Question 1: Muscle Mass Study (6 marks) A nutritionist is interested in studying

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Question 1: Muscle Mass Study (6 marks) A nutritionist is interested in studying the relationship between age and muscle mass in women of age 40, He obtains data on 60 women of age 40-79 randomly selected from his hospital's database. Since muscle mass and age are quantitative variables, he decides to use simple linear regression to model the relationship. Because he thinks muscle mass declines with age, he uses age as the explanatory variable and muscle mass as the response variable (a) 1 mark) Is this an observational study or experimen? (b) (1 mark) Based on the scenario, what is the target population for this study? What is the study population? (c) (1 mark) How might the differences between the study population and target population affect the results of the conclusions about the relationship between age and muscle mass? Use the following output from R to answer the questions in (d)- (f) Call: 1m(formula muscle age, data muscle) Residuals: 16.1884-6.2469 -0.7458 6.7650 26.3045 Coefficients: (Intercept) 156.00172 5.61749 27.77

Explanation / Answer

Answer with details explanations below. Write back in case of doubts:

a.The researcher has no control over the variables in an observational study. An experiment is a method of applying treatments to a group and recording the effects.

Since, there is no control over variables here, i.e. researcher is just recording data, it is an OBSERVATIONAL study

b.

Target population - Woman of age >=40
Study population - Woman of ages 40-79 ( there were 60 of them under research)

c. If the sample were skewed, for example all women were of age 79 then the target population for this study wouldrecord a completely different muscle mass compared to muscle mass of women of age 40. Hence, the former would not be a good representation of the sample and the relationship between age and muscle mass will be completely different

d. Slope and intercept: 156.00172 - 1.18341*Age = MuscleMass

e. SSE = 26.3045

f. Size of typical error when predicting muscle mass from age: .329 ( essentially the Residual standard error)

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