## 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.

**Answer:**

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).

**Answer:**

**
**

the estimated logit g(55)= ln(p(55)/(1-p (55) ))= 3.3181+ 1.4180*1-0.0975*55

= -.6264

P (55) = e^(-.6264)/(1+e^(-.6264) )

= 0.3483