Please do all the parts~ Thx! 1. Do we really need wine tasting experts? In a 20

Question

Please do all the parts~ Thx!

1. Do we really need wine tasting experts? In a 2009 paper, researchers tried to use machine learning to predict wine quality scores (given by wine tasting experts) using various chemical properties (determined through physicochemical measurements). Let's make robots as good as humans! One theory you might have is that wines with a higher alcohol concentration will make tasters happier, and hence, earn better scores. I ran this linear regression on the white wine dataset from the paper and got this regression equation: wine score 2.58+0.313 (alcohol concentration a. Interpret what the numbers mean in the above equation and give their units b. Suppose your model predicts that a wine will get a score of 9.2. What is the alcohol concentration for that wine? c. If the standard deviation in the quality scores is 0.8856, and the standard deviation in the alcohol concentrations is 1.2306, what is the correlation between these two variables? d. After seeing the above analysis, your friend, who is a negociant, has the idea of creating a wine with a very high alcohol concentration because this will lead to a wonderful rating. Give two statistical reasons why this logic is faulty.

Explanation / Answer

The general form of regression equation is

y^ = intercept + slope *x

a) We have given equation as : wine score = 2.58 + 0.313 * alcohol score.

So 2.58 is intercept and 0.313 is slope.

Interpretation of slope : If the alochol is increased by 1 unit , we predict the wine score will increase approximately 0.313 units .

Interpretation of intercept :If the alcohol score is 0 , then the win score is 2.58 units .

b) we have given wine score = y^ = 9.2 , we have to find x .

we have to plug y^ = 9.2 in givn equation

So 9.2 = 2.58 + 0.313 * x

    9.2 - 2.58 = 0.313 *x

    6.62 = 0.313 *x

So x = 6.62 / 0.313 = 21.15

c) We know that slope = r* Sy / Sx

So we can write r = Slope * Sx/ Sy

                           = 0.313 * (1.2306/0.8856)

                           = 0.4349

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