Question 3 An experiment was performed to study the effect of three different types of strings (factor A) - Polyester (Al), Synthetic gut (A2), and Multifilament (A3) and three different tennis racket types (factor B) - Wilson pro staff 97 (BI), Yonex EZONE 98 (B2), and Babolat Pure (B3) - - on the serve speed (y in km/hour) of tennis players. The experiment is designed with objective of achieving the highest serve speed. Three professional players (factor C) were involved in this experiment, and two replicates were run. The observed serving data are shown in the following Table Q3. Replicate 1 Replicate 2 Player Bottle Type B1 B2 B3 B1 B2 B3 C1 Al 103.5 124.2 174 100.8 125.7 156.9 A2 122.1 131.4 164.4 105.6 127.8 145.5 A3 126 127.8 170.1 110.4 131.1 167.4 C2 Al 144 156.6 186.3 132 141 176.4 A2 135.6 154.5 187.5 133.2 139.5 186 A3 148.8 155.1 180.9 131.7 142.5 191.4 C3 Al 122.4 118.2 154.2 109.5 122.4 134.7 A2 129 135.9 149.7 121.2 122.4 137.7 A3 125.1 145.8 145.5 116.4 134.4 147 Table 03 (a) Demonstrate the factorial design that can be used in this experiment and explain the reasons. (4 marks) (b) Based on the data (Table Q3), please show all the codes to construct the ANOVA table in R for the chosen design in Question 3(a). Further interpret your conclusion on the model, A, B, C and their interactions. (10 marks)(c) The interaction plot is shown in Figure Q3(c). Please analyse the figure and draw a conclusion. (4 marks) Racket Type 180 160 Serve Speed 120 140 N Player Figure 03(c)