Exercise 5:  correlation and regression

In a study one compared two instruments for measuring the peak expiratory flow. For a sample of 8 person, one measurement was taken with a high quality instrument (called "pef" below) and one measurement was taken with a cheaper instrument that people with asthma may have at home (called "minipef" below).

 

The results are given in the table (in liters per minute)

 

Person	1	2	3	4	5	6	7	8
pef	494	395	516	434	476	413	442	433
minipef	512	430	520	428	500	364	380	445

 

a) Read the data into R and make a plot of the data. What can you see from the plot? (See the introduction to R or ask the instructors if you do not remember how to read the data into R and/or make a scatter plot of them.)

 

b) Compute the Pearson correlation coefficient. (See slide 28 from the lectures for R help.)

 

c) Find 95% confidence interval for the (theoretical) correlation coefficient. (See slide 30 from the lectures for R help.)

 

d) Fit a linear regression model with "minipef" as the outcome and "pef" as the predictor. Give an interpretation of the estimated slope, i.e. the least square estimate for "pef". (See slide 35 from the lectures for R help.)

 

e) Multiply the estimated slope from question d with the ratio of the empirical standard deviations of "pef" and "minipef". Compare the result with the Pearson correlation from question b. What do you see?