(Solved): - (if \( \xi_{15}=0 \) ): a polynomial model function of twelve \( \alpha_{i} \) parameters: \[ f( ...

- (if \( \xi_{15}=0 \) ): a polynomial model function of twelve \( \alpha_{i} \) parameters: \[ f(x)=\alpha_{0}+\alpha_{1} x+\alpha_{2} x^{2}+\cdots+\alpha_{12} x^{12} \] - (if \( \xi_{15}=1 \) ): a Fourier series model function of 8 parameters \( A_{0}, \ldots, A_{3}, P, \varphi_{1}, \varphi_{2}, \varphi_{3} \) : \[ f(x)=A_{0}+A_{1} \cdot \cos \left(\frac{2 \pi}{P} x-\varphi_{1}\right)+A_{2} \cdot \cos \left(\frac{2 \pi}{P} 2 x-\varphi_{2}\right)+A_{3} \cdot \cos \left(\frac{2 \pi}{P} 3 x-\varphi_{3}\right) \] - (if \( \xi_{15}=2 \) ): a polynomial model function of ten \( \alpha_{i} \) parameters: \[ f(x)=\alpha_{0}+\alpha_{1} x+\alpha_{2} x^{2}+\cdots+\alpha_{10} x^{10} \] Calculate the OLS estimate, and the OLS ridge-regularized estimates for the parameters given the sample points of the graph of \( f \) given that the values are \( y=\xi_{16} \). Remember to include the steps of your computation which are more important than the actual computations. \( \xi_{15:} 0 \) \[ \begin{array}{l} \xi_{16:}(39,2986447991201698300),(-26,-34661007801235184),(-43,-8460601575970758000),(- \\ 17,-307313739288186.4),(-92,-3.4235516137643113 \mathrm{e}+22),(-24,-14312041926916620),(-66,- \\ 903516478709002500000),(-92,-3.6663473576792742 \mathrm{e}+22),(-94,-4.658873884238717 \mathrm{e}+22), \\ (-1,-60.31),(82,9.759421441456304 \mathrm{e}+21),(-47,-22196722731252257000),(37, \\ 1584011017120635400),(-77,-5.133278553019085 \mathrm{e}+21),(48,27555949062846760000),(69, \\ 1.5333374322919216 \mathrm{e}+21),(-91,-3.127329140861789 \mathrm{e}+22),(-27,-51340514540461160),(66, \\ 927661973911965800000),(30,157307804588004500),(90,2.9167566102767063 \mathrm{e}+22),(65, \\ 794767599792517800000),(44,10671835307564659000),(-61,-403838281541568230000) \end{array} \]