'"regression" analysis
Regression1
| SUMMARY OUTPUT | p.183 (typo) | ||||||||
| Model: Predicted Sales/cap = -114.83 +0.00229 GNP +4.219 Unemp +21.42 Educa | |||||||||
| Regression Statistics | |||||||||
| Multiple R | 0.7311064653 | ||||||||
| R Square | 0.5345166636 | 53.40% | average | ||||||
| Adjusted R Square | 0.4523725455 | ||||||||
| Standard Error | 58.4262570359 | 116.8525140718 | Threashold for residuals | ||||||
| Observations | 21 | ||||||||
| ANOVA | |||||||||
| df | SS | MS | F | Significance F | |||||
| Regression | 3 | 66638.0318631304 | 22212.6772877101 | 6.5070594887 | 0.0039402219 | < 5% | Statiscally sig. | ||
| Residual | 17 | 58031.6676908202 | 3413.6275112247 | ||||||
| Total | 20 | 124669.699553951 | |||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | ||
| Intercept | -114.8351502647 | 78.2899644903 | -1.4667927238 | 0.1606877493 | -280.0125369343 | 50.3422364049 | -280.0125369343 | 50.3422364049 | >5% |
| GNP per head | 0.0022977119 | 0.0009519296 | 2.413741341 | 0.0273548383 | 0.0002893159 | 0.0043061078 | 0.0002893159 | 0.0043061078 | <5% |
| Unemployment rate | 4.2195245732 | 4.8400058964 | 0.8718015357 | 0.395462657 | -5.9919952639 | 14.4310444103 | -5.9919952639 | 14.4310444103 | >5% |
| %age spend on education | 21.4226983038 | 12.736119575 | 1.6820428057 | 0.1108365431 | -5.4481651767 | 48.2935617842 | -5.4481651767 | 48.2935617842 | >5% |
| these coefficients give you the model | |||||||||
| RESIDUAL OUTPUT | |||||||||
| Observation | Predicted Sales/Capita | Residuals | Country | ||||||
| 1 | 141.1050110113 | -29.0573919637 | Austria | ||||||
| 2 | 153.9361699264 | 6.2447824546 | Belgium | ||||||
| 3 | 32.1578881741 | -11.8947302793 | Bulgaria | ||||||
| 4 | 54.7672884559 | 46.0856527206 | Czech Rep. | ||||||
| 5 | 229.7909035734 | -59.7181763006 | Denmark | ||||||
| 6 | 179.8197146177 | 192.0670778351 | Finland | Finland | Outlier | ||||
| 7 | 151.7406303742 | -55.9587240737 | France | ||||||
| 8 | 124.2402274129 | -41.5214395341 | Germany | ||||||
| 9 | 83.2552007781 | -10.6659150638 | Greece | ||||||
| 10 | 60.6308801233 | -15.7308801233 | Hungary | ||||||
| 11 | 142.7851158825 | -11.6714795188 | Ireland | ||||||
| 12 | 119.9588490055 | -54.4546045233 | Italy | ||||||
| 13 | 132.5310691088 | -1.1068266846 | Netherlands | ||||||
| 14 | 97.7164232545 | -22.7953706229 | Poland | ||||||
| 15 | 90.8053302087 | -22.7118722648 | Portugal | ||||||
| 16 | 6.7651463829 | 25.4977644152 | Romania | ||||||
| 17 | 120.2673826729 | -14.3343469586 | Spain | ||||||
| 18 | 168.3638233859 | -17.6438233859 | Switzerland | ||||||
| 19 | 193.9264924164 | 35.790898888 | Sweden | ||||||
| 20 | 23.5560006075 | 14.4255297355 | Turkey | ||||||
| 21 | 112.9313706531 | 49.1538752485 | UK |
data
| Source Economist Pocket World in Figures 2011 | Y=Sales/capita | X= GNP and Unemp and Educa | ||||||||
