Can you please help me solve the following ?

Suppose we conduct an experiment where we study the amount time taken (Y) for a matrix multiplication operation to be completed when a large square matrix is multiplied by itself using specific computer code (run-time is measured in minutes). The variables that are used in the experiment as factors that potentially affect the run-time include the version of the compiler used to compile the code Compiler version 0.1.0 X1 = Compiler version 1.2.0 , Compiler version 2.0.0 as well as the variable X2 which denotes the number of rows and columns of the square matrix used in the calculation (this variable can take on values anywhere between 1000 and 1 000 0000). NOTE: The same code is compiled on different versions of compilers and then the code is executed after it is compiled - it is thought that some versions of the compiler will perform better/worse for these kinds of matrix operations. The experiment is conducted 9 times and the following results are obtained: Y X1 X2 12.5 Compiler v0.1.0 1.25 x 105 11.3 Compiler v0.1.0 0.90 x 105 10.4 Compiler v0.1.0 0.95 x 105 12.7 Compiler v1.2.0 1.25 x 105 10.3 Compiler v1.2.0 0.90 x 105 11.6 Compiler v1.2.0 0.95 x 105 12.0 Compiler v2.0.0 1.25 x 105 12.1 Compiler v2.0.0 0.90 x 105 12.5 Compiler v2.0.0 0.95 x 105 Interest lies in comparing the mean run-times of the different compilers to one another. 1. Describe one technique of dealing with the qualitative 'compiler type' variable. Carefully define any new variables created using this technique. (1) 2. Briefly explain why you chose this particular technique. (1) 3. You must now decide whether to use a model that incorporates interactions or not. Make a decision and fully motivate your answer. (1) 4. Provide an expression for the model you chose above. Write out the full form of the design matrix for the model you specified. (2) 6 5. Use your specified model and test the hypothesis that Compiler v0.1.0 produces shorter run times than Compiler v2.0.0 when calculating matrices of size 1.00 x 103. Carefully state the hypothesis used and test the hypothesis at a = 0.05. (3)