1. (4 points) In least squares linear regression, our empirical risk is R - N (n-1...

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1. (4 points) In least squares linear regression, our empirical risk is R - N (n-1 (yn - 0xn), n=1 where xn Rd is a training sample, yn ER is its label. O contains the model parameters. Now we have four data points shown in the figure below. We use the least square error in regression. 4 3 2 1 yo -1 -2 -3 5 4 31 2 1 y o -1H : -2 -3 -4 -5 -5 -6 + 2 0 4 8 -6 + -2 0 2 4 6 X (a) x (b) 1) (3 points) In (a), draw the linear regression output and the first principal component. Are they of the same direction/orientation? Use no more than 3 sentences to explain why. 2) (3 points) In (b), draw the regression output, using language to describe when necessary. 1. (4 points) In least squares linear regression, our empirical risk is R - N (n-1 (yn - 0xn), n=1 where xn Rd is a training sample, yn ER is its label. O contains the model parameters. Now we have four data points shown in the figure below. We use the least square error in regression. 4 3 2 1 yo -1 -2 -3 5 4 31 2 1 y o -1H : -2 -3 -4 -5 -5 -6 + 2 0 4 8 -6 + -2 0 2 4 6 X (a) x (b) 1) (3 points) In (a), draw the linear regression output and the first principal component. Are they of the same direction/orientation? Use no more than 3 sentences to explain why. 2) (3 points) In (b), draw the regression output, using language to describe when necessary.