Mr.Azaza in the Department of Kinesiology at the University of Alberta conducted study on the effectiveness of Yoga on Body Mass Index (BMI). The study was published in the International Journal of Yoga in 2017, and the results were widely covered in the media. The following is from the abstract of the study:

Background:

Yoga, an ancient Indian system of exercise and therapy is an art of good living or an integrated system for the benefit of the body, mind, and inner spirit. Regular practice of yoga can help to increase blood flow to the brain, reduce stress, have a calming effect on the nervous system, and greatly help in reducing hypertension.

Aim:

Aim of the present study is to evaluate the effect of 1-month yoga practice on body mass index (BMI), and blood pressure (BP).

Materials and Methods:

The present study was conducted to determine the effect of yoga practice on 66 participants (treatment group) whereas the results were compared with 24 healthy volunteers (control group). We examined the effects of yoga on physiological parameters in a 1-month pilot study. Most of the participants were learner and practiced yoga for 1 hour daily in the morning for 1 month. BMI and BP (systolic and diastolic) were studied before and after 1 month of yoga practice.

Results:

Yoga practice causes decreased BMI (-1.18), systolic BP (-3.39 mmHg), and diastolic BP (-2.4 mmHg). On the other hand, no significant changes were observed in BMI and BP of control group.

Conclusion:

This study concludes that yoga practice has potential to control BMI and BP without taking any medication.

The treatment group was drawn from volunteers from a pool of participants who had enrolled in a 1-month free yoga program offered at the University of Alberta. When asked why they enrolled in the Yoga program, the typical response was that they were interested in a 'healthy lifestyle' or to 'meet people.' The control group was drawn from 24 students at the University of Alberta who did not enrol in the free yoga program. These students responded to an ad posted in the main concourse on campus. The reward for the control group was a \$10 gift certificate for Tim Horton's. The study was funded by The Central Council for Research in Yoga \& Naturopathy.

Denote the treatment variable by

Upper X Subscript i

,

which can take on values of 1 (enrolled in Yoga) or 0 (Not enrolled in Yoga).

Out of 90 students, 66 of them practiced yoga for 1-month. The outcome variable is an individual's change in BMI over the 1-month period, denoted by

Upper Y Subscript i

.

The professor considers the regression model:

Upper Y Subscript i Baseline equals beta 0 plus beta 1 times Upper X Subscript i Baseline plus u Subscript i What does u Subscript i mean?

A.

Is a constant, and has an expected value = 0

B.

u contains unobserved factors about people that determines whether they practice yoga

C.

is low for people who typically practice yoga

D.

u Subscript nothing

contains unobserved factors about people that affects their BMI aside from Yoga practice

The professor assumes that

Upper E left parenthesis u Subscript i Baseline | Upper X Subscript i Baseline right parenthesis equals 0

.

We can interpret this as:

A.

u Subscript nothing

is as-good-as randomly assigned

B.

This is just a normalisation since the professor includes a constent in the regression.

C.

unobserved factors are not all that important.

D.

Those who practice Yoga are on average the same as those who do not practice Yoga

The Sample regression is

ModifyingAbove Upper Y Subscript i with caret equals 0.01 minus 1.18 times Upper X Subscript i

What is the overal sample mean of the change in BMI?

A.

0.01

B.

-1.17

C.

-0.85

D.

-1.18

Suppose that a participant in the treatment group had an observed change in BMI of -1.5. What is this persons residual?

A.

-2.67

B.

-.33

C.

-.30

D.

-.32

The authors calculate that

Var left parenthesis Upper Y Subscript i Baseline right parenthesis equals 1

.

Calculate the t-statistic that the difference in means between the two groups is zero under the assumption of homoskedasticity.

A.

-4.908

B.

-11.010

C.

There is not enough information to calculate the t-statistic

D.

-4.9504