Regression analysis is commonly used in the construction industry to estimate costs. The analysis is particularly useful for very large projects such as bridge construction. For example, it is possible to identify the three largest components of bridge construction: concrete, reinforcing steel, and pre-stressed steel cables. A recent study examined 68 bridge construction projects and estimated the amount of concrete, the weight of reinforcing steel, and the weight of pre-stressed steel cables used in these projects; the study used each of these dependent variables as a proxy for the cost of these three cost elements. The two cost drivers, the independent variables, were the length of the bridge and the width of the bridge. The cost of lighting and sidewalks was not considered.
The data for the regression was obtained from a sample of 68 bridges, consisting of three types of construction: (1) 31 bridges with pre-cast beams which were built off-site and then moved to the construction site, (2) 22 bridges built "cast-in-situ" where the concrete is poured at the construction site, and (3) 15 bridges with balanced cantilever construction (each cantilever arm is balanced with another cantilever arm projecting the opposite direction, forming a balanced cantilever). Data on the regression R-squared and mean absolute percentage error (MAPE) follows. (The MAPE was derived from 10 tests in which the data were subdivided. A portion of data was used to develop the regression model and that model was used to obtain predictions for the remainder of the data set; the prediction errors were determined from these predictions.)

Required
Based on the information provided, which of the three bridge types has the most reliable bridge cost estimation, and why? Which bridge type has the highest cost?

R-squared Reinforced Pre-Stressed MAPE Reinforced Pre-Stressed Bridge Type Concrete Steel Precast Cost-in-situ 0.764 Balanced cantilever Steel 0.799 0.779 Bridge Type Concrete Steel Precast Cost-in-situ 4.48 Balanced cantilever Steel 16.14% 19.30 0.826 0.758 11.66% 15.42% 0.707 15.26 0.926 0.898 0.912 14.76 17.69 16.03