Question

CD4 cells are carried in the blood as part of the human immune system. One of the effects of the HIV virus is that these cells die. In this study of the effectiveness of a new anti-viral drug on HIV, 20 HIV-positive patients had their CD4 counts recorded (“Baseline”) and then were put on a course of treatment with this drug. After using the drug for one year, their CD4 counts were again recorded (“OneYear”). The aim was to show that patients taking the drug had increased CD4 counts which is not generally seen in HIV-positive patients.

Baseline	OneYear
2.12	2.47
4.35	4.61
3.39	5.26
2.51	3.02
4.04	6.36
5.1	5.93
3.77	3.93
3.35	4.09
4.1	4.88
3.35	3.81
4.15	4.74
3.56	3.29
3.39	5.55
1.88	2.82
2.56	4.23
2.96	3.23
2.49	2.56
3.03	4.31
2.66	4.37
3.00	2.40

1) What is the correlation between baseline and one year CD4 counts?

           

2) What does this suggest about the relationship between baseline and one year CD4 counts?

3) What is the least squares equation of the fitted regression line?

            OneYear =                                 

4) In terms of the above, what would be the null hypothesis to test the association between the baseline and one year follow-up values?

Answer 1

1) r=0.72 chack in image , with calculations

2) there is positive correlation between them, but not strong not bad relationships  between tham... check in image

draw scatter diagram you can see how they perform....

3) we crest model linear regression. Check in image...with calculations