3. When plotting data from a repeated experiment in order to test the validity of a supposed linear relationship between two variables x1 and x2, the data points are usually not located exactly on a straight line. There are several ways to find the best fitting line through the plotted points. One of these is the method of least absolute deviation regression. In least absolute deviation regression it is assumed that the exact underlying relationship is a straight line, say x2=x1+. Let {[a1b1],,[anbn]} be the data set. For each i=1,,n, the absolute error, ri, is defined by ri=aibi. The problem is to determine values of and such that the sum of the absolute errors, i=1nri, is as small as possible. a) Formulate the method of least absolute deviation regression as an optimisation model. In this answer, you can use the function abs(x) which computes the absolute value of a variable xR. b) Using the function abs(x) makes your model in a) non-linear. Linearise your model such that your optimisation problem is now a linear programming model. Hint: The absolute value of a variable xR can be computed with two non-negative variables x+0,x0 as follows: abs(x)=x+x as long as you know that at least one of the variables is set at zero and x++x=x. 3. When plotting data from a repeated experiment in order to test the validity of a supposed linear relationship between two variables x1 and x2, the data points are usually not located exactly on a straight line. There are several ways to find the best fitting line through the plotted points. One of these is the method of least absolute deviation regression. In least absolute deviation regression it is assumed that the exact underlying relationship is a straight line, say x2=x1+. Let {[a1b1],,[anbn]} be the data set. For each i=1,,n, the absolute error, ri, is defined by ri=aibi. The problem is to determine values of and such that the sum of the absolute errors, i=1nri, is as small as possible. a) Formulate the method of least absolute deviation regression as an optimisation model. In this answer, you can use the function abs(x) which computes the absolute value of a variable xR. b) Using the function abs(x) makes your model in a) non-linear. Linearise your model such that your optimisation problem is now a linear programming model. Hint: The absolute value of a variable xR can be computed with two non-negative variables x+0,x0 as follows: abs(x)=x+x as long as you know that at least one of the variables is set at zero and x++x=x