5. The coefficient of determination and the sample correlation coefficient Aa Aa

Question

5. 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 bowls 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 Data Set Sample Variables 4 Observations 59 Nambeware Random sample of Nambeware pieces Data and Story Library (DASL) Variables Observations Form Qualitative Nonnumeric Numeric Numeric Numeric Type Variable Type Diameter Values 59 59 59 59 Observations > Missing Quantitative TimeQuantitative Price Quantitative Variable Variable Variable Variable Correlation Correlation

Explanation / Answer

yhat=6.79+2.15x

for x=9 bowls

y hat=6.79+2.15(9)

=26.14

predicitng time for bowls with 9 inch dia is 26.14

For 7 inch bowl polishing time is

y hat=6.79+2.15(7)

=21.84

error=y-yhat

=0bserved-predicted

=27.12-21.84

=5.28 minutes

R sq=SSR/SST

SST=SSR+SSE

=841.40+1902.8

=2744.2

SST=2744.2

RSQ=841.4/2744.2

=0.30661

=0.30661*100

=30.66%

=30.7% (roundinf to nearest integer)

OPTIONC

CANNOT BE CONFIDENT USING THE REGRESSION EQUATION TO PREDICT THE POLISHING TIMES FOR THE NEW LINE OF BOWLS

correlation coefficient

rs q=0.30661

r=sqrt(0.30661)

r=0.553724

r=0.55

correlation coefficient=0.55

  

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