A research study compared three treatments on their effect in reducing blood pre

Question

A research study compared three treatments on their effect in reducing blood pressure in hypertensive individuals with approximately the same initial blood pressure. A total of 72 subjects were randomized into the three treatment groups as follows: 0=control (22 individuals), 1=experimental drug plus exercise regimen (28 individuals), 2=experimental drug only (22 individuals). The control group subjects received the current, most commonly prescribed drug.

You want to include data on patient age (in years) in this analysis, and so you fit a linear model where change in BP is explained by predictors: treatment, gender, and age. The regression output from this analysis is given below.

a. Interpret the estimate for age, in the context of the problem.

b. Interpret the estimate for gender, in the context of the problem.

c. Interpret the estimates for treatment, in the context of the problem.

d. Suppose a subject in treatment group 2 was a 60-year old female, what would be her estimated change in BP?

e. Suppose the subject in part (d) had an actual change in BP of 6.4 mmHg, what would her residual be?

f. How much of the variation in change in BP was explained by this model?

Suppose you wanted to separately study the effect of just gender on change in BP, which analysis/test would you use?

Suppose you wanted to separately study the effect of just age on change in BP, which analysis/test would you use?

Suppose you wanted to compare just treatments 2 and 1 on change in BP, which two analyses/tests could you use?

Estimate St. Error t-statistic p-value 2.99 0.04 1.13 1.01 0.81 25.15 Intercept Age Treatment2.77 Treatment2 | -0.61 GenderMale 1.73 Residual standard error: 2.99 on 67 degrees of freedom 8.24 7.1 2.44 0.60 2.14

Explanation / Answer

Part a)

Estimate for age is -0.28

Part b)

Estimate of gender is 1.73

Part c)

.

Part d)

the model is

y = 25.15 -0.28 (Age) -0.61(treatment II)

y = 25.15 - 0.28*60 - 0.61 = 7.74

Hence the BP will be 7.74 mmHg

.

Part e)

The residual error = Actual - Estimated

Actual = 6.4 mmHg

Expected = 7.74 mmHg

Residual Error = 6.4 - 7.74 = -1.04 mmHg

.

Part f)

the variation explained by this model is givn by R square

R squared = 0.7127

Hence the variance explained by this model is 71.27 %

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