Two deformities of the foot are metatarsus adductus (MA) and hallux abducto valgus (HAV). The former, MA, is common but usually the patient recovers without treatment. HAV is not common in youth, but when it occurs may require an operation. The angles of deformation relevant to both conditions in 38 young patients who presented for surgery to correct HAV were measured and the data are in the file Feet.csv. The column headings are; HAV - The HAV deformation angle in degrees, and MA - The MA deformation angle in degrees. (a) Obtain the following R output, treating HAV as the response variable: (i) scatter plot [3] (ii) standardised residual plot [2] (iii) distribution of residuals [3] (iv) regression analysis. [2] (b) What statistical model is assumed in the regression analysis? [2] (c) As far as possible, assess the extent to which the model is appropriate to the data. [5] (d) Use an appropriate hypothesis test to evaluate the evidence that HAV angle is related to MA angle among young patients presenting for HAV surgery. Use a 5% significance level, and describe any relationship you find. [5] (e) Provide a 95% prediction interval for the HAV angle expected in a young patient whose MA angle is 25.