Problem. 1- Linear Fit/ Variables transform.- 20 pts The logistic curve is given by It is used to model populations that should have growth that is close to exponential (when x is small) but that can only grow to a limiting value L. Ideally-for a given set of data points (x,yi), i-1..N, we would like to determine the best-fit parameters L, B and k via least squares, but this is a nonlinear problem. It is more difficult than the ones we have encountered in class. So Let's assume for the moment that we can get a good estimate of the value for L, the largest the population can grow. We still want to determine B and k via least squares. Que 1) [15 pts] Knowing L, turn this into a linear least-squares problem by using the right change of variables i.e. Y-a0+al X where the new variables Y' and X' have to be defined. 2) [5pts] Give an analytic formula for parameters B and k as a function of the data points (x,yi) jel..N . HINT : use the linear fit expressions for a0 and al you have obtained in 1) Problem. 1- Linear Fit/ Variables transform.- 20 pts The logistic curve is given by It is used to model populations that should have growth that is close to exponential (when x is small) but that can only grow to a limiting value L. Ideally-for a given set of data points (x,yi), i-1..N, we would like to determine the best-fit parameters L, B and k via least squares, but this is a nonlinear problem. It is more difficult than the ones we have encountered in class. So Let's assume for the moment that we can get a good estimate of the value for L, the largest the population can grow. We still want to determine B and k via least squares. Que 1) [15 pts] Knowing L, turn this into a linear least-squares problem by using the right change of variables i.e. Y-a0+al X where the new variables Y' and X' have to be defined. 2) [5pts] Give an analytic formula for parameters B and k as a function of the data points (x,yi) jel..N . HINT : use the linear fit expressions for a0 and al you have obtained in 1)