| Country | Pop (millions) | Computer Sales | Sales/Capita | GNP per head | Unemployment rate | %age spend on education | -114.8351502647 | 0.0022977119 | 4.2195245732 | 21.4226983038 |
| 1 | Austria | 8.4 | 941.2 | $112.05 | $49,600 | 4.2 | 5.8 | $141.11 | ||
| 2 | Belgium | 10.5 | 1681.9 | $160.18 | $47,090 | 8.1 | 5.9 | $153.94 | ||
| 3 | Bulgaria | 7.6 | 154 | $20.26 | $6,550 | 13.5 | 3.5 | $32.16 | ||
| 4 | Czech Rep. | 10.2 | 1028.7 | $100.85 | $20,670 | 6.6 | 4.4 | $54.77 | ||
| 5 | Denmark | 5.5 | 935.4 | $170.07 | $62,120 | 5.2 | 8.4 | $229.79 | ||
| 6 | Finland | 5.3 | 1971 | $371.89 | $51,320 | 9.9 | 6.3 | $179.82 | ||
| 7 | France | 61.9 | 5928.9 | $95.78 | $44,510 | 10 | 5.7 | $151.74 | ||
| 8 | Germany | 82.5 | 6824.3 | $82.72 | $44,450 | 9.1 | 4.6 | $124.24 | ||
| 9 | Greece | 11.2 | 813 | $72.59 | $31,670 | 9.9 | 3.9 | $83.26 | ||
| 10 | Hungary | 10 | 449 | $44.90 | $15,410 | 7.3 | 5.1 | $60.63 | ||
| 11 | Ireland | 4.4 | 576.9 | $131.11 | $60,460 | 6.3 | 4.3 | $142.79 | ||
| 12 | Italy | 58.9 | 3858.2 | $65.50 | $38,490 | 9.3 | 5 | $119.96 | ||
| 13 | Netherlands | 16.5 | 2168.5 | $131.42 | $52,960 | 4.4 | 5 | $132.53 | ||
| 14 | Poland | 38 | 2847 | $74.92 | $13,850 | 14.4 | 5.6 | $97.72 | ||
| 15 | Portugal | 10.7 | 728.6 | $68.09 | $22,920 | 6.3 | 5.9 | $90.81 | ||
| 16 | Romania | 21.3 | 687.2 | $32.26 | $9,300 | 7 | 3.3 | $6.77 | ||
| 17 | Spain | 44.8 | 4745.8 | $105.93 | $35,220 | 14.2 | 4.4 | $120.27 | ||
| 18 | Switzerland | 7.5 | 1130.4 | $150.72 | $64,430 | 3.6 | 5.6 | $168.36 | ||
| 19 | Sweden | 9.2 | 2113.4 | $229.72 | $51,950 | 6.3 | 7.6 | $193.93 | ||
| 20 | Turkey | 75.8 | 2879 | $37.98 | $9,940 | 8.6 | 3.7 | $23.56 | ||
| 21 | UK | 61 | 9887.2 | $162.09 | $43,540 | 5.9 | 4.8 | $112.93 |
Regression2
| SUMMARY OUTPUT | |||||||||
| Model: Predicted sales/cap=-32.2+0.0016GNP-0.527Unemp+15.22Educ | |||||||||
| Regression Statistics | |||||||||
| Multiple R | 0.8608056365 | ||||||||
| R Square | 0.7409863438 | 74% | closer to 1 | ||||||
| Adjusted R Square | 0.6924212833 | 69% | |||||||
| Standard Error | 29.9835812953 | 59.9671625906 | |||||||
| Observations | 20 | ||||||||
| ANOVA | |||||||||
| df | SS | MS | F | Significance F | |||||
| Regression | 3 | 41150.4447707765 | 13716.8149235922 | 15.2576015709 | 0.0000593265 | 0.00005932 | < 5% | Stat. Sig | |
| Residual | 16 | 14384.2423566816 | 899.0151472926 | ||||||
| Total | 19 | 55534.6871274582 | |||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | ||
| Intercept | -32.2087611353 | 41.8908213525 | -0.7688739465 | 0.4531689934 | -121.0133353092 | 56.5958130387 | -121.0133353092 | 56.5958130387 | >5% |
| GNP per head | 0.0016784164 | 0.0004965371 | 3.3802436956 | 0.0038159552 | 0.0006258048 | 0.002731028 | 0.0006258048 | 0.002731028 | <5% |
| Unemployment rate | -0.5278671458 | 2.5755796407 | -0.2049508147 | 0.8401951569 | -5.9878520746 | 4.932117783 | -5.9878520746 | 4.932117783 | >5% |
| %age spend on education | 15.227644607 | 6.5962029214 | 2.3085470215 | 0.0346578879 | 1.2443190793 | 29.2109701347 | 1.2443190793 | 29.2109701347 | <5% |
