This data table contains the listed prices and weights of the diamonds in 48 rings offered for sale in The Singapore Times. The prices are in Singapore dollars, with the weights in carats. Use price as the response and weight as the explanatory variable. These rings hold relatively small diamonds, with weights less than 1 / 2 carat. The Hope Diamond weighs in at 45.52 carats. Its history and fame make it impossible to assign a price, and smaller stones of its quality have gone for $600,000 per carat. Let’s say 45.52 carats × $750,000 / carat = $34,140,000 and call it $35 million. For the exchange rate, assume that 1 U.S. dollar is worth about 1.6 Singapore dollars.
(a) Add an imaginary ring with the weight and this price of the Hope Diamond (in Singapore dollars) to the data set as a 49th case. How does the addition of the Hope Diamond to these other rings change the appearance of the plot? How many points can you see?
(b) How does the fitted equation of the SRM to this data change with the addition of this one case?
(c) Explain how it can be that both R2 and se in-crease with the addition of this point.
(d) Why does the addition of one point, making up only 2% of the data, have so much influence on the fitted model?