Given raw training data (x, y) for i = 1,...,n and j = 1,...,d, we often...

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Given raw training data (x, y) for i = 1,...,n and j = 1,...,d, we often "standardize" the data before working with it, which gives standardized features zij = (x-T)/8 and targets y₁ = (y − ¹)/syr. Here, T; and s denote the sample mean and sample standard- deviation of the raw features {r}, and y" and sy denote the sample mean and sample standard-deviation of the raw targets {y}. ST (a) Show that the standardized training features and standardized training target each have zero sample-mean and unit sample-variance. (b) Suppose you would like to predict the standardized target y from the standardized features 1, 2,...,d using linear regression, i.e., y = Bo + B₁x₁ +...+ Bard. To fit the regression coefficients ß; for j = 0, 1,..., d, you would use the standardized training data {y} and {ij}. Show that the least-squares intercept term equals zero, i.e., ßo = 0. Given raw training data (x, y) for i = 1,...,n and j = 1,...,d, we often "standardize" the data before working with it, which gives standardized features zij = (x-T)/8 and targets y₁ = (y − ¹)/syr. Here, T; and s denote the sample mean and sample standard- deviation of the raw features {r}, and y" and sy denote the sample mean and sample standard-deviation of the raw targets {y}. ST (a) Show that the standardized training features and standardized training target each have zero sample-mean and unit sample-variance. (b) Suppose you would like to predict the standardized target y from the standardized features 1, 2,...,d using linear regression, i.e., y = Bo + B₁x₁ +...+ Bard. To fit the regression coefficients ß; for j = 0, 1,..., d, you would use the standardized training data {y} and {ij}. Show that the least-squares intercept term equals zero, i.e., ßo = 0.