# Discovering Statistical Insights through Correlation Structures and Model Comparison Using SAS

We explore the nuances of correlation structures, conduct meticulous model comparisons, and draw compelling inferences. From understanding within-subject errors to deciphering AICc values, this showcase provides a comprehensive glimpse into the power of SAS in unraveling complex data patterns. Join us on a journey through code, coefficients, and conclusions, demystifying statistical intricacies with clarity and precision.

## Assignment 1: Correlation Structure Analysis

### Problem Description:

This SAS assignment focuses on analyzing the correlation structure of a dataset related to weight changes over several weeks under different treatments. Three correlation structures—CS, AR (1), and UN—were evaluated, and their corresponding AICc values are presented for model comparison.

Solution:

/* First-order autoregressive */ proc mixed data=work.guineapig; class week trt; model weight = week trt week*trt / s; repeated / type=ar(1) sub=week rcorr r; run;

## Assignment 2: Correlation Coefficients

### Problem Description:

In this segment, the correlation coefficients between within-subject errors for specific weeks are explored for each correlation structure. The focus is on understanding the relationships within the dataset.

Correlation structure correlation between within-subject errors for weeks 1 and 2 correlation between within-subject errors for weeks 1 and 6
CS 0.200 0.200
AR (1) 0.4701 0.02297
UN 0.02462 0.09612

Table 1: the construction structure’s relationship with the coefficients

Correlation structure Correlation (Weeks 1 and 2) Correlation (Weeks 1 and 6) CS 0.200 0.200 AR (1) 0.4701 0.02297 UN 0.02462 0.09612

## Assignment 3: Model Comparison and Hypothesis Testing

### Problem Description:

This part delves into model comparison using the AICc values, identifying AR (1) as the best fit. The hypothesis testing involves a chi-square test statistic, concluding that the effect of the vitamin E treatment varies across weeks.

AICc-best: AR (1) Chi-square test statistic = 8.43, df = 1 Pr > Chisq = 0.0037 Conclusion: Reject null hypothesis, evidence of treatment effect variation across weeks.

## Assignment 4: Interpretation of Asterisks

### Problem Description:

Here, the meaning of asterisks () in statistical output is explained. For example, '' = 0.2 indicates a specific value, while '*' = "It is not possible to determine the value of the removed element" explains situations where certain values are indeterminable.

(a) * = 0.2 (b) * = It is not possible to determine the value of the removed element (c) * = 0.1

## Assignment 5: Statistical Inference

### Problem Description:

Comparing patients based on sex and ST segment depression, this task concludes the likelihood of coronary heart disease in older vs. younger patients.

Older patients are significantly less likely to have coronary heart disease than younger patients when controlling for sex and ST segment depression.

## Assignment 6: Logistic Regression Calculation

### Problem Description:

The assignment involves the calculation of logistic regression, estimating the logit for a specific value (55 in this case).