Suppose both the Repair record 1978 and Company headquarters are believed to be significant in explaining the vector (Price, Mileage, Weight). Here, because of the limited sample size, we compress the information in Repair record 1978 into a two level factor: level 1 is for 5 point and level 2 represents all the points lower than 5. Are the effects from the two factors, compressed Repair record 1978 and Company headquarters (also the possible interaction), significant in explaining the vector (Price, Mileage, Weight)? Please also specify what assumptions are made on your analysis (you do not need to check with these assumptions for this problem).