Question: A hospital administrator wished to study the relationship between patient satisfaction (Y) and patient's age (X₁, in years), severity of illness (X₂, an index), and anxiety level (X₃, index). The administrator randomly selected 23 patients and collected the data presented in patient_2008.JMP. Larger values of Y, X₂ and X₃ are associated with more satisfaction, increased severity of illness and more anxiety, respectively. Use the data to answer the following questions using JMP.

a. Obtain the scatter plot matrix and correlation matrix for the 4 variables. Interpret the correlations and state your principle findings.

b. i. Fit the regression model Y = β₀ + β₁(X₁) + β₂(X₂) + β₃(X₃) + ε (model 1)

to the data and state the estimated regression equation/function.

ii. Give the interpretation of b₂ (estimate of β₂).

c. Obtain the residuals and prepare a boxplot of the residuals. Do there appear to be any outliers?

d. Test that the regression model is significant in explaining satisfaction at the 0.05 level of significance. State hypotheses, test statistic, p-value and conclusion in the context of the problem.

e. Using SSR, SSE and SST, compute R-squared (show work) and explain what this value means.

f. Obtain a 95% interval estimate for the mean satisfaction when x₁ = 35, x₂ = 45 and x₃ = 2.2. What does this interval mean? Note: You may add a new observation (observation 24) where y (satif) is missing (.), and x₁=35, x₂=45 and x₃=2.2. JMP will fit the regression model only on the complete records but will make intervals for each observation in the dataset.

g. Obtain a 95% prediction interval for a new patient's satisfaction when x₁ = 35, x₂ = 45 and x₃ = 2.2 . What does this interval mean?

h. Looking at the correlation matrix, VIFs and scatterplots, is multi-collinearity a concern? Explain.

i. Fit the model = β₀ + β₁(X₁) + ε (model 2). Using this output and the previous model output, test H_o: β₂= β₃=0. Give test statistic (computed by hand), critical value and decision.

j. Based on adjusted R-Square for model 1 and model 2, which model would you use to explain patient satisfaction? Explain.