1.A study is conducted in patients with HIV. The primary outcome is CD4 cell count, which is a measure of the stage of the disease. Lower CD4 counts are associated with more advanced disease. The investigators are interested in the association between vitamin and mineral supplements and CD4 count. A multiple regression analysis is performed relating CD4 count to the use of supplements (coded as 1 = yes and 0 = no) and to the duration of HIV in years (i.e., the number of years between the diagnosis of HIV and the study date). For the analysis,y= CD4 count.You obtain the following linear regression line.

a.Based on the model, how much would use of supplements help offset the effects of duration on CD4 count?That is, if CD4 count declines an average of 30.23 per year, how much of a year of time does use of supplements offset?

b.If we were to compare two patients and one has had HIV for 5 years longer than the other, what is the expected difference in their CD4 counts?