data100_hw5

Graded Homework 5 Student Khankamol Chor Kongrukgreatiyos Total Points 27.75 / 32 pts 

Question 1 Linear regression residuals 5.5 / 7 pts 1.1 Question 1a 2 / 2 pts  + 2 pts Fully correct proof + 1 pt Sets up a key equation: either takes the average of the predictions ( ) or states that the sum/mean of residuals is zero ( ) + 0.5 pts Expands the key equation: either attempts to algebraically simplify the average of the predictions or expands the sum of residuals as + 0.5 pts Attempts proof, but no major milestones achieved + 0 pts Incorrect or blank − 0.35 pts Did not select pages in Gradescope 1.2 Question 1b 3 / 3 pts  + 3 pts Fully correct proof + 1 pt Sets up the equation for simple linear regression + 1 pt Attempts to substitute + 0.5 pts Attempts proof, but no major milestones achieved + 0 pts Incorrect/blank − 0.35 pts Did not select pages in Gradescope 1.3 Question 1c 0.5 / 2 pts + 2 pts Fully correct proof  + 0.5 pts Recognizes that the mean of the residuals is zero ( ) + 0.5 pts Manipulates the expression to produce the estimating equation + 0.5 pts Recognizes that the sum of the residuals is zero ( ) + 0.5 pts Attempts proof, but no major milestones achieved + 0 pts Incorrect or blank − 0.35 pts Did not select pages in Gradescope + n 1 ∑ i =1 n y ˉ r ( x − σ x σ y ) x ˉ e = ∑ i =1 n i 0 − ∑ i =1 n y i ^ y = ∑ i =1 n i 0 x = i x ˉ = e ˉ 0 e x ∑ i =1 n i i e = ∑ i n i 0

Question 3 Constant predictions 8 / 9 pts 3.1 Question 3a 2 / 2 pts  + 2 pts Fully correct proof + 0.75 pts Sets up the risk function, + 0.5 pts Takes the derivative of risk with respect to , attempting to compute + 0.5 pts Sets the derivative of risk equal to zero + 0.5 pts Attempts proof, but no major milestones achieved + 0 pts Incorrect or blank − 0.35 pts Did not select pages in Gradescope 3.2 Question 3b 3 / 3 pts  + 3 pts Fully correct proof + 0.75 pts Sets up the empirical risk, + 0.5 pts Attempts to take the derivative of loss with respect to to compute + 0.5 pts Sets derivative equal to 0 + 0.5 pts Attempts proof, but no major milestones achieved + 0 pts Incorrect or blank − 0.35 pts Did not select pages in Gradescope 3.3 Question 3c 2 / 2 pts  + 2 pts Fully correct: states that is the mode of the dataset and gives appropriate reasoning + 1 pt Correctly describes how to minimize L0 loss: choose the value of that minimizes the number of times + 0.5 pts Provides reasoning for how to identify the ideal + 0.25 pts Attempts solution, but no major milestones achieved + 0 pts Incorrect or blank − 0.35 pts Did not select pages in Gradescope M SE ( a ) = ( y − n 1 ∑ i =1 n i a ) 2 a M SE ( a ) ∂ a ∂ M AE = ∣ y − n 1 ∑ i =1 n i a ∣ a ∣ y − ∂ a ∂ i a ∣ a ^ a y = i  y i ^ a ^

3.4 Question 3d 1 / 2 pts + 2 pts Fully correct: identifies the optimal as the quantile and gives appropriate justification + 0.75 pts Attempts to take the derivative of loss or risk with respect to + 0.5 pts Sets the derivative equal to 0  + 0.5 pts Attempts to provide reasoning for the choice of quantile that gives the optimal  + 0.5 pts Attempts solution, but no major milestones achieved + 0 pts Incorrect or blank − 0.35 pts Did not select pages in Gradescope a ^ 1+ w 1 a a ^

Questions assigned to the following page: 1.1 and 1.2

Question assigned to the following page: 2.1

Question assigned to the following page: 2.2

Questions assigned to the following page: 3.3 and 3.4

Question assigned to the following page: 4.1