1. A multiple regression model was run to analyze the relationship between a dependent variable (Y) and 3 independent variables (X1, X2, X3) based on data from 1987-2016. 2. The results showed that a one unit increase in X1 would increase Y by 0.16, a one unit increase in X2 would increase Y by 0.13, and a one unit increase in X3 would increase Y by 0.007. However, none of these relationships were statistically significant. 3. Additional regression runs between the dependent variable and each independent variable individually did not show any statistically significant relationships either. This suggests the independent variables are not good predictors of the dependent variable based on this

1. Variables :
Dependent
Variable(Y)
Independent
Variable(X1)
Independent
Variable(X1)
(X3)
Modified: 1987
2016 // y=0
Modified: 1987
2016 // x1=0
Modified: 1987
2016 // x2=0
Modified:
1987
2016 //
x3=0
1987 11.7148706 1987 8.645396548 1987 3.253662 1987 11.98964
1988 5.047223238 1988 9.821312556 1988 2.73134 1988 -4.31257
1989 3.858500353 1989 4.651019111 1989 6.870276 1989 13.77469
1990 3.441261276 1990 6.429863505 1990 3.030677 1990 1.124974
1991 4.074109592 1991 5.134543499 1991 4.962108 1991 33.46523
1992 5.80040827 1992 7.164002896 1992 9.501318 1992 13.82098
1993 1.433358719 1993 4.897680651 1993 -5.28603 1993 1.317358
1994 3.715422914 1994 3.883654946 1994 5.227493 1994 3.110663
1995 6.862753358 1995 4.142869 1995 6.567737 1995 -3.07532
1996 3.438461989 1996 4.723542366 1996 11.72315 1996 1.994558
1997 0.503299454 1997 -0.32514251 1997 0.123629 1997 -6.53597
1998 6.060083229 1998 6.115267693 1998 4.517636 1998 -5.72997
1999 2.434257622 1999 4.92108861 1999 1.948661 1999 -2.85032
2000 0.616703174 2000 1.271685669 2000 6.093851 2000 16.016
2001 0.958138821 2001 4.132209518 2001 -2.17733 2001 12.18325
2002 5.269492231 2002 2.698001377 2002 0.103376 2002 9.96003
2003 5.9603827 2003 4.236617641 2003 4.147239 2003 28.37741
2004 6.22991061 2004 16.26298475 2004 2.432315 2004 -1.52783
2005 5.629891259 2005 12.11543748 2005 6.482853 2005 9.59049
2006 3.316735396 2006 4.105053722 2006 6.296945 2006 9.895027
2007 4.718421317 2007 7.729942079 2007 3.423502 2007 1.509728
2008 -0.02647973 2008 8.472590368 2008 1.807339 2008 -4.55208
2009 6.068582119 2009 -5.20687282 2009 3.497601 2009 -3.36118
2010 3.102410066 2010 3.424133773 2010 0.229546 2010 15.70766
2011 4.370612074 2011 4.507432635 2011 1.962012 2011 2.372198
2012 2.733560322 2012 2.547464577 2012 3.622132 2012 -15.0008
2013 4.713207063 2013 0.750434911 2013 2.675037 2013 13.58083
2014 6.042085106 2014 4.530246243 2014 2.49653 2014 -1.48018
2015 6.159293345 2015 5.180028864 2015 2.130033 2015 -6.34353
2016 7.202428884 2016 5.693378653 2016 0.153948 2016 -1.6033
Multiple Regression Model in Eviews

2. YEARS
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999

3. PPG, official creditors
(INT, current US$)
DEPENDENT VARIABLE (Y)
385153000
438764000
528510000
684016000
783280000
954972000
1154756000
1388663000
1719175000
2113843000
2567418000
3175295000
3780070000
4019276000
4270587000
4965719000
6265243000
7210609000
7618872000
7168222000
8144934000
8941504000
9477700000
9829241000
10521767000
14400079000
15573051000
14752739000
14153930000
14997728000

4. PPG,official creditors(NFL, current US$)
Independentvariable
X1
1186681000
1219739000
1531646000
1987612000
2596775000
3511578000
2837273000
3348667000
4272584000
4473179000
6769483000
7654860000
7185404000
6563748000
8143498000
6129229000
6550685000
3616158000
2033874000
3272601000
8282822000
4925930000
4699867000
9023010000
2303967000
17693933000
-3091625000
3896244000
12035014000
6122456000

