Many factors affect the price of wine including such qualitative chatecteristics

Question

Many factors affect the price of wine including such qualitative chatecteristics es the variety of grape location of winery and label Researchers developed a regression model considering two quantitative v8riables: the tastine score of the wine and the ege of the wine lin years) when released to merkel They found the following regress dollars) of a bottle of equation, with Pnoe 6.25 -22 Tasting Score +0.55 Age One of the folowing interpretations is correct. Which it? Explin what is wrong with the others. a Each year a bottle of wine ages, iE price increase RRbout Sa55 A. This interpretation has the wrong age It should be a $0.55 price for every 6.25 year O B. This interpretation does not mention the tasting score. is not oomeat soit OC The interpretation has the wong price inerease It should be a unit increace in price for every o55 inereaRe in age. O D. This interpretation is corect. b This mode fits 65% of the points exactly. O A. The R vauo is not the number of points that match exoctly, s the peroentvariation in tosting sooro expared by the model. OB The RE value is not the number of points that match exactly itis the percent rariation in age explained by the model. O C. The Ra value is not the number of points tha matchexactly ais the percent variation in price explained by the model D. The interpretetion is comect. c For unit increase in tasting score the price of a bottle of wine ineneases hbout S1.22. A. This interpretation has the wrong prioe It should be a unit price for every 1.22 B. This interpretation has the wrong tssting in proe or every 25 year increase in tasting O C. This interpretation does not mention the age soit is not correct O D. This interpretation is correct. d After slowing for the age of s bottle of a nine with a one unit higher tasting score can be expected to cost about S1.22 more. A. This interpretation does not occount for agecomectly lt should include of 0.55 in the age of the bottle. O B. This interpretation has the wrong tosting soore increase It should be $1.22 increase in price tor every 025 year increase in tasting soore. OC. This interpretation has the wong price It should be a unit increeee price for every 1.22 O D. This interpretation is oorect. Click to select your answer

Explanation / Answer

a) Each year the bottle of wine ages, the age will increase by 1. Now, from the regression, we see that coefficient of age is 0.56 (the picture is hazy, very difficult to see may be 0.66). So, it interprets that, for one unit increase in age, the price will increase by 0.56 unit contingent upon the condition that the value of tasting score remains same. Now, here, there is no tasting score mentioned, so it is not correct. So the option (B) is answer.

b) The model has the R2 = 65%, which implies that, 65% of the total variation in price has been explained by the regression model. It does not mean at all that the model will 65% of the point. In fact, a model with R2 as 99% is a very good model even if it does not fit any of the points. So, option (C) is the answer.

c) For the same reason as explaiined in a) - for one unit increase in tasting score, the price will increase by 1.22 unit contingent upon the condition that the value of age remains same. As the interpretation does not mention age so it is not correct. Option (C) is the answer.

d) For the same reason above, the interpretation is correct as it keeps the age constant. So option (D) is answer.

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