An article describes a factorial experiment designed to determine factors in a high-energy electron beam process that affect hardness in metals. The first factor is the travel speed in mm/s (three levels: 10, 20, 30). The second factor is the accelerating voltage in volts (three levels: 10, 25, 50). The outcome is Vickers hardness. There were six replications for each treatment. The data set is below. PLEASE show me how to do this in R. Thank you A B Hardness
10 10 875
10 10 896
10 10 921
10 10 686
10 10 642
10 10 613
10 25 712
10 25 719
10 25 698
10 25 621
10 25 632
10 25 645
10 50 568
10 50 546
10 50 559
10 50 757
10 50 723
10 50 734
20 10 876
20 10 835
20 10 868
20 10 812
20 10 796
20 10 772
20 25 889
20 25 876
20 25 849
20 25 768
20 25 706
20 25 615
20 50 756
20 50 732
20 50 723
20 50 681
20 50 723
20 50 712
30 10 901
30 10 926
30 10 893
30 10 856
30 10 832
30 10 841
30 25 789
30 25 801
30 25 776
30 25 845
30 25 827
30 25 831
30 50 792
30 50 786
30 50 775
30 50 706
30 50 675
30 50 568
a. Estimate all main effects and interactions.
b. Construct an ANOVA table. You may give ranges for the p-value.