Midterm2011_key

# Midterm2011_key - Stat 704 Midterm Exam Tuesday October 18...

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Unformatted text preview: Stat 704: Midterm Exam, Tuesday October 18 1. Increased arterial blood pressure in the lungs can lead to heart failure in patients with chronic obstructive pulmonary disease (COPD). Determining arterial lung pressure is invasive, difficult, and can hurt the patient. Radionuclide imaging is noninvasive, less risky way to estimate arterial pressure in lungs. A cardiologist measured three potential predictors of arterial blood pressure and the actual (invasive method) arterial blood pressure on n = 19 COPD patients: • x 1 = emptying rate of blood into the pumping chamber of the heart (from ra- dionuclide imaging). • x 2 = ejection rate of blood pumped out of the heart into the lungs (from radionu- clide imaging). • x 3 = a blood gas. • Y = invasive measure of systolic pulmonary arterial pressure Scatterplots of the response vs. each predictor follow (a) Describe the marginal relationship between the response and each predictor. Answer Arterial pressure descreases roughly linearly with emptying rate x 1 ; ar- terial pressure descreases with ejection rate, but the relationship levels off with large values; arterial pressure does not appear to be marginally related to the blood gas. (b) The plot for ejection rate appears curvy; suggest a transformation of ejection rate that could achieve a linear relationship. Answer Roughly, the functional form seems to follow 1 /x 2 or exp(- x 2 ). Here is SAS code and output for a main-effects model: data lung; input y x1 x2 x3 @@; x2sq=x2*x2; label y="arterial pressure" x1="emptying rate" x2="ejection rate" x3="blood gas"; datalines; 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 . 30.0 45.0 40.0 ; proc reg data=lung; model y=x1 x2 x3 / vif; test x1=x3=0;---------------------------------------------------------------------------------------------------- Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model dfR 4966.67801 MSR F 0.0021 Error dfE SSE MSE Corrected Total 18 8087.68421 Parameter Estimates Parameter Standard Variance Variable Label DF Estimate Error t Value Pr > |t| Inflation Intercept Intercept 1 87.18750 21.55246 4.05 0.0011 x1 emptying rate 1-0.56448 0.42791-1.32 0.2069 1.96410 x2 ejection rate 1-0.51315 0.22449-2.29 0.0372 2.38821 x3 blood gas 1-0.07196 0.45457-0.16 0.8763 1.37324 Test 1 Results for Dependent Variable y Mean Source DF Square F Value Pr > F Numerator 2 223.39037 1.07 0.3666 Denominator 15 208.06708 (c) What are the missing values of dfR, dfE, SSE, MSR, MSE, and F in the ANOVA table?...
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## This note was uploaded on 12/14/2011 for the course STAT 704 taught by Professor Staff during the Fall '11 term at South Carolina.

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Midterm2011_key - Stat 704 Midterm Exam Tuesday October 18...

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