EPBI6314: Advanced Regression Models
Homework#1
Reiss et al. compared point-of-care and standard hospital laboratory assays for monitoring patients receiving a single anticoagulant or a regimen consisting of a combination of anticoagulants. In the present study, the researchers obtained measures of international normalized ratio (INR) by assay of capillary and venous blood samples collected from 90 subjects taking warfarin. INR, used especially when patients are receiving warfarin, measures the clotting ability of the blood. Point-of-care testing for INR was conducted with the CoaguChek assay product. Hospital testing was done with standard hospital laboratory assays. The measurements are given in the dataset provided where the hospital assay INR level is denoted X and CoaguChek INR level is denoted Y.
It is quite common when comparing two measuring techniques, to use correlation or regression analysis in which one variable is used to predict another.
Question#1:
Using the given data, perform model diagnostics for both Pearson’s correlation and simple linear regression involving X and Y.
Question#2:

1. What is the strength and direction of the correlation between X and Y?
2. Is the relation statistically significant?
3. Is there a positive correlation between X & Y?
4. Is there a negative correlation between X & Y?
5. Is the relationship between X & Y strong?
6. Is the relationship between X & Y at least moderate?
7. Is the relationship between X & Y weak?

Question#3:

1. What is the correlation between Y and gender.
2. What is the correlation between X and gender.
3. Find partial correlation X & Y while controlling for gender.
4. Is there a statistically significant correlation between X and Y with each categorized such that values
5. the full dataset and
6. subset of first 20 subjects

Question#4:
The authors used the hospital assay INR level (X) to predict the CoaguChek INR level (Y).

1. Obtain the sample regression line and the corresponding ANOVA table.
2. Compute the coefficient of determination, R²
3. Test the over regression model by first stating the appropriate hypothesis and compute the p-value.
4. Test whether the slope and the intercepts are both 0.5 by constructing the appropriate 95% confidence intervals.
5. Construct a 95% confidence interval for the average and the 95% prediction interval for Y given that X=1.6.
6. Construct simultaneous confidence intervals for both the slope and intercept. Use the Bonferroni method to keep the individual and experimental error rates at =0.1.

N.B: Perform all test at the 5% level of significance.