5. PPG, official creditors (NTR,
cCcurrent US$)independent
vVariable X2
1528000
7 80975000
1 003136000
1 303596000
1 813495000
2 556606000
1 682517000
1 960004000
2 553409000
2 359336000
4 202065000
4 479565000
3405334000
2544472000
3872911000
1163510000
2 85442000
3594451000
5584998000
3895621000
1 37888000
4015574000
4777833000
806231000
8217800000
3293854000
18664676000
10856495000
2118916000
8875272000

6. PPG,official creditors(TDS, current US$)
Independent variable X3
1039170000
1150194000
1369192000
1669847000
1917276000
2166292000
2480238000
3056298000
3573448000
4778507000
6040441000
7300666000
8836791000
9823399000
9831935000
11171996000
14069449000
16612378000
19968902000
18428156000
19675791000
21932872000
23922042000
24750956000
28875089000
36451362000
46379785000
43789511000

7. 37415331000
42006051000
DependentVariable:Y
Method: LeastSquares
Date: 12/21/18 Time:16:03
Sample:1987 2016
Included observations:30
Variable Coefficient Std. Error t-Statistic Prob.
C 3.058243 0.857572 3.566162 0.0014
X1 0.161485 0.117875 1.369972 0.1824
X2 0.138396 0.137881 1.003728 0.3248
X3 0.007914 0.042692 0.185369 0.8544
R-squared 0.111796 Mean dependentvar 4.381646
Adjusted R-squared 0.009310 S.D. dependentvar 2.430616
S.E. of regression 2.419274 Akaike info criterion 4.728378
Sum squared resid 152.1751 Schwarz criterion 4.915204
Log likelihood -66.92567 Hannan-Quinn criter. 4.788145
F-statistic 1.090846 Durbin-Watson stat 1.594861
Prob(F-statistic) 0.370518
Interpretations :
1) Withthe one unitinincrease X1,Y will increase 0.1614 timesassumingX2and X3 are
constant.
2) Withthe one unitincrease inX2,Y will increase 0.1383 timesassumingX1and X3 are
constant.
3) Withthe one unitincrease inX3,Y will increase 0.0079 timesassumingX1and X2 are
constant.

8. Multicollinearity:
Correlation Matrix
Y X1 X2 X3
Y 1.000000 0.269157 0.217055 0.063439
X1 0.269157 1.000000 0.083008 -0.025165
X2 0.217055 0.083008 1.000000 0.184419
X3 0.063439 -0.025165 0.184419 1.000000
Ls y c x1
DependentVariable:Y
Method: LeastSquares
Date: 12/24/18 Time:17:11
Sample:1987 2016
Included observations:30
Variable Coefficient Std. Error t-Statistic Prob.
C 3.511931 0.731481 4.801123 0.0000
X1 0.170917 0.115576 1.478821 0.1504
R-squared 0.072446 Mean dependentvar 4.381646
Adjusted R-squared 0.039319 S.D. dependentvar 2.430616
S.E. of regression 2.382352 Akaike info criterion 4.638394
Sum squared resid 158.9168 Schwarz criterion 4.731807
Log likelihood -67.57591 Hannan-Quinn criter. 4.668278
F-statistic 2.186912 Durbin-Watson stat 1.770386
Prob(F-statistic) 0.150351
ls y c x2
DependentVariable:Y
Method: LeastSquares
Date: 12/24/18 Time:17:12
Sample:1987 2016
Included observations:30
Variable Coefficient Std. Error t-Statistic Prob.
C 3.850381 0.631055 6.101498 0.0000
X2 0.158510 0.134719 1.176596 0.2493
R-squared 0.047113 Mean dependentvar 4.381646
Adjusted R-squared 0.013081 S.D. dependentvar 2.430616
S.E. of regression 2.414666 Akaike info criterion 4.665339
Sum squared resid 163.2571 Schwarz criterion 4.758752
Log likelihood -67.98009 Hannan-Quinn criter. 4.695223
F-statistic 1.384379 Durbin-Watson stat 1.360324
Prob(F-statistic) 0.249263

