Problem 8 (12 points total} Suppose we have a sample of n observations in the form of ($1.11$1.21y1}:($2.11332.2192}:' " : (3711.15331121911}: where x\" and it\" are the input features and y,- is the response variable for sample i. We want to nd the least square estimators for 61 and 62 in the following model: y = 5131+ (32332- (a} Write Sum of Square of Error (88} formulation for this problem. (2 points} (b} Consider the following system of two equations, where {31 and {32 are the unknowns: ai+bz=c di+e2=f What is the solution of the above system (for .31 and (32} in terms of a, b, c, d, e, and f. (2 points} (0} Find the lease square estimators of {31 and {32- (Hint: you may need to use the results of parts (a} and (b) }. (6 points} (d} Use the formulas from part (0} to compute {31 and 32 for the following data set. (2 points} 3' $1 $2 293 1.6 851 230 15.5 816 172 22 1058 91 43 1201 113 33 1357 125 40 1115