Question: Hypertensive Patients

The data in the file Hypertensive.JMP comes from a random sample of n = 20 patients with hypertension. The variables measured on each patient are:

 Y MABP = mean arterial blood pressure (mmHg)

 X1 Age = age in years

 X2 Weight (kg) = patient’s weight in kilograms

 X3 BSA = body surface area (m ² )

 X4 Duration (yrs) = duration of hypertension (yrs.)

 X5 Basal Pulse (bpm) = basal pulse rate in beats per minute

 X6 Stress = measure of stress

1. Construct a scatter plot matrix of these data and find all pair-wise correlations between the variables. Which variable has the strongest correlation with mean arterial blood pressure, i.e. the response? Which variable has the weakest correlation with the response? For which variables do we have evidence that the population correlation coefficient is significantly different from 0? (8 pts.)
   To answer these questions complete the table below:

   Variable	Correlation (r) with mean arterial blood pressure ( p-value )
   Age (yrs.)
   Weight (kg)
   BSA (m 2 )
   Duration (yrs.)
   Basal Pulse (bpm)
   Stress Score

2. Is there any reason to be concerned about the use of the Pearson’s Product Moment Correlation ( r ) for these data? Explain. (2 pts.)
3. Using mean arterial blood pressure as the response and weight (kg) as the explanatory variable or predictor, perform simple linear regression to estimate E(MABP|Weight) using a line. Interpret both the estimated slope and y-intercept of the line and explain what these quantities mean in words. (3 pts.)
4. Check the model assumptions using the appropriate graphical displays. Summarize
   your findings. (3 pts.)
5. Construct and interpret a 95% CI for the true population slope (). (3 pts.)
6. Estimate the mean MABP for the population of individuals weighing 100 kg. (1 pt.)
7. Joe weighs 85.4 kg, estimate Joe’s and also find & interpret a 95% prediction interval
   (PI) for Joe’s mean arterial blood pressure.
   Note: the 1 ^st person in this study has the same weight as Joe. (3 pts.)
8. What the R-square for this regression? Explain in words what this value tells you for
   this particular regression. (2 pts.)
9. How is Pearson’s Product Moment Correlation (r) between MABP and Weight related
   to the R-square for our regression model? (1 pt.)
   Hint: Why do you think the R-square is called what is it?
10. Ernie weights 140 kg can safely estimate his mean arterial blood pressure?
    Explain. (1 pt.)

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