| RESIDUAL OUTPUT | |||||||||
| Observation | Predicted Sales/Capita | Residuals | Country | ||||||
| 1 | 137.1439896071 | -25.0963705595 | Austria | ||||||
| 2 | 132.3952470051 | 27.7857053758 | Belgium | ||||||
| 3 | 24.9554160194 | -4.6922581247 | Bulgaria | ||||||
| 4 | 66.0018192089 | 34.8511219676 | Czech Rep. | ||||||
| 5 | 197.2217719175 | -27.1490446448 | Denmark | ||||||
| 6 | 124.0164561638 | -28.2345498633 | France | ||||||
| 7 | 107.6404225426 | -24.9216346638 | Germany | ||||||
| 8 | 75.108615856 | -2.5193301417 | Greece | ||||||
| 9 | 67.4631931047 | -22.5631931047 | Hungary | ||||||
| 10 | 131.4216039245 | -0.3079675608 | Ireland | ||||||
| 11 | 103.6225451408 | -38.1183006587 | Italy | ||||||
| 12 | 130.4957796366 | 0.9284627877 | Netherlands | ||||||
| 13 | 68.7108290703 | 6.2102235612 | Poland | ||||||
| 14 | 92.7780831901 | -24.6846252462 | Portugal | ||||||
| 15 | 29.9566686787 | 2.3062421195 | Romania | ||||||
| 16 | 86.410987695 | 19.5220480193 | Spain | ||||||
| 17 | 159.3060963628 | -8.5860963628 | Switzerland | ||||||
| 18 | 167.3895074617 | 62.3278838426 | Sweden | (Typo in p. 184) | |||||
| 19 | 36.2773255918 | 1.7042047512 | Turkey | ||||||
| 20 | 110.8477673956 | 51.237478506 | UK |
Finland out
| Eliminate Finland: Outlier | |||||||
| 2007 Source Economist Pocket world in Figures | |||||||
| Country | Pop (millions) | Computer Sales | Sales/Capita | GNP per head | Unemployment rate | %age spend on education | |
| 1 | Austria | 8.4 | 941.2 | $112.05 | 49600 | 4.2 | 5.8 |
| 2 | Belgium | 10.5 | 1681.9 | $160.18 | 47090 | 8.1 | 5.9 |
| 3 | Bulgaria | 7.6 | 154 | $20.26 | 6550 | 13.5 | 3.5 |
| 4 | Czech Rep. | 10.2 | 1028.7 | $100.85 | 20670 | 6.6 | 4.4 |
| 5 | Denmark | 5.5 | 935.4 | $170.07 | 62120 | 5.2 | 8.4 |
| 7 | France | 61.9 | 5928.9 | $95.78 | 44510 | 10 | 5.7 |
| 8 | Germany | 82.5 | 6824.3 | $82.72 | 44450 | 9.1 | 4.6 |
| 9 | Greece | 11.2 | 813 | $72.59 | 31670 | 9.9 | 3.9 |
| 10 | Hungary | 10 | 449 | $44.90 | 15410 | 7.3 | 5.1 |
| 11 | Ireland | 4.4 | 576.9 | $131.11 | 60460 | 6.3 | 4.3 |
| 12 | Italy | 58.9 | 3858.2 | $65.50 | 38490 | 9.3 | 5 |
| 13 | Netherlands | 16.5 | 2168.5 | $131.42 | 52960 | 4.4 | 5 |
| 14 | Poland | 38 | 2847 | $74.92 | 13850 | 14.4 | 5.6 |
| 15 | Portugal | 10.7 | 728.6 | $68.09 | 22920 | 6.3 | 5.9 |
| 16 | Romania | 21.3 | 687.2 | $32.26 | 9300 | 7 | 3.3 |
| 17 | Spain | 44.8 | 4745.8 | $105.93 | 35220 | 14.2 | 4.4 |
| 18 | Switzerland | 7.5 | 1130.4 | $150.72 | 64430 | 3.6 | 5.6 |
| 19 | Sweden | 9.2 | 2113.4 | $229.72 | 51950 | 6.3 | 7.6 |
| 20 | Turkey | 75.8 | 2879 | $37.98 | 9940 | 8.6 | 3.7 |
| 21 | UK | 61 | 9887.2 | $162.09 | 43540 | 5.9 | 4.8 |
Regression3
| SUMMARY OUTPUT | ||||||||||||
| Model: Predicted Sales/cap=-38.48 + 0.0017GNP +15.31Educ | ||||||||||||
| Regression Statistics | ||||||||||||
