8.13. Lung pressure  Source: Neter Problem 8.13 po 357


Increased arterial blood pressure in the lungs frequently leads to 
the development of heart failure in patients with chronic 
obstructive pulmonary disease (COPD). The standard method for 
determining arterial lung pressure is invasive, technically 
difficult, and involves some risk to the patient. Radionuclide 
imaging is a noninvasive, less risky method for estimating 
arterial pressure in the lungs. To investigate the predictive 
ability of this method, a cardiologist collected data on 19 mild-
to-moderate COPD patients. The data that follow on page 358 
include the invasive measure of systolic pulmonary arterial 
pressure (Y) and three potential noninvasive predictor variables. 
Two were obtained by using radioouclide imaging  Ñ emptying rate 
of blood into the pumping chamber of the heart (X1) and ejection 
rate of blood pumped out of the heart into the lungs (X2) Ñ and 
the third predictor variable measures a blood gas (X3).

a. Prepare separate dot plots for each of the three predictor 
variables. Are there any noteworthy features in these plots? 
Comment.

b. Obtain the scatter plot matrix. Also obtain the correlation 
matrix of the X variables. What do the scatterplots suggest about 
the nature of the functional relationship between Y and each of 
the predictor variables? Are any serious multicollinearity 
problems evident? Explain.

c. Fit the multiple regression function containing the three 
predictor variables as first order terms. Does it appear that all 
predictor variables should be retained? 


8.14. Refer to Lung pressure Problem 8.13.

a. Using first-order and second-order terms for each of the three 
predictor variables (centered around the mean) in the pool of 
potential X variables (including cross products of the first-order 
terms), find the three best hierarchical subset regression models 
according to the Ra2 criterion.

b. Is there much difference in Ra2 for tbe three best subset 
models? 

    Y      X1     X2     X3

   49.0   45.0   36.0   45.0
   55.0   30.0   28.0   40.0
   85.0   11.0   16.0   42.0
   32.0   30.0   46.0   40.0
   26.0   39.0   76.0   43.0
   28.0   42.0   78.0   27.0
   95.0   17.0   24.0   36.0
   26.0   63.0   80.0   42.0
   74.0   25.0   12.0   52.0
   37.0   32.0   27.0   35.0
   31.0   37.0   37.0   55.0
   49.0   29.0   34.0   47.0
   38.0   26.0   32.0   28.0
   41.0   38.0   45.0   30.0
   12.0   38.0   99.0   26.0
   44.0   25.0   38.0   47.0
   29.0   27.0   51.0   44.0
   40.0   37.0   32.0   54.0
   31.0   34.0   40.0   36.0

Adapted from A. T. Marmor et al.. "Improved 
Radionuclide Method for Assessment of Pulmonary 
Artery Pressure in COPD," Chest 89 (1986), pp. 64-
69.