9. ls y c x3
DependentVariable:Y
Method: LeastSquares
Date: 12/24/18 Time:17:13
Sample:1987 2016
Included observations:30
Variable Coefficient Std. Error t-Statistic Prob.
C 4.312855 0.494942 8.713855 0.0000
X3 0.014390 0.042780 0.336367 0.7391
R-squared 0.004025 Mean dependentvar 4.381646
Adjusted R-squared -0.031546 S.D. dependentvar 2.430616
S.E. of regression 2.468656 Akaike info criterion 4.709565
Sum squared resid 170.6394 Schwarz criterion 4.802978
Log likelihood -68.64348 Hannan-Quinn criter. 4.739449
F-statistic 0.113143 Durbin-Watson stat 1.502513
Prob(F-statistic) 0.739102
RUN THE REGREESION MODEL:
 (Ls y c x1 x2 x3)
DependentVariable:Y
Method: LeastSquares
Date: 01/02/19 Time:11:45
Sample:1970 1999
Included observations:30
Variable Coefficient Std. Error t-Statistic Prob.
C -4.88E-06 1.15E-05 -0.422274 0.6763
X1 1.000000 1.44E-14 6.97E+13 0.0000
X2 -1.000000 1.60E-14 -6.26E+13 0.0000
X3 -2.84E-14 5.54E-15 -5.126760 0.0000
R-squared 1.000000 Mean dependentvar 6.07E+09
Adjusted R-squared 1.000000 S.D. dependentvar 5.04E+09
S.E. of regression 3.37E-05 Akaike info criterion -17.63607
Sum squared resid 2.95E-08 Schwarz criterion -17.44925
Log likelihood 268.5411 Hannan-Quinn criter. -17.57630
F-statistic 2.16E+29 Durbin-Watson stat 0.535900
Prob(F-statistic) 0.000000
INTERPRETATION OF RESULTS:
1.With one unit increase in x1,y will increase by 1.00 units assuming that x2
and x3 are constant.

10. 2.With one unit increase in x2 ,y will decreaseby 1.00 units assuming that x1
and x3 are constant.
3.With one unit increase in x3,y will decrease by 2.84 units assuming that x1
and x2 are constant.
4.The value of R-Squareshows that100% of the total variation in dependent
variable (Y) IS explained by the dependent variables (x`s).
DETECTION OF MULTICOLLINEARITY:
METHOD 1:
CORRELATION MATRIX:
Y X1 X2 X3
Y 1.000000 0.323049 -0.724657 0.993812
X1 0.323049 1.000000 0.418061 0.247646
X2 -0.724657 0.418061 1.000000 -0.773622
X3 0.993812 0.247646 -0.773622 1.000000
INTERPRETATION OF RESULTS:
This correlation matrix showing that there is no relationship exist among
the independents variables because all values in this matrix are less
than 0.9 among x’s so, multicollinearity problem does not exist in this
model.
Method 2:
Run the Regression linesof dependentvariable with each
independentvariable:

11.  COMMAND LINE Ls y c x1:
DependentVariable:Y
Method: LeastSquares
Date: 01/02/19 Time:12:20
Sample:1970 1999
Included observations:30
Variable Coefficient Std. Error t-Statistic Prob.
C 3.93E+09 1.48E+09 2.653365 0.0130
X1 0.425859 0.235768 1.806263 0.0816
R-squared 0.104361 Mean dependentvar 6.07E+09
Adjusted R-squared 0.072374 S.D. dependentvar 5.04E+09
S.E. of regression 4.85E+09 Akaike info criterion 47.50792
Sum squared resid 6.59E+20 Schwarz criterion 47.60133
Log likelihood -710.6188 Hannan-Quinn criter. 47.53780
F-statistic 3.262586 Durbin-Watson stat 0.278825
Prob(F-statistic) 0.081638
 COMMAND LINE Ls y c x2:
DependentVariable:Y
Method: LeastSquares
Date: 01/02/19 Time:12:21
Sample:1970 1999
Included observations:30
Variable Coefficient Std. Error t-Statistic Prob.
C 5.34E+09 6.58E+08 8.117756 0.0000
X2 -0.695588 0.125005 -5.564462 0.0000
R-squared 0.525128 Mean dependentvar 6.07E+09
Adjusted R-squared 0.508168 S.D. dependentvar 5.04E+09
S.E. of regression 3.53E+09 Akaike info criterion 46.87343
Sum squared resid 3.50E+20 Schwarz criterion 46.96684
Log likelihood -701.1014 Hannan-Quinn criter. 46.90331
F-statistic 30.96323 Durbin-Watson stat 1.338625
Prob(F-statistic) 0.000006

