Question: 1. [20 Points] Develop a polynomial (any order you choose) regression model for the data given in Probleml-exam1-2017.xls. Use the data in training dataset (Training

1. [20 Points] Develop a polynomial (any order

1. [20 Points] Develop a polynomial (any order you choose) regression model for the data given in Probleml-exam1-2017.xls. Use the data in training dataset (Training worksheet) for fitting the polynomial. a. Show the model and RMS error in the fit (RMS error is the cumulative root mean square of the pointwise error between the model and training data set) b. Find the RMS error in modeling the testing dataset (Testing worksheet) when you use the model determined in (a). 0.2 0.01 0.231895 0.02 0.264667 0.03 0.298191 0.04 0.332345 0.05 0.367008 0.06 0.402062 0.07 0.43739 0.08 0.472877 0.09 0.508413 0.1 0.543893 0.11 0.579212 0.12 0.614274 0.13 0.648984 0.14 0.683257 0.15 0.717008 0.16 0.750164 0.17 0.782653 0.18 0.814414 0.19 0.845388 0.2 0.875528 0.21 0.904792 0.22 0.933144 0.23 0.960557 0.24 0.987013 0.251.0125 0.26 1.037013 0.27 1.060557 0.28 1.083144 0.29 1,104792 o3 1 125528 Training Dataset 31 | 4 0.3 1.125528 0.31 1.145388 0.32 1.164414 0.33 1.182653 0.34 1.200164 0.35 1.217008 0.36 1.233257 0.37 1.248984 0.38 1.264274 0.39 1.279212 0.4 1.293893 0.41 1.308413 0.42 1.322877 0.43 1.33739 0.44 1.352062 0.45 1.367008 0.46 1.382345 0.47 1.398191 0.48 1.414667 0.49 1.431895 0.5 1.45 0.51 1.469105 0.52 1.489333 0.53 1.510809 0.54 1.533655 0.55 1.557992 0.56 1.583938 0.57 1.61161 0.58 1.641123 0.59 1.672587 A B 0.6 1.706107 0.61 1.741788 0.62 1.779726 0.63 1.820016 0.64 1.862743 0.65 1.907992 0.66 1.955836 0.67 2.006347 0.68 2.059586 0.69 2.115612 0.7 2.174472 0.71 2.236208 0.72 2.300856 0.73 2.368443 0.74 2.438987 0.75 2.5125 0.76 2.588987 0.77 2.668443 0.78 2.750856 0.79 2.836208 0.8 2.924472 0.81 3.015612 0.82 3.109586 0.83 3.206347 0.84 3.305836 0.85 3.407992 0.86 3.512743 0.87 3.620016 0.88 3.729726 0.89 3.841788 093956107 Training Dataset 90 91 A B 0.9 3.956107 0.91 4.072587 0.92 4.191123 0.93 4.31161 0.94 4.433938 0.95 4.557992 0.96 4.683655 0.97 4.810809 0.98 4.939333 0.99 5.069105 5.2 Training Dataset ITB 1 X Y* 0 0.2 0.01 0.2005 0.02 0.202 0.03 0.2045 0.04 0.208 0.05 0.2125 0.06 0.218 0.07 0.2245 0.08 0.232 0.09 0.2405 0.1 0.25 0.11 0.2605 0.12 0.272 0.13 0.2845 0.14 0.298 0.15 0.3125 0.16 0.328 0.17 0.3445 0.18 0.362 0.19 0.3805 0.2 0.4 0.21 0.4205 0.22 0.442 0.23 0.4645 0.24 0.488 0.25 0.5125 0.26 0.538 0.27 0.5645 0.28 0.592 31 0 29 06205 Testing Dataset 0.29 0.6205 0.3 0.65 0.31 0.6805 0.32 0.712 0.33 0.7445 0.340.778 0.35 0.8125 0.36 0.848 0.37 0.8845 0.38 0.922 0.39 0.9605 0.4 0.411.0405 0.42 1.082 0.43 1.1245 0.44 1.168 0.45 1.2125 0.46 1.258 0.47 1.3045 0.48 1.352 0.49 1.4005 0.5 1.45 0.511.5005 0.52 1.552 0.53 1.6045 0.54 1.658 0.55 1.7125 0.56 1.768 0.57 1.8245 0.58 1.882 159 19405 Testing Dataset 61 0.59 1.9405 0.6 0.61 2.0605 0.62 2.122 0.63 2.1845 0.64 2.248 0.65 2.3125 0.66 2.378 0.67 2.4445 0.68 2.512 0.69 2.5805 0.7 2.65 0.71 2.7205 0.72 2.792 0.73 2.8645 0.74 2.938 0.75 3.0125 0.76 3.088 0.77 3.1645 0.78 3.242 0.79 3.3205 0.8 3.4 0.81 3.4805 0.82 3.562 0.83 3.6445 0.84 3.728 0.85 3.8125 0.86 3.898 0.87 3.9845 0.88 4.072 0894 1605 Testing Dataset A B 0.89 0.9 0.91 0.92 0.93 0.94 4.1605 4.25 4.3405 4.432 4.5245 