Difference between revisions of "Diamonds Regression Lab"
| Line 7: | Line 7: | ||
weight = density*pi/4 * x*y*z. | weight = density*pi/4 * x*y*z. | ||
| − | If diamonds were cut as cones the relationship would be | + | If diamonds were cut as right-circular-cones the relationship would be |
weight = density*pi/12 * x*y*z. | weight = density*pi/12 * x*y*z. | ||
Revision as of 19:23, 26 August 2019
This Lab is Under Construction
The size of a diamond can described by its dimensions (x, y, and z) and by its weight (usually expressed in carats). We are going to investigate the relationship between these two descriptions.
The weight of a diamond is its volume times its density. As you might imagine, the shape of a diamond matters. If diamonds were cut as cylinders, the relationship would be:
weight = density*pi/4 * x*y*z.
If diamonds were cut as right-circular-cones the relationship would be
weight = density*pi/12 * x*y*z.
In both cases, the weight is a number (coefficient) times the product of the dimensions. The coefficient on x*y*z is the same for all diamonds of the same shape.
You are going to find this coefficient for "round cut" diamonds, but note the shape of different diamonds may be slightly different, depending on the diamond. You want to find a formula that predicts weight in terms of x, y, and z (listed in a data set). Your formula would be very useful for a jeweler! Measuring the dimensions of a diamond is sometimes prone to error, and if a round cut diamond doesn't follow the formula, that would suggest to the jeweler that they should check that the diamond really has a proper round cut and check that the measurement have been performed correctly.
