Problem 12.7 from Gujarati, D, Basic Econometrics, 4th Edition, McGraw-Hill, 2003

1. ECO303
Introduction to Econometrics
Term Paper
Dr. Wasiq Khan (WRK)
4/17/2014
ID. Name
11304043 Samiya Yesmin
13105042 Nazrina Haque
12104055 Adrita Rahman

2. 1
1.
From the regression we see, the R square is high, F value is significant and there
is only one independent variable H which is statistically insignificant.
P value of the independent variable I is 0.00934 which is less than 5% which means it is
statistically significant.
P value of the independent variable L is 0.02233 which is less than 5% which means it
is statistically significant.
P value of the independent variable H is 0.97154 which is more than 5% which means it
is statistically insignificant.
P value of the independent variable A is 0.00034 which is less than 5% which means it
is statistically significant.
So there should be a multicollinearity problem present in the independent variable A.
lnC lnI lnL lnH lnA
3.086 3.809 5.395 7.307 2.944
3.104 3.930 5.559 7.316 2.966
2.977 3.976 5.546 7.271 3.041
3.129 3.982 5.519 7.347 3.081
3.520 4.000 5.864 7.406 3.165
3.668 4.113 5.796 7.207 3.258
3.420 4.126 5.392 7.110 3.315
3.270 4.059 5.459 7.231 3.292
3.424 4.171 5.470 7.348 3.290
3.469 4.193 5.505 7.167 3.304
3.401 4.200 5.435 7.219 3.237
3.428 4.279 5.455 7.308 3.173
3.428 4.337 5.456 7.399 3.119
3.484 4.403 5.849 7.353 3.166
3.567 4.498 6.149 7.320 3.199
3.600 4.583 6.319 7.087 3.199
3.653 4.605 6.035 7.187 3.218
3.742 4.666 6.264 7.343 3.242
3.869 4.710 6.431 7.313 3.302
4.064 4.680 6.378 7.292 3.358
3.951 4.697 6.097 7.642 3.367
3.936 4.785 6.059 7.774 3.284
4.086 4.866 6.589 7.629 3.232
4.348 4.862 6.777 7.210 3.528
4.162 4.769 6.322 7.066 3.684
4.243 4.866 6.660 7.344 3.795
4.202 4.921 6.621 7.596 3.936
4.197 4.978 6.565 7.612 3.997
4.588 5.027 6.841 7.467 4.111
4.619 4.991 6.847 7.169 4.261

3. 2
2.
ANOVA
df SS MS F Significance F
Regression 4 5.427742 1.356935564 91.54311907 1.49104E-14
Residual 25 0.370573 0.014822912
Total 29 5.798315
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept -1.5004409 1.0030200 -1.4959231 0.1471920 -3.5661993 0.5653176 -3.5661993 0.5653176
lnI 0.4675085 0.1659867 2.8165414 0.0093397 0.1256524 0.8093646 0.1256524 0.8093646
lnL 0.2794425 0.1147257 2.4357447 0.0223276 0.0431605 0.5157245 0.0431605 0.5157245
lnH -0.0051516 0.1429470 -0.0360382 0.9715381 -0.2995564 0.2892533 -0.2995564 0.2892533
lnA 0.4414489 0.1065083 4.1447365 0.0003414 0.2220909 0.6608069 0.2220909 0.6608069
From the regression we can obtain, the coefficients of I, L and A are statistically significant. Only the coefficient of H is not statistically
significant. So from the model only the independent variable H has no economically meaningful impact on the dependent variable C but
the other independent variables do.
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.967517
R Square 0.93609
Adjusted R Square 0.925864
Standard Error 0.121749
Observations 30

4. 3
-2.500000
-2.000000
-1.500000
-1.000000
-0.500000
0.000000
0.500000
1.000000
1.500000
2.000000
2.500000
-0.300000 -0.200000 -0.100000 0.000000 0.100000 0.200000 0.300000
Standard Residuals Standard Residuals
3. RESIDUAL OUTPUT
Plotting the residuals and standardized residuals we find a regular straight line which
is upward slopping. So there is a pattern observed in the graph. Hence we can say, there
might be a positive autocorrelation present in these residuals
Observation Predicted lnC Residuals Ui Standard Residuals Ui/Se
1 3.050137 0.035893 0.317523
2 3.161713 -0.057574 -0.509322
3 3.213299 -0.236240 -2.089855
4 3.225369 -0.096418 -0.852941
5 3.367265 0.152308 1.347362
6 3.443269 0.224898 1.989516
7 3.361713 0.058633 0.518685
8 3.338336 -0.068767 -0.608333
9 3.392789 0.031474 0.278429
10 3.419636 0.049220 0.435416
11 3.373677 0.027520 0.243451
12 3.387650 0.039864 0.352653
13 3.390655 0.036860 0.326071
14 3.552463 -0.068150 -0.602880
15 3.694765 -0.128053 -1.132798
16 3.783448 -0.183400 -1.622411
17 3.722678 -0.069426 -0.614165
18 3.824710 -0.082290 -0.727963
19 3.918982 -0.049867 -0.441137
20 3.914482 0.149403 1.321669
21 3.846175 0.105069 0.929475
22 3.839094 0.096646 0.854957
23 4.003174 0.082802 0.732497
24 4.186830 0.160864 1.423057
25 4.085422 0.076581 0.677459
26 4.273138 -0.030374 -0.268694
27 4.348781 -0.147077 -1.301093
28 4.386541 -0.189339 -1.674956
29 4.537897 0.050127 0.443436
30 4.59025949 0.028813601 0.254894094

