A study was conducted in Boston, Massachusetts, in the late 1970s and early 1980s to investigate change in pulmonary function over time in a large group of children. The data for this question (in GirlsFEV.csv) 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 FEV of a girl 150 cm in height.