4. The coefficient of determination and the sample correlation coefficient Nambe manufactures a line of metal tableware called Nambewa re. A piece of Nambeware is produced by sand casting a special alloy of several metals. After casting, the piece goes through a series of shaping, grinding, bufng, and polishing steps. Nambe is analyzing how to adjust its production schedule to accommodate the polishing step of a new line of plates that it is adding to its product line. Nambe selects a random sample of its tableware pieces and collects data on the type of piece (tray, dish, bowl, plate, or casserole), its diameter (in inches), its polishing time (in minutes), and its price {in dollars). [Source: Data and Story library {DASL).] The sample data are located in the data set Nambeware. Use the DataView tool to answer the following questions. Sample Variables = 4 0 mm = 59 Random sample of Nambeware pieces Data and Story Liblary iDASL] Observations Variable V Type V Form 9' Values V Missing V Type Qualitative Nonnumeric 59 0 Diameter Quantitative Numeric 59 0 Tlme Quantitative Numeric 59 0 Price Quantitative Numeric 59 0 hriahIe hriahIe hriahIe h'iahie Correlation Correlation Nambe decides to use the 9 pieces in its sample that are plates to form the following estimated regression equation: 3" = 1741 + 0.621 where y = polishing time of aplate (in minutes) and I = the plate '5 diameter (in inches) Using the estimated regression equation, you predict that the polishing time for plates with a 12inch diameter is V minutes. The sample mean polishing time of the Na mbeware sample pieces that are plates is )7 = 24.19. (Note: You can connn this by using the variable Type in the tool to lter the Nambeware pieces so that only plates are included and then obtain lire mean for the ltered sample.) Consider a parlicular plate in lire sample, say, plate 7. Plate 7 is identied as P07 in the column labeled Piece in the tool's Observation view. The error involved in using if to predict the polishing time for plate 7 is V minutes. Consider the contribution of a particular sample observationsay plate }'to the SST, SSR, and SSE. Plate Ts contribution to the SST is V its contribution to the SSR is V , and its contribution to the SSE is V . In this regression analysis, the SSR is 39.60, and lire SSE is 106.0. What percentage of the variability in the polishing lime of Nambeware plates can be explained by the estimated regression equation? 0 52% O 212% O 0.5% 0 0.271918% Use the convention from the social sciences regarding the usefulness of the estimated regression equation based on its :2. The Nambeware managers V be condent using the estimated regression equation to predict the polishing limes for the new line of plates. The sample correlation coefficient r\" is v