I want to taste the meat, not the heat. I have switched from a charcoal grill to a Vogner Charking ImperialTM propane grill, and I want to know if I can save money on propane gas. I have sampled 35 gas cylinders randomly from 5 different companies, where I measured their weights in kilograms and all cylinders cost the same price. Table 1: Weight in kgs for 7 cylinders randomly selected from 5 di'erent companies. Company number 1 2 3 4 5 14.36 13.51 13.74 14.09 13.51 14.15 13.60 13.94 14.52 14.03 14.20 13.71 14.10 14.58 13.84 14.12 13.94 13.93 14.08 13.29 14.05 13.95 13.61 13.66 13.97 14.15 13.67 13.97 13.90 13.44 14.17 13.79 13.88 14.13 13.94 Obs. 'JCQ'li-BCDMH (a) (6 marks) Create the design matrix X (print it) and t an appropriate categorical linear regression model to compare companies. Diagnose any problems with this regression model t. (b) (4 marks) Test the hypothesis that g = 31 = 52 = 33 = 64. Interpret the hypothesis and state your conclusion. (c) (4 marks) Test the hypothesis that .30 + 261 362 + 64 = 14. State your conclusion. (d) (2 marks) Which company should I buy my propane from