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Scenario: Multivariate Regression with Diagnostics in SAS

A graduate student is given a dataset containing variables related to healthcare expenditure. The task is to build a multiple linear regression model predicting annual medical cost based on age, BMI, smoking status, and exercise frequency. Additionally, the student must test for multicollinearity, heteroscedasticity, and influential observations.

Expert Solution Approach

Step One: Data Preparation

Our expert first ensures the dataset is clean and properly formatted.

proc import datafile="health_data.csv"
out=healthdb
dbms=csv
replace;
getnames=yes;
run;

Next, categorical variables such as smoking status are converted into dummy variables.

data healthdb;
set healthdb;
if smoker="Yes" then smoker_dummy=1;
else smoker_dummy=0;
run;

Step Two: Running the Regression Model

proc reg data=healthdb;
model medical_cost = age bmi smoker_dummy exercise_freq / vif tol;
output out=regout rstudent=r p=predicted cookd=cookd;
run;
quit;

Explanation of Key Components:

The vif and tol options assess multicollinearity.

The rstudent option calculates studentized residuals.

Cook’s Distance identifies influential observations.

Step Three: Checking Heteroscedasticity

proc sgplot data=regout;
scatter x=predicted y=r;
refline 0 / axis=y;
run;

A random scatter of residuals around zero suggests homoscedasticity. If a funnel pattern appears, heteroscedasticity may exist.

Interpretation:

If VIF values exceed 10, multicollinearity is problematic.

Significant predictors are identified via p-values.

Observations with high Cook’s D require further examination.

Our expert would conclude by summarizing the statistical significance, model fit (R-square), and any assumption violations. This structured explanation ensures that the student not only submits correct SAS code but also understands the interpretation required at the master’s level.

Scenario: Logistic Regression with Model Validation

Another advanced assignment involves predicting whether a patient develops a chronic condition based on cholesterol level, blood pressure, and family history. Since the outcome variable is binary, logistic regression is appropriate. The student must also evaluate model performance using ROC analysis.

Expert Solution Approach

Data Preparation

data patientdb;
set patient_data;
if family_history="Yes" then famhist=1;
else famhist=0;
run;

Running Logistic Regression

proc logistic data=patientdb descending;
model disease_status = cholesterol bp famhist;
output out=logout p=predprob;
run;

The descending option ensures that the model predicts the probability of disease occurrence.

Generating ROC Curve

proc logistic data=patientdb plots=roc;
model disease_status = cholesterol bp famhist;
run;

Interpreting Results

Odds ratios explain how a one-unit increase in a predictor affects the odds of disease.

A significant Wald Chi-Square test indicates meaningful predictors.

The ROC curve evaluates classification accuracy.

An Area Under the Curve (AUC) above 0.7 indicates acceptable discrimination.

Our expert would carefully explain the meaning of odds ratios in context. For example, if the odds ratio for cholesterol equals 1.08, it suggests that each unit increase in cholesterol increases disease odds by 8%, holding other variables constant.

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Verification of model assumptions

Diagnostic evaluation

Professional formatting and documentation

Logical conclusions tied to theory

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