(20 points) We are given with the following set of input-output (x,y) data. x: Temperature (C) y: Corrosion (mm/yr) 26.6 1.58 26.0 1.45 27.4 1.13 21.7 0.96 Suppose that we want to model the above set of data with a linear model y = ax + b. Since our model may be perfect and there might be some noise in the measurements y , we assume y = ax + b + e, where e is the error in our modeling. a) Write down the matrix structure for this problem using the given model and the input- out data. b) Write down the structure of the solution for the coefficients a and b. You are not required to solve for the unknown parameters in our model but rather the form of the solution using least-squares error method. c) Suppose that the least squares solution for the unknown parameters are a = 0.0691 and b = -0.4761, resulting in y = 0.0691 x - 0.4761. Using this model and the given input-output data, find the squared-error defined as follows e? = Ex-()'n - In) , where yn is the ath measurement and ), is the output of the model evaluated at the nth input data