12.  COMMAND LINE Ls y c x3:
DependentVariable:Y
Method: LeastSquares
Date: 01/02/19 Time:12:23
Sample:1970 1999
Included observations:30
Variable Coefficient Std. Error t-Statistic Prob.
C 5.30E+08 1.56E+08 3.384648 0.0021
X3 0.353030 0.007457 47.34280 0.0000
R-squared 0.987662 Mean dependentvar 6.07E+09
Adjusted R-squared 0.987221 S.D. dependentvar 5.04E+09
S.E. of regression 5.70E+08 Akaike info criterion 43.22310
Sum squared resid 9.08E+18 Schwarz criterion 43.31651
Log likelihood -646.3465 Hannan-Quinn criter. 43.25298
F-statistic 2241.341 Durbin-Watson stat 1.322517
Prob(F-statistic) 0.000000
Interpretation of results:
According to this method there is a problem of multicollinearity exist in this
model because the signs of x3 coefficient is change in individual regression
model as compareto original regression model.
Method 3:
Run the auxiliary regression
 Commandline Ls x1 c x2 x3:
DependentVariable:X1
Method: LeastSquares
Date: 01/02/19 Time:12:33
Sample:1970 1999
Included observations:30
Variable Coefficient Std. Error t-Statistic Prob.
C 1.65E+08 1.52E+08 1.091323 0.2848
X2 1.105615 0.025210 43.85641 0.0000
X3 0.383267 0.009330 41.08118 0.0000
R-squared 0.987006 Mean dependentvar 5.03E+09
Adjusted R-squared 0.986043 S.D. dependentvar 3.82E+09
S.E. of regression 4.52E+08 Akaike info criterion 42.78896
Sum squared resid 5.51E+18 Schwarz criterion 42.92908
Log likelihood -638.8344 Hannan-Quinn criter. 42.83379
F-statistic 1025.407 Durbin-Watson stat 0.511375
Prob(F-statistic) 0.000000

13.  Ls x2 c x1 x3
DependentVariable:C
Method: LeastSquares
Date: 01/02/19 Time:12:37
Sample:1970 1999
Included observations:30
Variable Coefficient Std. Error t-Statistic Prob.
X2 4.78E-24 9.40E-25 5.086546 0.0000
C 1.000000 6.79E-16 1.47E+15 0.0000
X1 -4.34E-24 8.44E-25 -5.135509 0.0000
X3 1.65E-24 3.26E-25 5.072230 0.0000
Mean dependentvar 1.000000 S.D. dependentvar 0.000000
S.E. of regression 1.98E-15 Sum squared resid 1.02E-28
Durbin-Watson stat 0.514808
 Ls x3 c x1 x2
DependentVariable:X3
Method: LeastSquares
Date: 01/02/19 Time:12:41
Sample:1970 1999
Included observations:30
Variable Coefficient Std. Error t-Statistic Prob.
C -2.12E+08 3.99E+08 -0.531559 0.5994
X1 2.568061 0.062512 41.08118 0.0000
X2 -2.872205 0.045518 -63.10025 0.0000
R-squared 0.993678 Mean dependentvar 1.57E+10
Adjusted R-squared 0.993209 S.D. dependentvar 1.42E+10
S.E. of regression 1.17E+09 Akaike info criterion 44.69113
Sum squared resid 3.69E+19 Schwarz criterion 44.83125
Log likelihood -667.3670 Hannan-Quinn criter. 44.73596
F-statistic 2121.773 Durbin-Watson stat 0.526551
Prob(F-statistic) 0.000000
Interpretation ofresults:
Under this method there is multicollinearity problem exist in this model because the
value of R-squared in all three above mentioned auxiliary regression models is more
than 0.9.
Detection of Heteroskedasticity

