1) The file Diamond.xls contains data on pricing of ladies' diamond rings, based on the weights of the diamonds. The data were originally given in a full page advertisement placed in the Straits Times newspaper issue of February 29, 1992, by a Singapore based retailer of diamond jewelry. The 48 rings considered in this data set were similar in terms of design, gold weight, and the diamond qualities of cut, color and clarity. Therefore, the carat size of the diamond stones becomes the obvious factor to use in pricing the rings. The variables in Diamond.xls are Weight (in carats), and Price (of the ring, in Singapore Dollars). A) Make a scatterplot of Price versus Weight, and comment on the reasonableness of fitting a linear regression model to this data. B) Run the regression of Price on Weight. Copy and paste the Minitab regression output. C) What is the equation of the fitted tine? Use this equation to predict the price of a diamond ring which weighs 0.23 carats. D) Is there evidence of a significant linear relationship between the price and the weight of the diamond? Justify your answer. E) Interpret the estimated slope of the fitted model, and construct a 95% CI for the true slope coefficient. What is the practical meaning of the true slope coefficient? F) Discuss and give a practical interpretation of the coefficient of determination, R- Squared for this problem. G) What is the estimate of the typical fluctuation of data points from the true regression line, measured in the vertical direction for this problem? H) At the 1% level of significance, can we reject the null hypothesis that the true slope is 3500 in favor of the alternative that it is not 3500? |) Using Minitab, construct a 95% confidence interval for the expected price of a ring which weighs 0.23 carats