Homework 5 (30 points)
STAT 310
Name(s) _____SOLUTION__________
Due: Friday, April 5th by 4pm
A hospital administrator wished to study the relationship between patient satisfaction (PSat) and a
patient’s age (Age), severity of illness (Ill), and anxiety level (Anx) where both the severity of illness and
anxiety level variables are on an index scale. The administrator randomly selected 46 patients and
collected the data which can be found in the file patient.jmp on the course website. Larger values for
patient satisfaction, severity of illness and anxiety level are associated with more satisfaction, increased
severity of illness, and more anxiety, respectively.
1. Using JMP, create a scatterplot matrix of the variables. Provide a detailed sketch of or paste
your plot below. (1 point)
2. Which variable appears to have the strongest linear relationship with patient satisfaction?
(1 point)
Age, since the points are in the tightest linear band.
3. Using JMP, find the estimated correlation between: (1 point)
a. Age and severity of illness
r̂ (Age, Ill) = 0.5680
b. Anxiety level and severity of illness
r̂ (Anx, Ill) = 0.6705
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4. Using JMP fit the multiple linear regression model with all possible predictors. Test for the
overall usefulness of the regression model. Make sure to include your hypotheses, test statistic,
p-value, and conclusion. Provide a detailed sketch of or paste your JMP output below. (5 points)
H0: Regression is not useful
Ha: Regression is useful
Test Statistic = 30.05
p-value = 0.0001
There is evidence that regression is useful
5. Using backward elimination, find the best regression model. Make sure to show each step of
the process. Provide a detailed sketch of or paste your JMP output below. (5 points)
Step 1: Start by fitting the model with all possible predictors.
-
Severity of Illness has the largest p-value = 0.3741
0.3741 > 0.10 so the variable should be removed from the model
Step 2: Fit the model with remaining variables – Age and Anx.
-
Anxiety level has the largest p-value = 0.0086
0.0086 < 0.10 so the variable IS NOT removed.
The elimination process ends and the “best” model has Age and anxiety
level as predictors.
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6. Using the “best” model identified in Question 5, give the estimated regression equation.
(2 points)
Ê (Psat | Age, Anx) = 145.94 – 1.20Age – 16.74Anx
7. Interpret each of the regression coefficients in context from the equation given in Question 6.
(5 points)
Intercept: When Age = 0 and Anx = 0 the best guess for a patient’s satisfaction score is
145.94.
Age: Holding anxiety level constant, for every 1 year increase in Age, a patient’s
satisfaction score decreases by 1.20 points.
Anx: Holding age constant, for every 1 point increase in anxiety level scale, a patient’s
satisfaction score decreases by 16.74 points.
8. Check the assumptions for the model identified in Question 5. Make sure provide a detailed
sketch of or paste ALL the appropriate JMP output below. (10 points)

Looking at the plot of the fitted values vs. residuals, there appears to be a
horizontal band present. There also does not seem to be any patterns/trends.
Thus, the linearity assumption is OK.
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
In both the above plots, there appears to be a horizontal band and no
trends/patterns. Therefore, the assumption of constant variance is OK.

The histogram is approximately bell-shaped and the majority of points follow the
reference line. Therefore, the assumption of normality is OK.

Looking at the above plots, there does not seem to be any obvious outliers.
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