| Multiple R | 0.8604105733 | Check assumptions on the best model | Issue or not | Solutions if problem | ||||||||
| R Square | 0.7403063547 | 74% | close to 1 Good | Normality | Check range for kurtosis and Skewness | No problem | Change the Y | |||||
| Adjusted R Square | 0.7097541611 | 71% | better adjusted Rsquare | Heteroscedasticity | Check graph of predicted Y with abs residuals | There is heteroscedasticity issue | Change the Y | |||||
| Standard Error | 29.1265043448 | 58.2530086896 | Autocorrelation | (we don't have time series data) | ||||||||
| Observations | 20 | Multicollinearity | Check correlation between all Xs (close to 1 highly correlated - not good) OR check VIF (must be lower than 5 for each X) | No problem | Eliminate the X with highest p-value | |||||||
| ANOVA | ||||||||||||
| df | SS | MS | F | Significance F | ||||||||
| Regression | 2 | 41112.6817865343 | 20556.3408932671 | 24.2308740653 | 0.000010542 | <5% | Stat. Sig | |||||
| Residual | 17 | 14422.0053409239 | 848.3532553485 | |||||||||
| Total | 19 | 55534.6871274582 | ||||||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |||||
| Intercept | -38.4802612076 | 27.79129164 | -1.3846157892 | 0.1840755133 | -97.1147612378 | 20.1542388226 | -97.1147612378 | 20.1542388226 | >5% | |||
| GNP per head | 0.0017231683 | 0.0004332016 | 3.9777511063 | 0.0009730057 | 0.0008091927 | 0.0026371438 | 0.0008091927 | 0.0026371438 | <5% | |||
| %age spend on education | 15.3097398355 | 6.3958258117 | 2.3937080662 | 0.0284865891 | 1.8157269048 | 28.8037527661 | 1.8157269048 | 28.8037527661 | <5% | |||
| skewness | 0.8317848946 | check range in book p. 196 | between -1.02 and 1.03 | Nomality is not violated | ||||||||
| RESIDUAL OUTPUT | kurtosis | 0.1798015122 | check range in book p. 196 | between -1.27 and 2.46 | Nomality is not violated | |||||||
| Observation | Predicted Sales/Capita | Residuals | abs resid | |||||||||
| 1 | 135.7853766433 | -23.7377575957 | 23.7377575957 | |||||||||
| 2 | 132.9911982381 | 27.1897541428 | 27.1897541428 | SUMMARY OUTPUT | ||||||||
| 3 | 26.390580466 | -6.1274225713 | 6.1274225713 | |||||||||
| 4 | 64.5004824649 | 36.3524587116 | 36.3524587116 | Regression Statistics | ||||||||
| 5 | 197.1647671107 | -27.092039838 | 27.092039838 | Multiple R | 0.4031625579 | |||||||
| 6 | 125.4834761025 | -29.701569802 | 29.701569802 | R Square | 0.1625400481 | p-value>.05 so no significant heteroscedacity | ||||||
| 7 | 108.5393721866 | -25.8205843078 | 25.8205843078 | Adjusted R Square | 0.1160144952 | |||||||
| 8 | 75.8004636532 | -3.2111779389 | 3.2111779389 | Standard Error | 16.4937627235 | |||||||
| 9 | 66.1534351845 | -21.2534351845 | 21.2534351845 | Observations | 20 | |||||||
| 10 | 131.5343744366 | -0.4207380729 | 0.4207380729 | |||||||||
| 11 | 104.3931851579 | -38.8889406757 | 38.8889406757 | ANOVA | ||||||||
| 12 | 129.3274302037 | 2.0968122206 | 2.0968122206 | df | SS | MS | F | Significance F | ||||
