Analysis of Scientific Data – Semester 1, 2022
Week 10 Tutorial Questions
Question 1
Lung function data for 25 cystic fibrosis patients in a study by O’Neill et al. (1983) was presented in
Douglas Altman’s Practical Statistics for Medical Research (1991). The data contains variables recorded
for each patient and here we are interested in the relationship between two of these, weight (weight,
kg) and pemax (maximum expiratory pressure, cm of H2O).
a) Write down the linear model and its assumptions to study the relationship between the
response variable, pemax, and the explanatory variable, weight.
b) The R output for the linear model is presented below. Compute the values of A and C, and then
give a value for B.
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 63.5456 A 5.003 4.63e-05 ***
weight 1.1867 0.3009 3.944 B
Residual standard error: 26.38 on C degrees of freedom
c) Based on the linear model, what is the estimated mean maximum expiratory pressure for
patients with a weight of 50 kg?
d) The Pearson correlation coefficient, 𝑟, between the variables pemax and weight is 0.635.
Describe the strength and the direction of the relationship between pemax and weight.
e) Conduct a hypothesis test to determine whether there is any evidence of a linear association
between pemax and weight. What do you conclude?
Week 10 Tutorial Questions
Question 1
Lung function data for 25 cystic fibrosis patients in a study by O’Neill et al. (1983) was presented in
Douglas Altman’s Practical Statistics for Medical Research (1991). The data contains variables recorded
for each patient and here we are interested in the relationship between two of these, weight (weight,
kg) and pemax (maximum expiratory pressure, cm of H2O).
a) Write down the linear model and its assumptions to study the relationship between the
response variable, pemax, and the explanatory variable, weight.
b) The R output for the linear model is presented below. Compute the values of A and C, and then
give a value for B.
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 63.5456 A 5.003 4.63e-05 ***
weight 1.1867 0.3009 3.944 B
Residual standard error: 26.38 on C degrees of freedom
c) Based on the linear model, what is the estimated mean maximum expiratory pressure for
patients with a weight of 50 kg?
d) The Pearson correlation coefficient, 𝑟, between the variables pemax and weight is 0.635.
Describe the strength and the direction of the relationship between pemax and weight.
e) Conduct a hypothesis test to determine whether there is any evidence of a linear association
between pemax and weight. What do you conclude?
