## Statistics- 6.4 Yield strength of steel alloy. Industrial engineers

6.4Yield strength of steel alloy. Industrial engineers at the University of Florida usedregression modeling as a tool to reduce the time and cost associated with developing newmetallic alloys (Modelling and Simulation in Materials Science and Engineering, Vol. 13,2005). To illustrate, the engineers built a regression model for the tensile yield strength(y) of a new steel alloy. The potential important predictors of yield strength are listedbelow.x 1=Carbon amount ( weight )x 2=Manganese amount ( weight )x 3=Chromuimamount ( weight )x 4=Nickel amount ( weight )x 5=Molybdenum amount ( weight )x 6=C opper amount ( weight )x 7=Nitrogen amount ( weight )x 8=Vanadium amount ( weight )x 9=Plate thickness(millimeters)x 10 =Solution treating (millimeters)x 11= Aging temperature (degrees , Celsius)a. The engineers used stepwise regression in order to search for a parsimonious set ofpredictor variables. Do you agree with the decision? Explain.b. The stepwise regression selected the following independent variables:x 1=Carbon, x 2=Manganese , x 3=Chromium , x5 =Molybdenum , x6 =Copper , x 8=Vanadium , x 9=Plate tc. Refer to b. All these variables were statistically significant in the stepwise model topredict yield strength. Do you agree with this decision? Explain.7.4Women in top management. The Journal of Organizational Culture, Communicationsand Conflict (July 2007) published a study on women in upper-management positions atU.S. firms. Observational data (n=252 months) were collected for several variables in anattempt to model the number of females in managerial positions (y). The independentvariables included the number of females with a college degree ( x 1) , the number offemale high school graduates with no college degree (x 2) , the number of males inmanagerial positions (x 3) , the number of males with a college degree (x 4 ) , and thenumber of male high school graduates with no college degree (x 5)a. The correlation relating number of females in managerial positions and number offemales with a college degree was determined to be r=.983. Can the researchers concludethat an increase in the number of females with a college degree will cause the number offemales in managerial positions to increase? Explain.b. The correlation relating number of males in managerial positions and number of maleswith a college degree was determined to be r=.722. What potential problem can occur inthe regression analysis? Explain.7.6Characteristics of sea ice melt ponds. Surface albedo is defined as the ratio of solarenergy directed upward from a surface over energy incident upon the surface. Surfacealbedo is a critical climatological parameter of sea ice. The National Snow and Ice DataCenter (NSIDC) collects data on the albedo, depth, and physical characteristics of icemelt ponds in the Canadian Arctic, including ice type (classified as first-year ice,multiyear ice, or landfast ice). Data for 504 ice melt ponds located in the Barrow Straitin the Canadian Arctic are saved in the PONDICE file. Environmental engineers want tomodel the broadband surface albedo level, y, of the ice as a function of pond depth, x 1(meters), and ice type, represented by the dummy variables x 2 ={1 if first-year ice, 0 ifnot} and x 3 ={1 if multiyear ice, 0 if not}. Ultimately, the engineers will use themodel to predict the surface albedo level of an ice melt pond. Access the data in thePONDICE file and identify the experimental region for the engineers. What advice doyou give them about the use of the prediction equation?7.10FDA investigation of a meat-processing plant. A particular meat-processing plantslaughters steers and cuts and wraps the beef for its customers. Suppose a complaint hasbeen filed with Food and Drug Administration (FDA) against the processing plant. Thecomplaint alleges that the consumer does not get all the beef from the steer he purchases.In particular, one consumer purchased a 300-pound steer but received only 150 pounds ofcut and wrapped beef. To settle the complaint, the FDA collected data on the live weightsand dressed weights of nine steers processed by a reputable meat-processing plant (notthe firm in question). The results are listed in the table.STEERSLIVE WEIGHTx, pounds420380480340450460430370390a. Fit the model,DRESSED WEIGHTy, pounds280250310210290280270240250E ( y )=β 0 +β 1 x, to the data.b. Construct a 95% prediction interval for the dressed weight y of a 300-pound steer.c. Would you recommend that the FDA use the interval obtained in part b to determinewhether the dressed weight of 150 pounds is a reasonable amount to receive from a 300pound steer? Explain.7.14Yield strength of steel alloy. Industrial engineers at the University of Florida usedregression modeling as a tool to reduce the time and cost associated with developing newmetallic alloys (Modelling and Simulation in Materials Science and Engineering, Vol. 13,2005) study in which engineers built a regression model for the tensile yield strength (y)of a new steel alloy. The potential important predictors of yield strength are listed below.The engineers discovered that the independent variable Nickel (x 4 ) was highlycorrelated with each of the other 10 potential independent variables. Consequently,Nickel was dropped from the model. Do you agree with this decision? Explain.x 1=Carbon amount ( weight )x 2=Manganese amount ( weight )x 3=Chromuimamount ( weight )x 4=Nickel amount ( weight )x 5=Molybdenum amount ( weight )x 6=Copper amount ( weight )x 7=Nitrogen amount ( weight )x 8=Vanadium amount ( weight )x 9=Plate thickness(millimeters)x 10 =Solution treating (millimeters)x 11= Aging temperature (degrees , Celsius)

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