14.  Breusch-PaganLM Test
DependentVariable:UTSQ
Method: LeastSquares
Date: 01/02/19 Time:12:52
Sample:1970 1999
Included observations:30
Variable Coefficient Std. Error t-Statistic Prob.
C 4.51E-10 5.21E-10 0.866583 0.3941
X1 9.30E-19 6.47E-19 1.436646 0.1627
X2 -1.12E-18 7.21E-19 -1.557350 0.1315
X3 -3.39E-19 2.50E-19 -1.353965 0.1874
R-squared 0.243614 Mean dependentvar 9.83E-10
Adjusted R-squared 0.156339 S.D. dependentvar 1.65E-09
S.E. of regression 1.52E-09 Akaike info criterion -37.64902
Sum squared resid 6.00E-17 Schwarz criterion -37.46219
Log likelihood 568.7353 Hannan-Quinn criter. -37.58925
F-statistic 2.791329 Durbin-Watson stat 2.337041
Prob(F-statistic) 0.060360
LM=0.24 x 30=7.2
Interpretation ofresults:
There is no significant evidence of heteroskedasticity because value of LM<chi
square (7.2<9.487).
 White’s Test
DependentVariable:UTSQ
Method: LeastSquares
Date: 01/02/19 Time:13:11
Sample:1970 1999
Included observations:30
Variable Coefficient Std. Error t-Statistic Prob.
C 3.69E-11 1.58E-11 2.334009 0.0301
X1 -5.76E-19 7.90E-20 -7.284871 0.0000
X2 6.45E-19 8.65E-20 7.456016 0.0000
X3 2.25E-19 3.14E-20 7.174262 0.0000
X1SQ 5.22E-27 3.14E-29 166.1156 0.0000
X2SQ 6.54E-27 3.58E-29 182.7214 0.0000
X3SQ 7.98E-28 3.79E-30 210.6161 0.0000
X1X2 -1.17E-26 6.67E-29 -175.2639 0.0000
X1X3 -4.08E-27 2.18E-29 -187.6107 0.0000
X2X3 4.57E-27 2.33E-29 196.0407 0.0000
R-squared 0.999831 Mean dependentvar 9.83E-10
Adjusted R-squared 0.999755 S.D. dependentvar 1.65E-09
S.E. of regression 2.59E-11 Akaike info criterion -45.65662
Sum squared resid 1.34E-20 Schwarz criterion -45.18956
Log likelihood 694.8493 Hannan-Quinn criter. -45.50720
F-statistic 13162.74 Durbin-Watson stat 2.039349

15. Prob(F-statistic) 0.000000
LM=0.99 x 30=29.7
 There is significant evidence of heteroskedasticity because
value of LM>chi square (29.7>9.487)

16. Assumption no 4
Mis-specification
JERQUE BERA TEST:
0
4
8
12
16
20
-0.00010 -5.0e-05 2.5e-10 5.0e-05 0.00010
Series: RESID
Sample 1970 1999
Observations 30
Mean -1.36e-07
Median 8.81e-06
Maximum 8.12e-05
Minimum -7.90e-05
Std. Dev. 3.19e-05
Skewness -0.353188
Kurtosis 3.730937
Jarque-Bera 1.291545
Probability 0.524257

17. Interpretation ofresults:
J-B value is less than the chi square value (1.291545<9.487)so,there is
a misspecification isexistin the model.
Similarly,histogram of the result(resid.)series showsskewed italso
representthatthere is a misspecifications existin the model.
RESIDUAL VALUE
Last updated:
01/02/19 - 12:50
Modified: 1970
1999 // ut=resid
1970 1.34E-05
1971 1.23E-05
1972 1.40E-05
1973 1.41E-05
1974 1.78E-05
1975 1.91E-05
1976 5.89E-06
1977 7.72E-06
1978 2.87E-06
1979 6.61E-06
1980 2.58E-05
1981 1.96E-05
1982 9.91E-06
1983 1.36E-05
1984 6.72E-06
1985 -2.91E-05
1986 -4.89E-05
1987 -7.90E-05
1988 -3.03E-05
1989 -2.74E-05
1990 -2.84E-05
1991 -5.65E-05
1992 -4.58E-05
1993 -1.45E-05
1994 -1.08E-05
1995 2.09E-05

18. 1996 2.52E-05
1997 8.12E-05
1998 1.93E-05
1999 3.05E-05