Data have been collected on diamonds where x = size as measured in carats and y = price in dollars. The diamonds in this study ranged in size from just over a tenth of a carat to just over a third of a carat. If these data are used to obtain a least-squares regression line, should we use that line to predict the cost of a 2.0 carat diamond?

Question

24-12-2019
Mathematics

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Data have been collected on diamonds where x = size as measured in carats and y = price in dollars. The diamonds in this study ranged in size from just over a tenth of a carat to just over a third of a carat. If these data are used to obtain a least-squares regression line, should we use that line to predict the cost of a 2.0 carat diamond?

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AlonsoDehner AlonsoDehner · Answer 1 · 2019-12-26T06:15:25+01:00

Answer:

Since 2 carat is not near to the range (1/10, 1/3) we can say this will not help to

predict the cost of a 2.0 carat diamond

Step-by-step explanation:

given that data have been collected on diamonds where x = size as measured in carats and y = price in dollars.

Also given that here x the size measured ranged in size from just over a tenth of a carat to just over a third of a carat.

Thus the regression equation obtained using these sizes would be accurate only in predicting the prices of diamonds if sizes are nearly in this range.

Otherwise, the regression equation cannot help to predict the price.

Since 2 carat is not near to the range (1/10, 1/3) we can say this will not help to

predict the cost of a 2.0 carat diamond