1. An article in the Journal of Statistics Education reported the price of diamo
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Question
1. An article in the Journal of Statistics Education reported the price of diamonds of ditferent US dollars in dollars (SGD). The following table contains a data set that is consistent with this data, adjusted to 2004: 68824 0.1 63 a) the the size of the diamond (carat) and the cost (in US dollars) based on the ncrecses he model to predict diamond costs from the size of the diamond that isthe regression equation is 559+8225 x b) Do you think a linear model is appropriate here? Esplain, tho duts are cuose enungn ro Rsvm a Pro c) Interpret the slope of your model in context. The Slope oF the mo c is d) Interpret the intercept of your model in context The intercept iS the meam vane o e) Explain the meaning of R2 in the context of this problem. (R2-0.987.) 2- 0 What is the correlation between cost and size? Explain the meaning.ge dire s the inrease de cart aJedt un us clurars The ayne (ancn berween cca and SIZE nen taSize of the Cart menocses, +he cost in is 8) Would it be better for a customer buying a diamond to have a negative residual or a positive residual from 1S this model? Explain. It Is beic or a Cushamo ing a dependar diamumel tne pace othe diamund wouid bocause tho Pnce oExplanation / Answer
D) The intercept is the expected mean value of Y when all X=0. Start with a regression equation with one predictor, X. If X never = 0, then the intercept has no intrinsic meaning.
E) R2 = 0.987 = 98.7%
98.7% of the variation in the diamond cost (dependent variable) is explained by size of the diamond(independent variable)
F) We have R2 = 0.987
Therefore R = 0.9935
There exists a high positive correlation(R= 0.9935) (from the scatter diagram) between size of the diamond and diamond cost. I.e. both the variables are deviated in the same direction.
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