Question

STAT
PatientID	Age	Sex	County	CardioRisk	Height	Weight	BloodGroup	Stroke	RegularEx	Group	Cholesterol1	Cholesterol2
225	58	Male	Offaly	Low	179.2	103.5	AB	N	N	Placebo	6.1	4.6
226	61	Male	Carlow	Medium	174.9	63	AB	Y	N	Control	2.2	5.7
227	57	Female	Donegal	Medium	161.9	76.1	B	N	Y	Control	5.8	5
228	43	Male	Offaly	High	176	83.7	AB	Y	N	Control	3.6	2.4
229	37	Female	Longford	Low	157.8	68	B	N	Y	Control	4.9	6
230	29	Male	Leitrim	Medium	166.1	79.1	A	Y	Y	Placebo	3.5	5.3
231	52	Male	Cavan	Low	167.6	60.4	A	Y	Y	Placebo	2.9	4
232	47	Female	Westmeath	Low	167.8	63.6	B	N	Y	Control	4	3.2
233	28	Male	Wicklow	Low	170.5	67.2	O	Y	N	Control	4.2	4

The commands to these questions using rstudio

Q1

The researchers want to explore the relationship between Cholesterol level and BMI.

a. Using the cholesterol level before the study (Cholesterol1), compute the correlation coefficient between

BMI and cholesterol level.

b. Fit the regression line between BMI and cholesterol level, using cholesterol level as the response variable.

Write down the equation of the estimated regresison line and your specify your parameter values.

c. What is the value of the coefficient of determination?

d. Perform a model utility test. Write down the hypothesis your are testing, the value of the test statistic

and of the corresponding p-value. For a significance level of 0.05, what is the outcome of the test?

Answer 1

R-code:

data=read.table("clipboard",sep="\t",header=T)

BMI=data$Weight/((data$Height/100)^2) ## weight/(height in m.)^2
BMI

Cholesterol1=data$Cholesterol1
cor(BMI,Cholesterol1)## correlation
model=lm(Cholesterol1~BMI)## model fitting
summary(model)
anova(model)