Question: The price (in $) and the carat weight of a diamond are its two most known characteristics. In order to understand the role carat weight has in determining the price of a diamond, the carat weight and price of 20 loose round diamonds, all of color D and clarity VS1, were obtained recently as shown below.

1. Draw a scatter diagram of the data: carat weight ( x ) and price ( y ).
2. Does the data suggest a linear relationship for the domain 0.50 to 0.66 carats?? Discuss your findings in question 205.
3. Diamonds smaller than 0.50 carats and diamonds larger than 0.66 carats may not fit the linear pattern demonstrated by this data. Explain.
4. Use computer to find the equation for the line of best fit.
5. According to the results obtained in question 208, what would be a typical price for a 0.50 carat loose diamond of this quality?
6. On the average, by how much does the price increase for each extra 0.01 carat in weight? Within what interval of x- values would you expect this to be true?
7. Use computer to find the variance of y about the regression line.
8. Graph and display the line of best fit on the scatter diagram. What characteristics in the scatter diagram support the large value obtained in question 211?

Price: $2.99

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