4.618 4.7125 4.808 4.9045 5.002 5.1005 5.2 0.95 0.96 0.97 0.98 0.99 1 Testing Dataset 1. [20 Points] Develop a polynomial (any order you choose) regression model for the data given in Probleml-exam1-2017.xls. Use the data in training dataset (Training worksheet) for fitting the polynomial. a. Show the model and RMS error in the fit (RMS error is the cumulative root mean square of the pointwise error between the model and training data set) b. Find the RMS error in modeling the testing dataset (Testing worksheet) when you use the model determined in (a). 0.2 0.01 0.231895 0.02 0.264667 0.03 0.298191 0.04 0.332345 0.05 0.367008 0.06 0.402062 0.07 0.43739 0.08 0.472877 0.09 0.508413 0.1 0.543893 0.11 0.579212 0.12 0.614274 0.13 0.648984 0.14 0.683257 0.15 0.717008 0.16 0.750164 0.17 0.782653 0.18 0.814414 0.19 0.845388 0.2 0.875528 0.21 0.904792 0.22 0.933144 0.23 0.960557 0.24 0.987013 0.251.0125 0.26 1.037013 0.27 1.060557 0.28 1.083144 0.29 1,104792 o3 1 125528 Training Dataset 31 | 4 0.3 1.125528 0.31 1.145388 0.32 1.164414 0.33 1.182653 0.34 1.200164 0.35 1.217008 0.36 1.233257 0.37 1.248984 0.38 1.264274 0.39 1.279212 0.4 1.293893 0.41 1.308413 0.42 1.322877 0.43 1.33739 0.44 1.352062 0.45 1.367008 0.46 1.382345 0.47 1.398191 0.48 1.414667 0.49 1.431895 0.5 1.45 0.51 1.469105 0.52 1.489333 0.53 1.510809 0.54 1.533655 0.55 1.557992 0.56 1.583938 0.57 1.61161 0.58 1.641123 0.59 1.672587 A B 0.6 1.706107 0.61 1.741788 0.62 1.779726 0.63 1.820016 0.64 1.862743 0.65 1.907992 0.66 1.955836 0.67 2.006347 0.68 2.059586 0.69 2.115612 0.7 2.174472 0.71 2.236208 0.72 2.300856 0.73 2.368443 0.74 2.438987 0.75 2.5125 0.76 2.588987 0.77 2.668443 0.78 2.750856 0.79 2.836208 0.8 2.924472 0.81 3.015612 0.82 3.109586 0.83 3.206347 0.84 3.305836 0.85 3.407992 0.86 3.512743 0.87 3.620016 0.88 3.729726 0.89 3.841788 093956107 Training Dataset 90 91 A B 0.9 3.956107 0.91 4.072587 0.92 4.191123 0.93 4.31161 0.94 4.433938 0.95 4.557992 0.96 4.683655 0.97 4.810809 0.98 4.939333 0.99 5.069105 5.2 Training Dataset ITB 1 X Y* 0 0.2 0.01 0.2005 0.02 0.202 0.03 0.2045 0.04 0.208 0.05 0.2125 0.06 0.218 0.07 0.2245 0.08 0.232 0.09 0.2405 0.1 0.25 0.11 0.2605 0.12 0.272 0.13 0.2845 0.14 0.298 0.15 0.3125 0.16 0.328 0.17 0.3445 0.18 0.362 0.19 0.3805 0.2 0.4 0.21 0.4205 0.22 0.442 0.23 0.4645 0.24 0.488 0.25 0.5125 0.26 0.538 0.27 0.5645 0.28 0.592 31 0 29 06205 Testing Dataset 0.29 0.6205 0.3 0.65 0.31 0.6805 0.32 0.712 0.33 0.7445 0.340.778 0.35 0.8125 0.36 0.848 0.37 0.8845 0.38 0.922 0.39 0.9605 0.4 0.411.0405 0.42 1.082 0.43 1.1245 0.44 1.168 0.45 1.2125 0.46 1.258 0.47 1.3045 0.48 1.352 0.49 1.4005 0.5 1.45 0.511.5005 0.52 1.552 0.53 1.6045 0.54 1.658 0.55 1.7125 0.56 1.768 0.57 1.8245 0.58 1.882 159 19405 Testing Dataset 61 0.59 1.9405 0.6 0.61 2.0605 0.62 2.122 0.63 2.1845 0.64 2.248 0.65 2.3125 0.66 2.378 0.67 2.4445 0.68 2.512 0.69 2.5805 0.7 2.65 0.71 2.7205 0.72 2.792 0.73 2.8645 0.74 2.938 0.75 3.0125 0.76 3.088 0.77 3.1645 0.78 3.242 0.79 3.3205 0.8 3.4 0.81 3.4805 0.82 3.562 0.83 3.6445 0.84 3.728 0.85 3.8125 0.86 3.898 0.87 3.9845 0.88 4.072 0894 1605 Testing Dataset A B 0.89 0.9 0.91 0.92 0.93 0.94 4.1605 4.25 4.3405 4.432 4.5245 4.618 4.7125 4.808 4.9045 5.002 5.1005 5.2 0.95 0.96 0.97 0.98 0.99 1 Testing Dataset

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