5. 4
4.
Plotting 𝑈𝑖
2̂against 𝑌𝑖
̂and then separately against each of the explanatory variables we observe, there is no pattern observed in the graph
so there is so heteroscedasticity problem. But in lnH we observe a slight pattern and for that we will go for the park test.
-0.400000
-0.200000
0.000000
0.200000
0.400000
0.000 1.000 2.000 3.000 4.000 5.000 6.000
Residuals
lnI
lnI Residual Plot
-0.400000
-0.200000
0.000000
0.200000
0.400000
0.000 2.000 4.000 6.000 8.000
Residuals
lnL
lnL Residual Plot
-0.400000
-0.200000
0.000000
0.200000
0.400000
7.000 7.200 7.400 7.600 7.800 8.000
Residuals
lnH
lnH Residual Plot
-0.400000
-0.200000
0.000000
0.200000
0.400000
0.000 1.000 2.000 3.000 4.000 5.000Residuals
lnA
lnA Residual Plot

6. 5
5. Durbin-Watson d statistic
d-test =
∑(Ut−1−Ut)2
∑ Ut
2
d-test = (0.3697426/0.3705728) = 0.9977596
Estimating the Durbin-Watson d statistic we find a positive autocorrelation present in the data.
Ut
2
Ut-1 (Ut-1-Ut)2
0.0012883
0.0033148 -0.0934677 0.0012883
0.0558095 -0.1786658 0.0033148
0.0092964 0.1398226 0.0558095
0.0231976 0.2487254 0.0092964
0.0505790 0.0725900 0.0231976
0.0034378 -0.1662649 0.0505790
0.0047289 -0.1273997 0.0034378
0.0009906 0.1002409 0.0047289
0.0024226 0.0177460 0.0009906
0.0007574 -0.0217000 0.0024226
0.0015892 0.0123444 0.0007574
0.0013586 -0.0030049 0.0015892
0.0046445 -0.1050100 0.0013586
0.0163976 -0.0599027 0.0046445
0.0336355 -0.0553466 0.0163976
0.0048200 0.1139736 0.0336355
0.0067716 -0.0128638 0.0048200
0.0024867 0.0324232 0.0067716
0.0223214 0.1992702 0.0024867
0.0110395 -0.0443342 0.0223214
0.0093404 -0.0084236 0.0110395
0.0068563 -0.0138431 0.0093404
0.0258774 0.0780619 0.0068563
0.0058646 -0.0842835 0.0258774
0.0009226 -0.1069545 0.0058646
0.0216318 -0.1167039 0.0009226
0.0358494 -0.0422620 0.0216318
0.0025127 0.2394662 0.0358494
0.0008302 -0.0213131 0.0025127
Sum 0.3705728 0.3697426

7. 6
6. Park test for detecting the presence of heteroscedasticity
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.001849167
R Square 3.41942E-06
Adjusted R Square -0.035710744
Standard Error 0.115042154
Observations 30
ANOVA
df SS MS F Significance F
Regression 1 1.26714E-06 1.26714E-06 9.5744E-05 0.992262
Residual 28 0.370571523 0.013234697
Total 29 0.370572791
Coefficients
Standard
Error t Stat P-value
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept 0.017749 1.814051 0.009784 0.992263
-
3.69817 3.733664
-
3.69817 3.733664
ln(lnH) -0.00891 0.910447 -0.00978 0.992262
-
1.87387 1.856057
-
1.87387 1.856057
Residuals ln(lnH)
0.035893238 1.98886048
-0.057574474 1.990047807
-0.236240262 1.983895008
-0.096417691 1.99424513
0.152307737 2.002304442
0.224897742 1.975069268
0.058632859 1.961485291
-0.06876685 1.978417029
0.031474028 1.994481849
0.049220012 1.969503207
0.027520041 1.976703931
0.039864417 1.988998079
0.036859539 2.001390391
-0.068150483 1.995119534
-0.128053134 1.990564731
-0.183399706 1.958201542
-0.069426143 1.972249541
-0.082289949 1.993752661
-0.049866784 1.989638134
0.149403412 1.986824095
0.105069199 2.03369655
0.096645642 2.050813815
0.082802495 2.031989142
0.160864443 1.97542873
0.0765809 1.955288165
-0.030373578 1.993946372
-0.147077474 2.027594069
-0.189339482 2.029789678
0.050126702 2.01048177
0.028813601 1.969761297

8. 7
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
1.94 1.96 1.98 2 2.02 2.04 2.06
Residuals
ln(lnH)
ln(lnH) Residual Plot
After the park test we observe the coefficient of lnH is not statistically
significant. So there can’t be any heteroscedasticity present in lnH.
RESIDUAL OUTPUT
Observation Predicted Residuals Residuals
1 3.10992E-05 0.035862139
2 2.05218E-05 -0.057594996
3 7.53347E-05 -0.236315597
4 -1.68706E-05 -0.096400821
5 -8.86679E-05 0.152396405
6 0.00015396 0.224743782
7 0.000274974 0.058357885
8 0.000124136 -0.068890986
9 -1.89794E-05 0.031493008
10 0.000203546 0.049016466
11 0.000139397 0.027380643
12 2.98734E-05 0.039834544
13 -8.0525E-05 0.036940064
14 -2.46603E-05 -0.068125823
15 1.59167E-05 -0.12806905
16 0.000304228 -0.183703934
17 0.00017908 -0.069605222
18 -1.24834E-05 -0.082277466
19 2.41714E-05 -0.049890955
20 4.92406E-05 0.149354172
21 -0.000368328 0.105437527
22 -0.000520819 0.097166461
23 -0.000353118 0.083155613
24 0.000150758 0.160713686
25 0.000330182 0.076250718
26 -1.42091E-05 -0.030359369
27 -0.000313964 -0.14676351
28 -0.000333523 -0.189005959
29 -0.000161517 0.050288219
30 0.000201247 0.028612355