Chu (1996) discusses the development of a regression model to predict the price of diamond rings from the size of their diamond stones (in terms of their weight in carats). Data on both variables were obtained from a full page advertisement placed in the Straits Times newspaper by a Singapore-based retailer of diamond jewelry. Only rings made with 20 carat gold and mounted with a single diamond stone were included in the data set. There were 48 such rings of varying designs. (Information on the designs was available but not used in the modeling.) The weights of the diamond stones ranged from 0.12 to 0.35 carats (a one carat diamond stone weighs 0.2 gram) and were priced between $223 and $1086. The data are available on the course web site in the file diamonds. txt. Part 1
(a) Develop a simple linear regression model based on least squares that directly predicts Price from Size (that is, do not transform either the predictor nor the response variable). Ensure that you provide justification for your choice of model.
(b) Describe any weaknesses in your model.
Part 2
(a) Develop a simple linear regression model that predicts Price from Size (i. e., feel free to transform either the predictor or the response variable or both variables). Ensure that you provide detailed justification for your choice of model.
(b) Describe any weaknesses in your model.
Part 3
Compare the model in Part A with that in Part B. Decide which provides a better model. Give reasons to justify your choice.