Question: I have been asked to perform two linear regression as it follows. The 1st one: the dependent variables from a set of values A and
I have been asked to perform two linear regression as it follows. The 1st one: the dependent variables from a set of values A and the independent variables from the a set of values B. For the second one: the same dependent variables from A but the independent variables from B are natural logarithms, in this case. Why do the results of the two regressions differ? (besides the fact that one has logarithms an the other doesn't)


SUMMARY OUTPUT Regression Statistics Multiple R 0,725859767 R Square 0,526872401 Adjusted R Square 0,523800144 Standard Error 0,103930441 Observations 156 ANOVA df SS MS F Significance F Regression 1 1,8523943 1,8523943 171,4935886 8,26959E-27 Residual 154 1,6634366 0,0108015 Total 155 3,5158309 Coefficients andard Em t Stat P-value Lower 95% Upper 95% ower 95,0%Upper 95,0% Intercept 0,489119963 0,0103102 47,440577 8,3241E-94 0,468752364 0,5094876 0,4687524 0,5094876 GDP per capita, PPP 5,38299E-06 4,111E-07 13,095556 8,26959E-27 4,57096E-06 6,195E-06 4,571E-06 6,195E-06SUMMARY OUTPUT LOG Regression Statistics Multiple R 0,878552 R Square 0,771853 Adjusted F 0,770372 Standard E 0,072171 Observatic 156 ANOVA df SS MS F ignificance F Regression 1 2,713706 2,713706 521,0045 2,79E-51 Residual 154 0,802125 0,005209 Total 155 3,515831 Coefficientsandard Er t Stat P-value Lower 95% Upper 95% ower 95,09/pper 95,0% Intercept -0,19509 0,033963 -5,744118 4,79E-08 -0,262184 -0,127995 -0,262184 -0,127995 log GDP 0,088432 0,003874 22,82552 2,79E-51 0,080778 0,096085 0,080778 0,096085
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