this is all given by my teacher

Question 2. (30 points) Supposed you are asked by Tony Stark (Iron Man) to help with the efficiency and manufacture of arc reactors. Hermione Granger has been contracted to develop a spell to magically increase the longevity of a material that is used in the new design, but is a primary cause of failure. Work with Ms. Granger to pick one of her newly developed spells. 10 series of heat maps from experimentation are provided in heat_images.mat each with 10 samples in time, along with 2 competing spell designs in spells.mat. a) Hermione originally asked Han Solo to take a look at this problem and help select a spell, but being so roguish, he tried to reduce dimension too far. He ran a linear regression on the simple scalar mean of each image. Examine the series of images for samples 1 and 2, from heat_images.mat, and explain why you would expect regression with tensor inputs will be much more useful. (You do not need to include plots of the images in your response.) b) Load the candidate spell readings to be predicted from spells.mat. Convert all images (training samples & candidate spells) to gray scale. Form tensors of each sample and the candidates. Provide: Plots of the grayscale 10th (last) images of spells and spell2. (Do not show scaled images, e.g., scale should be 0-255, not normalized to a colormap by min/max values). According to the slides (57-58), how many parameters would we have to estimate for this data, un- decomposed? c) Perform CP decompositions on the data from the 10 samples and spells 1 & 2. Then train a linear regression model from the CP decompositions and predict the time to failure for spells 1 & 2. Response values are given in heat_resp.mat. Try different ranks, at least 1-5, and calculate MSE from the training data. Then predict the time to failure for each candidate spell. Report: Your MSE for ranks 1-5 Which rank you would pick and (briefly) why. Predicted time to failure for the two candidate spells. d) Perform Tucker decompositions on the data from the 10 samples and spells 1 & 2. Train a linear regression model from the Tucker decompositions and predict the time to failure for spells 1 & 2. Provide the estimated times to failure for each. Try different ranks again, at least 1-5 and calculate the MSE from the training data. Predict the time to failure for the candidate spells. Report: .Your MSE for ranks 1-5 Which rank you would pick and (briefly) why. Predicted time to failure for the two candidate spells. e) Which spell do you recommend is used for the arc reactors? The case study in lecture had similar performance between regression with CP & Tucker decompositions, would you say that held true here? Question 2. (30 points) Supposed you are asked by Tony Stark (Iron Man) to help with the efficiency and manufacture of arc reactors. Hermione Granger has been contracted to develop a spell to magically increase the longevity of a material that is used in the new design, but is a primary cause of failure. Work with Ms. Granger to pick one of her newly developed spells. 10 series of heat maps from experimentation are provided in heat_images.mat each with 10 samples in time, along with 2 competing spell designs in spells.mat. a) Hermione originally asked Han Solo to take a look at this problem and help select a spell, but being so roguish, he tried to reduce dimension too far. He ran a linear regression on the simple scalar mean of each image. Examine the series of images for samples 1 and 2, from heat_images.mat, and explain why you would expect regression with tensor inputs will be much more useful. (You do not need to include plots of the images in your response.) b) Load the candidate spell readings to be predicted from spells.mat. Convert all images (training samples & candidate spells) to gray scale. Form tensors of each sample and the candidates. Provide: Plots of the grayscale 10th (last) images of spells and spell2. (Do not show scaled images, e.g., scale should be 0-255, not normalized to a colormap by min/max values). According to the slides (57-58), how many parameters would we have to estimate for this data, un- decomposed? c) Perform CP decompositions on the data from the 10 samples and spells 1 & 2. Then train a linear regression model from the CP decompositions and predict the time to failure for spells 1 & 2. Response values are given in heat_resp.mat. Try different ranks, at least 1-5, and calculate MSE from the training data. Then predict the time to failure for each candidate spell. Report: Your MSE for ranks 1-5 Which rank you would pick and (briefly) why. Predicted time to failure for the two candidate spells. d) Perform Tucker decompositions on the data from the 10 samples and spells 1 & 2. Train a linear regression model from the Tucker decompositions and predict the time to failure for spells 1 & 2. Provide the estimated times to failure for each. Try different ranks again, at least 1-5 and calculate the MSE from the training data. Predict the time to failure for the candidate spells. Report: .Your MSE for ranks 1-5 Which rank you would pick and (briefly) why. Predicted time to failure for the two candidate spells. e) Which spell do you recommend is used for the arc reactors? The case study in lecture had similar performance between regression with CP & Tucker decompositions, would you say that held true here