| 13 | 71.1201625817 | 3.8008900498 | 3.8008900498 | Regression | 1 | 950.4041552658 | 950.4041552658 | 3.4935651067 | 0.0779681637 | |||
| 14 | 91.3422208534 | -23.2487629095 | 23.2487629095 | Residual | 18 | 4896.7957580359 | 272.0442087798 | |||||
| 15 | 28.0673452754 | 4.1955655227 | 4.1955655227 | Total | 19 | 5847.1999133016 | ||||||
| 16 | 89.5725809733 | 16.360454741 | 16.360454741 | |||||||||
| 17 | 158.2780143036 | -7.5580143036 | 7.5580143036 | Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
| 18 | 167.3923538107 | 62.3250374937 | 62.3250374937 | Intercept | 5.1279973743 | 9.114043699 | 0.562647881 | 0.5806154642 | -14.0198979087 | 24.2758926574 | -14.0198979087 | 24.2758926574 |
| 19 | 35.2940689103 | 2.6874614327 | 2.6874614327 | Predicted Sales/Capita | 0.1520429404 | 0.0813451828 | 1.8691081046 | 0.0779681637 | -0.018856947 | 0.3229428277 | -0.018856947 | 0.3229428277 |
| 20 | 110.0332370167 | 52.0520088849 | 52.0520088849 | |||||||||
| sample size = 20 |
135.785376643295 132.991198238111 26.3905804660167 64.5004824648947 197.164767110683 125.483476102523 108.53937218657 75.8004636531507 66.153435184493 131.534374436555 104.393185157875 129.327430203661 71.1201625817398 91.3422208534079 28.0673452754208 89.5725809732703 158.278014303639 167.392353810684 35.2940689103188 110.033237016713 23.737757595676 27.1897541428409 6.12742257127982 36.3524587115759 27.0920398379561 29.7015698020384 25.820584307782 3.21117793886496 21.253435184493 0.420738072919022 38.8889406757017 2.096812220581 3.80089004983917 23.2487629094826 4.19556552270128 16.3604547410154 7.55801430363917 62.3250374936639 2.68746143268912 52.0520088849264
Predicted Y
Abs Resid
Reg Interaction
| SUMMARY OUTPUT | ||||||||
| Regression Statistics | ||||||||
| Multiple R | 0.8615115717 | |||||||
| R Square | 0.7422021881 | |||||||
| Adjusted R Square | 0.6938650984 | |||||||
| Standard Error | 29.9131250736 | |||||||
| Observations | 20 | |||||||
| ANOVA | ||||||||
| df | SS | MS | F | Significance F | ||||
| Regression | 3 | 41217.9663007715 | 13739.3221002572 | 15.3547139925 | 0.0000571751 | |||
| Residual | 16 | 14316.7208266866 | 894.7950516679 | |||||
| Total | 19 | 55534.6871274582 | ||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
| Intercept | -4.6235008111 | 102.7456889769 | -0.0449994628 | 0.964664582 | -222.4346313453 | 213.1876297232 | -222.4346313453 | 213.1876297232 |
| GNP per head | 0.0017559593 | 0.0004550554 | 3.858781671 | 0.0013893627 | 0.000791285 | 0.0027206336 | 0.000791285 | 0.0027206336 |
| %age spend on education | 2.5031306672 | 37.9082099165 | 0.0660313603 | 0.9481709009 | -77.8586844188 | 82.8649457531 | -77.8586844188 | 82.8649457531 |
| EducSquare | 1.0998013269 | 3.2062233847 | 0.3430208052 | 0.7360482386 | -5.6970886167 | 7.8966912705 | -5.6970886167 | 7.8966912705 |
| RESIDUAL OUTPUT | ||||||||
| Observation | Predicted Sales/Capita | Residuals | ||||||
| 1 | 133.9875545043 | -21.9399354566 | ||||||
