Dr. Hans Riedwyl, a statistician at the University of Berne was asked by local authorities to analyze data on Swiss Bank
Posted: Tue Apr 26, 2022 12:21 pm
Dr. Hans Riedwyl, a statistician at the University of Berne was
asked by local authorities to analyze data on Swiss Bank notes. In
particular, the statistician was asked to develop a model to
predict whether a particular banknote is counterfeit ( y = 0) or
genuine ( y = 1) based on the following physical measurements (in
millimeters) of 100 genuine and 100 counterfeit Swiss Bank notes:
Length = length of the banknote Left = length of the left edge of
the banknote Right = length of the right edge of the banknote Top =
distance from the image to the top edge Bottom = distance from the
image to the bottom edge Diagonal = length of the diagonal The data
were originally reported in Flury and Riedwyl (1988) and they can
be found in alr3 library and on the book web site in the file
banknote.txt. Figure 8.20 contains a plot of Bottom and Diagonal
with different symbols for the two values of y .(a) Fit a logistic
regression model using just the last two predictor variables listed
above (i.e., Bottom and Diagonal). R will give warnings including
“fitted probabilities numerically 0 or 1 occurred”. (b) Compare the
predicted values of y from the model in (a) with the actual values
of y and show that they coincide. This is a consequence of the fact
that the residual deviance is zero to many decimal places. Looking
at Figure 8.20 we see that the two predictors completely separate
the counterfeit ( y = 0) and genuine ( y = 1) banknotes – thus
producing a perfect logistic fit with zero residual deviance. A
number of authors, including Atkinson and Riani (2000, p. 251),
comment that for perfect logistic fits, the estimates of the β′ s
approach infinity and the z -values approach zero.
asked by local authorities to analyze data on Swiss Bank notes. In
particular, the statistician was asked to develop a model to
predict whether a particular banknote is counterfeit ( y = 0) or
genuine ( y = 1) based on the following physical measurements (in
millimeters) of 100 genuine and 100 counterfeit Swiss Bank notes:
Length = length of the banknote Left = length of the left edge of
the banknote Right = length of the right edge of the banknote Top =
distance from the image to the top edge Bottom = distance from the
image to the bottom edge Diagonal = length of the diagonal The data
were originally reported in Flury and Riedwyl (1988) and they can
be found in alr3 library and on the book web site in the file
banknote.txt. Figure 8.20 contains a plot of Bottom and Diagonal
with different symbols for the two values of y .(a) Fit a logistic
regression model using just the last two predictor variables listed
above (i.e., Bottom and Diagonal). R will give warnings including
“fitted probabilities numerically 0 or 1 occurred”. (b) Compare the
predicted values of y from the model in (a) with the actual values
of y and show that they coincide. This is a consequence of the fact
that the residual deviance is zero to many decimal places. Looking
at Figure 8.20 we see that the two predictors completely separate
the counterfeit ( y = 0) and genuine ( y = 1) banknotes – thus
producing a perfect logistic fit with zero residual deviance. A
number of authors, including Atkinson and Riani (2000, p. 251),
comment that for perfect logistic fits, the estimates of the β′ s
approach infinity and the z -values approach zero.