6.4
Yield strength of steel alloy. Industrial engineers at the University of Florida used
regression modeling as a tool to reduce the time and cost associated with developing new
metallic 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 listed
below.
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 of
predictor 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 t
c. Refer to b. All these variables were statistically significant in the stepwise model to
predict yield strength. Do you agree with this decision? Explain.
7.4
Women in top management. The Journal of Organizational Culture, Communications
and Conflict (July 2007) published a study on women in upper-management positions at
U.S. firms. Observational data (n=252 months) were collected for several variables in an
attempt to model the number of females in managerial positions (y). The independent
variables included the number of females with a college degree ( x 1) , the number of
female high school graduates with no college degree (x 2) , the number of males in
managerial positions (x 3) , the number of males with a college degree (x 4 ) , and the
number of male high school graduates with no college degree (x 5)
a. The correlation relating number of females in managerial positions and number of
females with a college degree was determined to be r=.983. Can the researchers conclude
that an increase in the number of females with a college degree will cause the number of
females in managerial positions to increase? Explain.
b. The correlation relating number of males in managerial positions and number of males
with a college degree was determined to be r=.722. What potential problem can occur in
the regression analysis? Explain.
7.6
Characteristics of sea ice melt ponds. Surface albedo is defined as the ratio of solar
energy directed upward from a surface over energy incident upon the surface. Surface
albedo is a critical climatological parameter of sea ice. The National Snow and Ice Data
Center (NSIDC) collects data on the albedo, depth, and physical characteristics of ice
melt 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 Strait
in the Canadian Arctic are saved in the PONDICE file. Environmental engineers want to
model 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 if
not} and x 3 ={1 if multiyear ice, 0 if not}. Ultimately, the engineers will use the
model to predict the surface albedo level of an ice melt pond. Access the data in the
PONDICE file and identify the experimental region for the engineers. What advice do
you give them about the use of the prediction equation?
7.10
FDA investigation of a meat-processing plant. A particular meat-processing plant
slaughters steers and cuts and wraps the beef for its customers. Suppose a complaint has
been filed with Food and Drug Administration (FDA) against the processing plant. The
complaint 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 of
cut and wrapped beef. To settle the complaint, the FDA collected data on the live weights
and dressed weights of nine steers processed by a reputable meat-processing plant (not
the firm in question). The results are listed in the table.
STEERS
LIVE WEIGHT
x, pounds
420
380
480
340
450
460
430
370
390
a. Fit the model,
DRESSED WEIGHT
y, pounds
280
250
310
210
290
280
270
240
250
E ( 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 determine
whether the dressed weight of 150 pounds is a reasonable amount to receive from a 300pound steer? Explain.
7.14
Yield strength of steel alloy. Industrial engineers at the University of Florida used
regression modeling as a tool to reduce the time and cost associated with developing new
metallic 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 highly
correlated 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)
