below.
The residuals that have absolute values over 9 are in bold: (note there are others with values near 9; 9 is an arbitrary cutoff point.)
RESID =================================================================== Last updated: 02/28/98 - 17:54 1915 3.590703 4.243941 -5.229786 -6.045869 4.284621 1920 -1.212403 -5.540562 3.094281 9.495950 0.136206 1925 -0.560048 3.289923 -2.058828 -1.831165 2.819159 1930 -12.90689 -11.90410 -17.40243 -5.141860 4.353963 1935 4.758457 10.08610 1.796987 -7.625791 4.544439 1940 4.199656 9.527733 8.606488 -0.239746 -1.300503 1945 -6.350234 -0.043979 -1.939323 1.251375 -3.354685 1950 5.612538 2.589378 0.021078 1.231581 -3.645527 1955 3.335193 -0.593930 -1.236150 -3.282037 2.967425 1960 -0.688404 -0.385380 1.580729 1.290056 2.273051 1965 2.730666 1.827576 -0.671611 0.785562 -0.391364 1970 -2.535118 0.468764 2.575059 2.203462 -3.373036 1975 -4.195150 1.858301 1.582365 2.190687 -0.482279 1980 -3.190959 -1.124885 -5.614083 0.495162 3.541703 1985 0.281572 -0.214503 0.285960 0.777179 ===================================================================
The largest residuals are the following:
1928 9.495950 1930 12.90689 1931 -11.90410 1932 -17.40243 1942 9.52773The model works poorly during the early part of the great depression and in 1942. There were other factors affecting the GNP during the depression besides military mobilization. In 1942, one might surmise that the war was having a positive effect on the economy in the United States, but no real build up of the military had yet occurred as the United States had just entered the war. The residual graph is shown below.
======================================================== OBS YEAR MILMOB GNP RESID ======================================================== 2 1946.000 -6.516724 -21.11658 -0.043979
============================================================ LS // Dependent Variable is GNP Date: 02/28/98 Time: 18:10 Sample: 1915 1945 Included observations: 31 ============================================================ Variable CoefficienStd. Errort-Statistic Prob. ============================================================ C 2.834469 1.281825 2.211276 0.0351 MILMOB 3.594665 1.330917 2.700893 0.0114 ============================================================ R-squared 0.200988 Mean dependent var 3.819669 Adjusted R-squared 0.173436 S.D. dependent var 7.525475 S.E. of regression 6.841829 Akaike info criter 3.908451 Sum squared resid 1357.508 Schwarz criterion 4.000966 Log likelihood -102.5681 F-statistic 7.294821 Durbin-Watson stat 1.101443 Prob(F-statistic) 0.011426 ============================================================ ============================================================ LS // Dependent Variable is GNP Date: 02/28/98 Time: 18:11 Sample: 1947 1988 Included observations: 42 ============================================================ Variable CoefficienStd. Errort-Statistic Prob. ============================================================ C 3.235515 0.372849 8.677815 0.0000 MILMOB 5.290072 1.427013 3.707093 0.0006 ============================================================ R-squared 0.255711 Mean dependent var 3.078169 Adjusted R-squared 0.237103 S.D. dependent var 2.748479 S.E. of regression 2.400630 Akaike info criter 1.797910 Sum squared resid 230.5210 Schwarz criterion 1.880657 Log likelihood -95.35153 F-statistic 13.74254 Durbin-Watson stat 2.112150 Prob(F-statistic) 0.000635 ============================================================In both regressions the slope coefficient of MILMOB is significant, i.e. significantly different from 0. However, after World War II the effect of MILMOB on the change in GNP is even greater. It is 5.29*change in MILMOB after 1945 as compare to 3.59*change in MILMOB before 1945. The value of this coefficient in the original (whole data set) regression was very close to that in the pre 1945 regression, but somewhat different from the post 1945 regression results. The R coefficients are not high in either case, which indicates that the data do not fit the linear model all that well. However, assuming these models do work one might say the effect of military mobilization on the economy is even greater since World War II.
_{^} 106155 - (1/10)*720*721 54243 Hence b_{1} = ----------------------- = ------- = .9913916 106554 - (1/10)*720*720 54714 _{^} and b_{0} = 721/10 - .9913916*(720/10) = .7198048 The least squares straight line is: _{^} _{^} _{^} and y = b_{0} + b_{1}x = .7198048 + .9913916*x The expected change in audited value (y) for a one-unit change in _{^} book value (x), is b_{1} = .9913916 When x = 100, the best estimate of y is _{^} and y = .7198048 + .9913916*100 = 99.858965
============================================================ LS // Dependent Variable is Y Date: 02/28/98 Time: 18:21 Sample: 1 10 Included observations: 10 ============================================================ Variable CoefficienStd. Errort-Statistic Prob. ============================================================ C 0.719805 1.176355 0.611894 0.5576 X 0.991392 0.011396 86.99447 0.0000 ============================================================ R-squared 0.998944 Mean dependent var 72.10000 Adjusted R-squared 0.998812 S.D. dependent var 77.33973 S.E. of regression 2.665648 Akaike info criter 2.137751 Sum squared resid 56.84544 Schwarz criterion 2.198268 Log likelihood -22.87814 F-statistic 7568.037 Durbin-Watson stat 2.455810 Prob(F-statistic) 0.000000 ============================================================