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# ECO303- Introduction to Econometrics- term paper

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

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

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• 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