| 2 | 131.1171773043 | 29.0637750766 | ||||||
| 3 | 29.1115561314 | -8.8483982367 | ||||||
| 4 | 63.978106348 | 36.8748348285 | ||||||
| 5 | 203.0849695454 | -33.0122422727 | ||||||
| 6 | 123.534637123 | -27.7527308225 | ||||||
| 7 | 108.2150867978 | -25.496298919 | ||||||
| 8 | 77.4779177031 | -4.8886319888 | ||||||
| 9 | 63.8076307709 | -18.9076307709 | ||||||
| 10 | 132.6405862956 | -1.526949932 | ||||||
| 11 | 102.9740587886 | -37.4698143065 | ||||||
| 12 | 128.3827897221 | 3.0414527022 | ||||||
| 13 | 68.2038367103 | 6.7172159213 | ||||||
| 14 | 88.6756412531 | -20.5821833092 | ||||||
| 15 | 31.9440882422 | 0.3188225559 | ||||||
| 16 | 89.5273140246 | 16.4057216896 | ||||||
| 17 | 157.0202576235 | -6.3002576235 | ||||||
| 18 | 169.1469020429 | 60.5704892614 | ||||||
| 19 | 37.1485981704 | 0.8329321727 | ||||||
| 20 | 109.1854164715 | 52.8998294302 |
Reg Interaction 2
| SUMMARY OUTPUT | ||||||||
| Then after trying Interactions we need to check assumptions | ||||||||
| Regression Statistics | ||||||||
| Multiple R | 0.8606615376 | |||||||
| R Square | 0.7407382823 | |||||||
| Adjusted R Square | 0.6921267102 | |||||||
| Standard Error | 29.9979357384 | |||||||
| Observations | 20 | |||||||
| ANOVA | ||||||||
| df | SS | MS | F | Significance F | ||||
| Regression | 3 | 41136.6687503818 | 13712.2229167939 | 15.2379001695 | 0.000059774 | |||
| Residual | 16 | 14398.0183770764 | 899.8761485673 | |||||
| Total | 19 | 55534.6871274582 | ||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
| Intercept | -28.846752865 | 65.5808169087 | -0.4398657142 | 0.665918108 | -167.871874157 | 110.1783684269 | -167.871874157 | 110.1783684269 |
| GNP per head | 0.0015026329 | 0.001422549 | 1.0562960951 | 0.3065220677 | -0.0015130362 | 0.004518302 | -0.0015130362 | 0.004518302 |
| %age spend on education | 13.1513869246 | 14.7700751885 | 0.8904075813 | 0.386440352 | -18.1597737374 | 44.4625475866 | -18.1597737374 | 44.4625475866 |
| GNP*Educ | 0.0000473736 | 0.0002901615 | 0.1632661944 | 0.8723532506 | -0.0005677412 | 0.0006624884 | -0.0005677412 | 0.0006624884 |
| RESIDUAL OUTPUT | ||||||||
| Observation | Predicted Sales/Capita | Residuals | ||||||
| 1 | 135.590307996 | -23.5426889483 | ||||||
| 2 | 132.6672559418 | 27.5136964391 | ||||||
| 3 | 28.111385676 | -7.8482277812 | ||||||
| 4 | 64.3873019352 | 36.4656392413 | ||||||
| 5 | 199.6883538608 | -29.6156265881 | ||||||
| 6 | 125.0173459979 | -29.2354396974 | ||||||
| 7 | 108.1281306401 | -25.4093427613 | ||||||
| 8 | 75.8832902901 | -3.2940045758 | ||||||
| 9 | 65.1040286646 | -20.2040286646 | ||||||
| 10 | 130.8694787326 | 0.2441576311 | ||||||
| 11 | 103.8635631458 | -38.3593186636 | ||||||
| 12 | 129.0341380661 | 2.3901043582 | ||||||
| 13 | 69.2867726566 | 5.634279975 | ||||||
| 14 | 89.5930074123 | -21.4995494684 | ||||||
| 15 | 29.981204445 | 2.2817063532 | ||||||
| 16 | 89.2834657683 | 16.649569946 | ||||||
| 17 | 158.7084100041 | -7.9884100041 | ||||||
