3. [25 marks] Two deformities of the foot are metatarsus udductus 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; 0 HAV The HAV deformation angle in degrees, and 0 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. [7-] (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% signicance level, and describe any relationship you nd. [5] (e) Provide a 95% prediction interval for the HAV angle expected in a young patient whose MA angle is 25. [3] mummawwu HAV 28 32 25 34 38 26 25 18 30 26 28 16 20 21 17 16 21 23 26 32 25 21 22 20 18 26 16 30 30 20 25 23 26 28 31 35 32 21 MA 18 16 22 17 33 10 18 13 19 10 17 14 20 15 16 10 11 15 12 16 16 18 10 15 16 10 12 10 10 12 25 30 22 24 20 37 23