10.16 Characteristics ot diamonds sold at retail . Kele to //Journal of Statisti

Question

10.16 Characteristics ot diamonds sold at retail . Kele to //Journal of Statistics Education data on 308 diamonds for sale on the open market, saved in the DIAMONDS file. In Exercise 2.121 (p. 93), you related the size of the diamond (number of carats) to the asking price (dollars) using a scatterplot. Write the equation of a straight-line model relating asking a. price v) to number of carats (x) b. A Minitab simple linear regression printout for the data is shown on page 574. Find the equation of the least squares line. c. Give a practical interpretation of the y-intercept of the least squares line. If a practical interpretation is not possible, explain why d. Give a practical interpretation of the slope of the least squares line. Over what range of x is the interpretation meaningful? e. Use the least squares line to predict the asking price of a 52-carat diamond

Explanation / Answer

a) The equation of a striaght line model is
price = 2298 + 11599 Carat

b) From the the regression equation is
price = 2298 + 11599 Carat

c) If carat is zero then the price will be 2298 + 11599 (0) = $ 2298
which is meaning less becasue there is no carat generally the price is zero but the prediction equation given 2298.

d) slope of the carat is 11599 which is >0, so there exist positive correlation between them
that means, as carat increase 1 unit then price will be increase 11599
e) the predict the asking price at 52 carat diamond is 2298 + 11599 *52 = 605446

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