Question

A B С D E F G H 1 WinterRain HarvestRain 160 Age 31 2 600 3 690 80 4. 502 130 Year 1952 1953 1955 1957 1958 1959 1960 5 420 110 187 30 28 26 25 24 23 6 7 582 485 763 830 8 9 1961 22 10 1962 697 21 20 11 12 1963 1964 608 402 19 13 602 18 Price 7.495 8.0393 7.6858 6.9845 6.7772 8.0757 6.5188 8.4937 7.388 6.7127 7.3094 6.2518 7.7443 6.8398 6.2435 6.3459 7.5883 7.1934 6.2049 6.6367 6.2941 7.292 7.1211 6.2587 7.186 1965 1966 1967 1968 AGST 17.1167 16.7333 17.15 16.1333 16.4167 17.4833 16.4167 17.3333 16.3 15.7167 17.2667 15.3667 16.5333 16.2333 16.2 16.55 16.6667 16.7667 14.9833 17.0667 16.3 16.95 17.65 15.5833 15.8167 14 15 16 France Pop 43183.569 43495.03 44217.857 45152.252 45653.805 46128.638 46583.995 47128.005 48088.673 48798.99 49356.943 49801.821 50254.966 50650.406 51034.413 51470.276 51918.389 52431.647 52894.183 53332.805 53689.61 53955.042 54159.049 54378.362 54602.193 187 290 38 52 155 96 267 86 118 292 244 89 112 158 123 184 819 714 610 575 622 551 17 16 15 14 1969 17 18 19 13 12 11 20 536 10 21 22 23 1970 1971 1972 1973 1974 1975 1976 1977 1978 376 574 9 572 418 171 247 8 7 24 6 821 763 87 51 5 25 26 27 28 29 30 31 Sheet 1 Sheet 2 +

Answer 1

Regression Statistics Multiple R 0.658917271 R Square 0.43417197 Adjusted R Square 0.409570751 Standard Error 0.49882487 Observations 25 ANOVA df SS Regression Residual Total MS F gnificance F 1 4.391383 4.391383 17.64839 0.000341 23 5.723004 0.248826 24 10.11439 Intercept AGST Coefficients andard Errt Stat P-value Lower 95%Upper 95%ower 95.0%pper 95.0% -3.389977742 2.490931 -1.36093 0.186723 -8.54286 1.762905 -8.54286 1.762905 0.633338721 0.150759 4.200999 0.000341 0.32147 0.945208 0.32147 0.945208

SUMMARY OUTPUT Regression Statistics Multiple R 0.755467129 R Square 0.570730583 Adjusted R Square 0.531706091 Standard Error 0.444245892 Observations 25 ANOVA df SS 2 Regression Residual Total MS F gnificance F 2.886295041 14.62493288 9.12E-05 0.197354413 5.772590083 4.341797083 10.11438717 22 24 Coefficients -6.53722872 Intercept Winter Rain Standard Error t Stat P-value Lower 95%Upper 95%ower 95.09 pper 95.0% 2.51724882 -2.596973595 0.016455461 -11.7577 -1.31677 -11.7577 -1.31677 0.000723866 2.645488726 0.014774232 0.000414 0.003416 0.000414 0.003416 0.141770729 5.316786327 2.45498E-05 0.45975 1.047779 0.45975 1.047779 0.001914979 0.753764674 AGST

SUMMARY OUTPUT Regression Statistics Multiple R 0.868385496 R Square 0.75409337 Adjusted R Square 0.718963851 Standard Error 0.344148007 Observations 25 ANOVA df SS 3 Regression Residual Total MS F gnificance F 2.542397434 21.46608892 1.34E-06 0.118437851 7.627192302 2.487194864 10.11438717 21 24 Intercept Winter Rain AGST Coefficients Standard Error t Stat P-value Lower 95%Upper 95%ower 95.0%pper 95.0% -4.285779136 2.031366584 -2.109800944 0.047047602 -8.51024 -0.06132 -8.51024 -0.06132 0.001182748 0.000590505 2.00294273 0.058260019 -4.5E-05 0.002411 -4.5E-05 0.002411 0.679705501 0.111410036 6.100936026 4.70571E-06 0.448016 0.911395 0.448016 0.911395 -0.003941686 0.000996098 -3.957128276 0.000719773 -0.00601 -0.00187 -0.00601 -0.00187 HarvestRain

SUMMARY OUTPUT Regression Statistics Multiple R 0.909905031 R Square 0.827927165 Adjusted R Square 0.793512597 Standard Error 0.294992481 Observations 25 ANOVA df 4 Regression Residual Total SS MS F gnificance F 8.373975887 2.093494 24.05746272 2.11E-07 1.740411278 0.087021 10.11438717 20 24 Intercept WinterRain AGST HarvestRain Age Coefficients Standard Error t Stat P-value Lower 95%Upper 95%ower 95.0%pper 95.0% -3.421772008 1.766023894 -1.93756 0.066927997 -7.10563 0.262089 -7.10563 0.262089 0.001082608 0.000507315 2.133997 0.045411328 2.44E-05 0.002141 2.44E-05 0.002141 0.606537577 0.098709279 6.144687 5.27962E-06 0.400634 0.812442 0.400634 0.812442 -0.003964868 0.000853859 -4.64347 0.00015669 -0.00575 -0.00218 -0.00575 -0.00218 0.023721107 0.008097454 2.929452 0.008289937 0.00683 0.040612 0.00683 0.040612

SUMMARY OUTPUT Regression Statistics Multiple R 0.910843772 R Square 0.829636378 Adjusted R Square 0.784803845 Standard Error 0.301148996 Observations 25 ANOVA df SS Regression Residual Total MS F gnificance F 5 8.39126353 1.678253 18.50523129 1.03E-06 19 1.723123635 0.090691 24 10.11438717 Intercept WinterRain AGST HarvestRain Age FrancePop Coefficients Standard Errol t Stat P-value Lower 95%Upper 95%ower 95.09pper 95.0% -3.566803928 1.833228053 -1.94564 0.066644378 -7.40379 0.270186 -7.40379 0.270186 0.001128613 0.000528513 2.135451 0.045960162 2.24E-05 0.002235 2.24E-05 0.002235 0.622160308 0.106933849 5.818179 1.32358E-05 0.398345 0.845975 0.398345 0.845975 -0.003949842 0.000872358 -4.52777 0.000230214 -0.00578 -0.00212 -0.00578 -0.00212 0.021857361 0.009303567 2.349353 0.029771428 0.002385 0.04133 0.002385 0.04133 -2.39869E-06 5.49399E-06 -0.4366 0.667320685 -1.4E-05 9.1E-06 -1.4E-05 9.1E-06

We can see that Adjusted R square keep on increasing as we add more and more variables but on final table adjusted R square has decresed and P value for the variable named FrancePop (in Red colored is greater than 0.05 so that variable is insignificant.

Therefore, we have only these four variables in the model

AGST, Age, WinterRain, HarvestRain (Option third)