3. [26 marks] A study was conducted in Boston, Massachusetts, in the late 1970s and early 19805 to investigate change in pulmonary function over time in a large group of children. The data for this question [in GfdsFElcsv] are extracted from that study, and give measurements of lung function and height for girls aged 5 to 10 years. Lung function is measured using Forced Expiratory Volume [FEV], which is the amount of air that can be expelled in the first second of forced exhalation. Since FEV and height both reflect a person's size, we expect these variables to be positively related. The variables in the data file are as follows: FEV Air volume in litres (L) Height Height in centimetres [cm] (a) Obtain the following R output, treating FEV as the response variable: [i] scatter plot [3] [ii] standardised residual plot [2] [iii] distribution of residuals [3] [iv] regression analysis. [2, total = 10] [b] What statistical model is assumed in the above regression analysis? [2] (c) As far as possible, assess the extent to which the model is appropriate to the data. [5] [d] Assuming that any problems found in part [c] can be resolved, identify and evaluate the evidence that, on average, FEV increases with height among girls aged 5 to 10 years. If you find a relationship, describe it. [5] [e] Provide a 90% prediction interval for the FE! of a girl 150 cm in height. [4] FMh I'll? AQIGMMFNT