| 18 | 167.8695945581 | 61.8477967462 | ||||||
| 19 | 36.4918544827 | 1.4896758603 | ||||||
| 20 | 109.6052352992 | 52.4800106024 |
Reg Hetero
| SUMMARY OUTPUT | |||||||||
| Model: predicted sales/cap = 2.96 + 2.299 GNP +0.132 Educ | |||||||||
| Regression Statistics | |||||||||
| Multiple R | 0.8801524423 | We improved Heteroscedasticity based on the graph | |||||||
| R Square | 0.7746683217 | ||||||||
| Adjusted R Square | 0.7481587125 | ||||||||
| Standard Error | 0.3122437451 | 0.6244874901 | |||||||
| Observations | 20 | ||||||||
| ANOVA | |||||||||
| df | SS | MS | F | Significance F | |||||
| Regression | 2 | 5.6980986183 | 2.8490493092 | 29.2221705608 | 0.0000031549 | <5% | |||
| Residual | 17 | 1.6574346575 | 0.0974961563 | ||||||
| Total | 19 | 7.3555332758 | |||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | ||
| Intercept | 2.9600956906 | 0.2979299156 | 9.9355436814 | 0.000000017 | 2.3315185135 | 3.5886728676 | 2.3315185135 | 3.5886728676 | <5% |
| GNP per head | 0.0000229976 | 0.000004644 | 4.9520705368 | 0.0001211517 | 0.0000131995 | 0.0000327956 | 0.0000131995 | 0.0000327956 | <5% |
| %age spend on education | 0.1320067348 | 0.0685649256 | 1.9252807997 | 0.0710914359 | -0.0126526133 | 0.276666083 | -0.0126526133 | 0.276666083 | <5% |
| RESIDUAL OUTPUT | |||||||||
| Observation | Predicted Ln(sales/per cap) | Residuals | Abs Resid | ||||||
| 1 | 4.8664151216 | -0.1474911706 | 0.1474911706 | ||||||
| 2 | 4.821891849 | 0.2544122795 | 0.2544122795 | ||||||
| 3 | 3.5727534645 | -0.5639491094 | 0.5639491094 | ||||||
| 4 | 4.0162854696 | 0.5973779583 | 0.5973779583 | ||||||
| 5 | 5.4975624351 | -0.361336282 | 0.361336282 | ||||||
| 6 | 4.7361567248 | -0.1740829272 | 0.1740829272 | ||||||
| 7 | 4.5895694612 | -0.1741227039 | 0.1741227039 | ||||||
| 8 | 4.2032555711 | 0.0815617602 | 0.0815617602 | ||||||
| 9 | 3.9877228706 | -0.1832850759 | 0.1832850759 | ||||||
| 10 | 4.918158826 | -0.0420944256 | 0.0420944256 | ||||||
| 11 | 4.5053065302 | -0.3231915884 | 0.3231915884 | ||||||
| 12 | 4.8380816297 | 0.0403489526 | 0.0403489526 | ||||||
| 13 | 4.0178500007 | 0.2985849269 | 0.2985849269 | ||||||
| 14 | 4.266040145 | -0.0451590019 | 0.0451590019 | ||||||
| 15 | 3.6095954847 | -0.1356771868 | 0.1356771868 | ||||||
| 16 | 4.3509003762 | 0.3119067797 | 0.3119067797 | ||||||
| 17 | 5.181068006 | -0.1656441951 | 0.1656441951 | ||||||
| 18 | 5.1580715764 | 0.2787782436 | 0.2787782436 | ||||||
| 19 | 3.677116635 | -0.0400166371 | 0.0400166371 | ||||||
| 20 | 4.595043003 | 0.4930794031 | 0.4930794031 |
4.86641512164656 4.82189184903841 3.57275346447401 4.01628546958415 5.49756243505022 4.7361567248122 4.58956946120262 4.20325557109386 3.98772287064779 4.91815882598398 4.50530653015494 4.83808162973825 4.01785000065614 4.26604014503506 3.60959548473841 4.35090037621422 5.18106800597221 5.15807157635807 3.6771166350487 0.147491170642622 0.254412279531499 0.563949109352671 0.59737795826261 0.36133628199686 0.174082927188254 0.174122703852715 0.0815617601528986 0.183285075899581 0.042094425645347 0.323191588358695 0.04034895263064 0.298584926895512 0.0451590019284591 0.135677186783743 0.311906779722502 0.165644195144155 0.278778243593867 0.0400166370848507 0.493079403088434
