Problem 3 The data in the sheet diamond relates diamond carats (y) to purchase prices (m). It appeared in Singapore's Business Times, February 18, 2000. a. Graph the data. What is the relation between carat and price? Is there an outlier? b. Fit a. simple linear regression model. c. Test for significance of the regression model and calculate R2. What conclusions can you draw? d. Analyze the residuals and comment on model adequacy. Identify problematic high leverage points and outliers. c. Fit two regression models, one with all the data and the other with unusual data omitted. Estimate the slope coefficient with a 95% confidence interval in both cases. Comment on any difference