Weight Price

0.19 509

0.27 806

0.36 974

0.12 124

0.15 372

0.35 1,120

0.38 1,164

0.38 1,099

0.34 935

0.31 902

The accompanying data table contains the prices and weights of the diamonds in 10 rings oered for sale. The prices are in dollars and the weights in carats. A simple regression model (SRM) of the data is also found below. Add an imaginary diamond that weighs 41.45 carats and cask $35 million to the dam and construct a new SRM. Use price as the response and weight as the explanatory variable. Complete parts a through d below. a Click the icon to view the data. Click the icon to view the SRM. (a) How does the addition of the imaginary diamond to the other rings change the appearance of the plot? How many points can you see? 0 A. Only the nearly vertical least squares line passing through the point for the imaginary diamond is visible. 0 B. All the points are visible, but due to the scaling, the 10 smaller rings are tightly clustered. O 6. Due to the scaling, only two points are visible, one for the imaginary diamond and one for the other 10 rings. 0 D. Only the neariy horizontal least squares line passing through the point for the imaginary diamond is visible. (b) How does the tted equation of the SRM to this data change with the addition of this one case? The slope W from 3.521 to dollars/carat and the intercept from -203 to dollars. (Round to the nearesT whole number as needed.) (c) Explain how it can be that both r2 and se increase with the addition of this point. The value of l2 increases because V of the variation in the new V variable is the difference between the rings with small diamonds and the huge imaginary diamond. The value of se increases because a V error in tting the imaginary diamond is i: compared to the i: of the smaller diamonds. (d) Why does the addition of one point have so much inuence on the tted model? 0 A. There are lurking variables that determine the price of a diamond. O B. The addition of the imaginary diamond causes the variation to change. 0 C. The imaginary diamond is a leveraged outlier. O D. The data about weight and price are not independent