A study is conducted in a patient with HIV.Lower CD4 count is associated with advance disease. A researcher is interested in the association between vitamin supplement and CD4 count.A MULTIPLE REGRESSION ANALYSIS is performed relating CD4count to the use of supplements(coaded as 1=yes, 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= CD4count
y hat= 501.41+12.67(supplement)-30.23(duration of HIV).
a) What is expected CD4 count for patient taking supplement who has had HIV for 2.5 yyears?
b) what is expected CD4 count for patient not taking supplement who was dignosed with HIV at study enrollment?
c) what is expected CD4 count for patient not taking supplement who has had HIV for 2.5 years?
To answer these questions, we will use the multiple regression equation given:
y hat = 501.41 + 12.67(supplement) - 30.23(duration of HIV)
a) What is expected CD4 count for a patient taking supplement who has had HIV for 2.5 years?
To calculate the expected CD4 count, we substitute the values into the equation:
y hat = 501.41 + 12.67(1) - 30.23(2.5)
y hat = 501.41 + 12.67 - 75.575
y hat = 438.505
Therefore, the expected CD4 count for a patient taking a supplement who has had HIV for 2.5 years is approximately 438.505.
b) What is the expected CD4 count for a patient not taking a supplement who was diagnosed with HIV at study enrollment?
To calculate the expected CD4 count, we substitute the values into the equation:
y hat = 501.41 + 12.67(0) - 30.23(0)
y hat = 501.41
Therefore, the expected CD4 count for a patient not taking a supplement who was diagnosed with HIV at study enrollment is 501.41.
c) What is the expected CD4 count for a patient not taking a supplement who has had HIV for 2.5 years?
To calculate the expected CD4 count, we substitute the values into the equation:
y hat = 501.41 + 12.67(0) - 30.23(2.5)
y hat = 501.41 - 75.575
y hat = 425.835
Therefore, the expected CD4 count for a patient not taking a supplement who has had HIV for 2.5 years is approximately 425.835.