1. The coefficient of determination and the sample correlation coefficient Aa Aa
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Question
1. The coefficient of determination and the sample correlation coefficient Aa Aa Nambe manufactures a line of metal tableware called Nambeware. 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, buffing, and polishing steps Nambe is analyzing how to adjust its production schedule to accommodate the polishing step of a new line of dishes 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 question:s Data Set Sample Variables 4 Observations 59 Nambeware Random sample of Nambeware pieces Data and Story Library (DASL) Observations values 59 59 59 59 Variable Type Missing Form Qualitative Nonnumeric Numeric Numeric Numeric Observations > Type Diameter Quantitative Time Quantitative Price Quantitative Variable Variable Variable Variable Let equal the mean polishing time of the population of Nambeware dishes. The point estimate of is minutes Hint: The data contained in the DataView tool includes five different types of Nambeware. To filter the data in order to display the data for the pieces in the sample that are dishes only, click on a Variable sliding panel on the bottom left of the tool and from the dropdown menu, select Type. In the Filter column, uncheck all the types except Dish. Check that the bottom of the tool display shows Filter: Type Dish. Then click another Variable sliding panel and from the dropdown menu, select Time. Statistics for the Nambeware pieces that are dishes are now shown on the tool display in the column labeled "Filtered." Now consider a particular dish in the sample, say, dish 7. Dish 7 is identified as D07 in the column labeled Piece in the tool's Observation view. The error involved in using the point estimate of as the polishing time for dish 7 is (Hint: To see individual observations, click on Data Set in the top left side of the tool, click on Data Set. Then click on the Observations button to switch from Variables view to Observations view.) minutes Nambe uses the 7 pieces in its sample that are dishes to estimate the simple linear regression model that predicts the polishing time from the dish's diameter: where y polishing time of a dish (in minutes) and x the dish's diameter (in inches) The estimated regression equation is y-5.43 + 4.55 Using the estimated regression equation, the estimated mean polishing time for dishes with a 9-inch diameter is minutes Consider the contribution of a particular sample observation-say dish 7-to the SST, SSR, and SSE. Dish 7's contribution to the SST is , its contribution to the SSR is , and its contribution to the SSE isExplanation / Answer
The estimated mean polishing times is: -5.73+4.55*9=35.22
The percentage of variability which can be explained by the estimated regression equation is:
SSE/SSR
=501.9/668=75.1%
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