Biology Forums - Study Force

An article in the Journal of Statistics Education reported the price of diamonds of different sizes in Singapore dollars (SGD). The following table contains a data set that is consistent with this data, adjusted to US dollars in 2004:


Make a scatterplot and describe the association between the size of the diamond (carat) and the cost (in US dollars).

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An article in the Journal of Statistics Education reported the price of diamonds of different sizes in Singapore dollars (SGD). The following table contains a data set that is consistent with this data, adjusted to US dollars in 2004:


Create a model to predict diamond costs from the size of the diamond.

The regression equation is
2004 US $ = - 559 + 8225 Carat


Predicted cost = -558.52 + 8225.1(carat)

TY

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An article in the Journal of Statistics Education reported the price of diamonds of different sizes in Singapore dollars (SGD). The following table contains a data set that is consistent with this data, adjusted to US dollars in 2004:


Do you think a linear model is appropriate here? Explain.

A linear model is appropriate for this problem. The residual plot shows no obvious pattern.

An article in the Journal of Statistics Education reported the price of diamonds of different sizes in Singapore dollars (SGD). The following table contains a data set that is consistent with this data, adjusted to US dollars in 2004:


Interpret the slope of your model in context.

The slope of the model is 8225.1. The model predicts that for each additional carat, the cost of the diamond will increase by $8225.10, on average. This can also be interpreted as for each additional 0.01 carat, the cost of the diamond will increase by $82.251, on average.

Thank you, thank you, thank you!

An article in the Journal of Statistics Education reported the price of diamonds of different sizes in Singapore dollars (SGD). The following table contains a data set that is consistent with this data, adjusted to US dollars in 2004:


Interpret the intercept of your model in context.

The intercept of the model is -558.52. The model predicts that a diamond of 0 carats costs -$558.52. This is not realistic.

An article in the Journal of Statistics Education reported the price of diamonds of different sizes in Singapore dollars (SGD). The following table contains a data set that is consistent with this data, adjusted to US dollars in 2004:


What is the correlation between cost and size?

The correlation, r, is r = = 0.993 . Since the scatterplot shows a positive relationship, the positive value must be used.

An article in the Journal of Statistics Education reported the price of diamonds of different sizes in Singapore dollars (SGD). The following table contains a data set that is consistent with this data, adjusted to US dollars in 2004:


Explain the meaning of R² in the context of this problem.

R² = 0.987 . So 98.7% of the variation in diamond prices can be accounted for by the variation in the size of the diamond.

An article in the Journal of Statistics Education reported the price of diamonds of different sizes in Singapore dollars (SGD). The following table contains a data set that is consistent with this data, adjusted to US dollars in 2004:


Would it be better for a customer buying a diamond to have a negative residual or a positive residual from this model? Explain.

It would be better for customers to have a negative residual from this model, since a negative residual would indicate that the actual cost of the diamond was less than the model predicted it to be.