Unemployment out
| 2007 Source Economist Pocket world in Figures | 0.574 is Pearson Correlation | |||||||||||
| Country | Pop (millions) | Computer Sales | Sales/Capita | GNP per head | %age spend on education | Ln(sales/per cap) | GNP*Educ | EducSquare | ||||
| 1 | Austria | 8.4 | 941.2 | $112.05 | 49600 | 5.8 | 4.718923951 | 287680 | 33.64 | GNP per head | %age spend on education | |
| 2 | Belgium | 10.5 | 1681.9 | $160.18 | 47090 | 5.9 | 5.0763041286 | 277831 | 34.81 | GNP per head | 1 | |
| 3 | Bulgaria | 7.6 | 154 | $20.26 | 6550 | 3.5 | 3.0088043551 | 22925 | 12.25 | %age spend on education | 0.5741560564 | 1 |
| 4 | Czech Rep. | 10.2 | 1028.7 | $100.85 | 20670 | 4.4 | 4.6136634278 | 90948 | 19.36 | close to 1 means highly correlated | ||
| 5 | Denmark | 5.5 | 935.4 | $170.07 | 62120 | 8.4 | 5.1362261531 | 521808 | 70.56 | |||
| 7 | France | 61.9 | 5928.9 | $95.78 | 44510 | 5.7 | 4.5620737976 | 253707 | 32.49 | |||
| 8 | Germany | 82.5 | 6824.3 | $82.72 | 44450 | 4.6 | 4.4154467573 | 204470 | 21.16 | |||
| 9 | Greece | 11.2 | 813 | $72.59 | 31670 | 3.9 | 4.2848173312 | 123513 | 15.21 | |||
| 10 | Hungary | 10 | 449 | $44.90 | 15410 | 5.1 | 3.8044377947 | 78591 | 26.01 | |||
| 11 | Ireland | 4.4 | 576.9 | $131.11 | 60460 | 4.3 | 4.8760644003 | 259978 | 18.49 | |||
| 12 | Italy | 58.9 | 3858.2 | $65.50 | 38490 | 5 | 4.1821149418 | 192450 | 25 | |||
| 13 | Netherlands | 16.5 | 2168.5 | $131.42 | 52960 | 5 | 4.8784305824 | 264800 | 25 | |||
| 14 | Poland | 38 | 2847 | $74.92 | 13850 | 5.6 | 4.3164349276 | 77560 | 31.36 | |||
| 15 | Portugal | 10.7 | 728.6 | $68.09 | 22920 | 5.9 | 4.2208811431 | 135228 | 34.81 | |||
| 16 | Romania | 21.3 | 687.2 | $32.26 | 9300 | 3.3 | 3.473918298 | 30690 | 10.89 | |||
| 17 | Spain | 44.8 | 4745.8 | $105.93 | 35220 | 4.4 | 4.6628071559 | 154968 | 19.36 | |||
| 18 | Switzerland | 7.5 | 1130.4 | $150.72 | 64430 | 5.6 | 5.0154238108 | 360808 | 31.36 | |||
| 19 | Sweden | 9.2 | 2113.4 | $229.72 | 51950 | 7.6 | 5.43684982 | 394820 | 57.76 | |||
| 20 | Turkey | 75.8 | 2879 | $37.98 | 9940 | 3.7 | 3.637099998 | 36778 | 13.69 | |||
| 21 | UK | 61 | 9887.2 | $162.09 | 43540 | 4.8 | 5.0881224061 | 208992 | 23.04 |
Time series
| Country1 | Year 2018 | |
| Year 2019 | ||
| Year 2020 | ||
| Country2 | Year 2018 | This kind of data is called time series data |
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| Year 2020 | ||
| Country3 | Year 2018 | |
| Year 2019 | ||
| Year 2020 | ||
| Country 4 | Year 2018 | |
| Year 2019 | ||
| Year 2020 | ||
| Country 5 | Year 2018 | |
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| Year 2020 | ||
| Country24 |