1. Given raw data samples xij'Vi for i 1, . . . , N and j 1, . . . , d, we often "standardize" the data before working with it, which gives normalized features iT)/s and target Vi = (Vi-yr)/Syr. Here, x, and sz, denote the sample mean and sample standard-deviation of the raw feature x, andy and syr denote the sample mean and sample standard-deviation of the raw targets y. (a) Show that the standardized features and standardized 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 x1,x2, ,xd using linear regression, i.e., y = 0+Ax1 + +Baxd. To fit the regression coefficients B, for j - 0,1,...,d, you would use the standardized training data {yi} and xij. Show that the least-squares intercept term equals zero, i.e., A,-0. (c) Let the regression coefficients determined for the normalized data be A, 2, , BalT Now say that you instead would like to predict the raw target y" associated with some raw features a using a corresponding predictor %,B B. How do the raw features x using a correspondin 0 1.od regression coefficients r relate to 1. Given raw data samples xij'Vi for i 1, . . . , N and j 1, . . . , d, we often "standardize" the data before working with it, which gives normalized features iT)/s and target Vi = (Vi-yr)/Syr. Here, x, and sz, denote the sample mean and sample standard-deviation of the raw feature x, andy and syr denote the sample mean and sample standard-deviation of the raw targets y. (a) Show that the standardized features and standardized 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 x1,x2, ,xd using linear regression, i.e., y = 0+Ax1 + +Baxd. To fit the regression coefficients B, for j - 0,1,...,d, you would use the standardized training data {yi} and xij. Show that the least-squares intercept term equals zero, i.e., A,-0. (c) Let the regression coefficients determined for the normalized data be A, 2, , BalT Now say that you instead would like to predict the raw target y" associated with some raw features a using a corresponding predictor %,B B. How do the raw features x using a correspondin 0 1.od regression coefficients r relate to