The following is a regression analysis of the natural log of the price of wine a

Question

The following is a regression analysis of the natural log of the price of wine against the wine's sensory traits.  

A. How much of the variation in the log of wine's price in this sample is accounted for by the variation in the wine's sensory traits?

B. If wine markets were perfect, so that consumers had perfect information, would we see the results that we do in the regression? explain

SUMMARY OUTPUT Regression Statistics Multiple R 0.572221101 R Square 0.327436988 Adjusted R Square 0.266294897 Standard Error 29.11490437 Observations 193 ANOVA df SS MS F Significance F Regression 16 72633.699 4539.606187 5.35534487 3.66435E-09 Residual 176 149191.2675 847.6776563 Total 192 221824.9665 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 50.63930177 34.11619533 1.484318555 0.139513167 -16.6901829 117.9687864 -16.6901829 117.9687864 INTE 1.52588823 2.932912573 0.520263797 0.603533545 -4.262315589 7.314092049 -4.262315589 7.314092049 FINE -1.90636587 6.081581805 -0.313465466 0.754298238 -13.9085767 10.09584495 -13.9085767 10.09584495 COMP 3.733290514 5.046860369 0.739725342 0.460452202 -6.226861974 13.693443 -6.226861974 13.693443 FIRM -8.78923405 5.22321285 -1.682725615 0.094201367 -19.09742423 1.518956118 -19.09742423 1.518956118 ACID -9.99975600 6.86466925 -1.45669888 0.146981247 -23.54741683 3.54790482 -23.54741683 3.54790482 SUPP -8.53856665 5.087402441 -1.678374526 0.095048703 -18.57873032 1.501597002 -18.57873032 1.501597002 FLAT -10.3418197 7.897668104 -1.309477635 0.192079465 -25.92813934 5.244499836 -25.92813934 5.244499836 FAT -1.74600711 4.971011997 -0.351237758 0.725830092 -11.55647023 8.064456007 -11.55647023 8.064456007 WCON 15.18056455 6.37483207 2.381327757 0.018317871 2.599614247 27.76151486 2.599614247 27.76151486 HARM -2.078335281 3.643660511 -0.570397619 0.569135517 -9.269224597 5.112554035 -9.269224597 5.112554035 TANI -0.494227574 5.58262664 -0.088529577 0.929556432 -11.51173322 10.52327807 -11.51173322 10.52327807 FINI 2.74552043 3.566668488 0.76977169 0.442467258 -4.293422482 9.784463341 -4.293422482 9.784463341 ALCO -7.272123677 8.559785307 -0.849568467 0.396719205 -24.16515433 9.620906978 -24.16515433 9.620906978 STAL 7.04402292 9.780842309 0.720185716 0.47236602 -12.25880572 26.34685156 -12.25880572 26.34685156 REDU -3.798500458 18.83831661 -0.201636937 0.840433428 -40.97656609 33.37956517 -40.97656609 33.37956517 KEEP 23.23849987 5.895770634 3.941554261 0.00011665 11.60299378 34.87400596 11.60299378 34.87400596

Explanation / Answer

Answer to the question with details below:

a. The variation in the dependent variable explained by predictor variables is given by Rsquare. Rsquare is .3274 is 32.74% of variaition in dependent vatriable is being explained by predicted variable.

b. No. instead we would have had a perfect relation such that Rsquare was 1. But since this isn't the case, there are more factors influencing the dependent variable we conclude that we wouldn't see this result if wine markets were and customers had perfect info

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