Diamond Rings 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.
(a) Scatterplot the listed prices of the rings on the weights of the rings. Does the trend in the average price seem linear?
(b) Estimate the linear equation using least squares. Interpret the fitted intercept and slope. Be sure to include their units. Note if either estimate represents a large extrapolation and is consequently not reliable.
(c) Interpret the summary values
and
associated with the fitted equation. Attach units to these summary statistics as appropriate.
(d) What is the estimated difference in price (on average) between diamond rings with diamonds that weigh 0.25 and 0.35 carat?
(e) The slope in this regression is a lot larger than the slope for the emerald diamonds discussed in this chapter. Or is it? Notice that one Singapore dollar is currently worth about
and convert the slope to an analysis in U.S. dollars.
(f) These are rings, not diamonds. How would you expect the cost of the setting to affect the linear equation between weight and price?
(g) A ring with a 0.18-carat diamond lists for $325 Singapore. Is this a bargain?
(h) Plot the residuals from this regression. If appropriate, summarize these by giving the mean and standard deviation of the collection of residuals. What does the standard deviation of the residuals tell you about the fit of this equation?