Question

2. Researchers at an infectious disease clinic interested in investigating the relationship between mortality and a number of comorbidities in their patients that are HIV positive.  Researchers hypothesize that early mortality is most strongly associated with heroin use in their patient population. In order to better assess their relationship, the researchers decided to control for a variety of other comorbidities along with age and gender. The following is a representation of their multiple linear regression model (NOTE: the output is a bit different as it was prepared with SAS, but it has the main elements you need to answer the questions)

Parameter Estimates
Variable	Label	DF	Parameter Estimate	Standard Error	t Value	Pr > |t|
Intercept	Intercept	1	-0.01305	0.06941	-0.19	0.8510
EVEROIN	Heroin	1	0.25738	0.04337	5.93	<.0001
HEPC	HepC	1	0.11499	0.06466	1.78	0.0763
HEPB	HepB	1	0.06106	0.09432	0.65	0.5179
LIVDZ	LiverDisease	1	0.58833	0.12178	4.83	<.0001
VL	ViralLoad	1	5.347417E-7	9.786719E-8	5.46	<.0001
STI	STI	1	-0.10648	0.04453	-2.39	0.0174
AGE	AGE	1	0.00253	0.00174	1.45	0.1478
SEXN	SEX	1	-0.05454	0.03569	-1.53	0.1275

A)  Write out the null and alternative hypotheses for the formal test of inference that the researchers conducted.

B)  Write out your final regression model using the beta coefficients provided.

C)  Which of the variables was significant in the final model?

Answer 1

SolutionA:

A)  Write out the null and alternative hypotheses for the formal test of inference that the researchers conducted.

Ho:There is no linear relatiosnhip between mortality and a number of comorbidities in their patients that are HIV positive.

Ha::There is a linear relatiosnhip between mortality and a number of comorbidities in their patients that are HIV positive.

SolutionB:

Mortality=-0.01305+0.25738*EVEROIN+0.11499*HEPC+0.06106*HEPB+0.58833*LIVDZ+5.347417*10^-7*VL+

0.10648*STI+0.00253*Age+-0.05454*SEXN

SolutionC:

C)  Which of the variables was significant in the final model?

p<0.05 significant variable

For EVEROIN ,p=<.0001,p<0.05, significant in the final model

For HEPC,p=0.0763,p>0.05,Not significant in the final model

For HEPB,p=0.5179,p>0.05,Not significant in the final model

For LIVDZ,p=0.0001,p<0.05, significant in the final model

For VL,p=0.0001,p<0.05, significant in the final model

For STI,p=0.0174,p<0.05,significant in the final model

For AGE,p=0.1478,p>0.05,Not significant in the final model

For SEXN,p=0.1275,p>0.05,Not significant in the final model

variables which are significant are:

EVEROIN

LIVDZ

VL

STI