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A new simplified formulation for inverse space mapping optimization of microwave circuits is presented in this work. In contrast to previous inverse space mapping algorithms, where artificial neural networks are trained to approximate the inverse space mapping at each iteration, our approach makes use of a linear regression formulation to calculate in closed form the inverse mapping parameters at each iteration, making faster and more robust the prediction of the next iterates. The inverse mapping parameters are obtained by inverting a small matrix of base points that is warranted to be full-rank. Direct input space mapping by linear regression is also discussed. Our technique is illustrated by the design optimization of a four-section 1:3 Butterworth stripline impedance transformer, and by a microstrip notch filter with mitered bends.