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- Question 3. Regression need answer of part b Consider real-valued variables X and Y. The Y variable is generated, conditional on X, from the fol- lowing process: E~N(0,0²) YaX+e where every e is an independent variable, called a noise term, which is drawn from a Gaussian distri- bution with mean 0, and standard deviation σ. This is a one-feature linear regression model, where a is the only weight parameter. The conditional probability of Y has distribution p(YX, a) ~ N(aX, 0²), so it can be written as p(YX,a) = exp(- (-202 (Y-ax)²) 1 ν2πσ The following questions are all about this model. MLE estimation (a) Assume we have a training dataset of n pairs (X, Y) for i = 1..n, and σ is known. Which ones of the following equations correctly represent the maximum likelihood problem for estimating a? Say yes or no to each one. More than one of them should have the answer "yes." a 1 [Solution: no] arg max > 2πσ 1 [Solution: yes] arg max II a [Solution: no] arg max a [Solution: yes] arg max a 1…You are provided with last year’s data showing which high school students chose standard or advanced coursework. The predictor variables include their writing score, math score, and science scores from previous years. Your task is to build a model that predicts if this year's incoming students are in advanced or standard coursework given the above predictor variables. Which model is suitable for this task? Linear regression k-means Clustering Logistic Regression Regression treeQuestion 4: Consider two recurrence relations P(n) = 2P(n/2) +n and Q(n) = 4Q (n/4) +2n. What is the relationship between P and Q? Is P = O(Q), P = N(Q), or P = O(Q)? Prove your answer using limit of ratio definition of asymptotic notations.
- how does different values of λ affects the forecasted results in a double exponential smoothing methodMary: "Before we run the multivariate linear regression, feature scaling should be performed." Give one reason to support Mary's idea. Moreover, should we perform feature scaling before or after the gradient descent?Credit Scoring
- Three disease-carrying organisms decay exponentially in seawater according to the following model: Using numerical methods, estimate the initial concentration (at t=0) of each organism (A,B, and C) using multiple linear regression given the following measurements (Hint: Linearize the said equation first before proceeding using the transformation at Figure 4.5)A. Suppose that every random variable in the joint distribution of P(A,B,C,D,E) = P(E|C,D)P(D|C)P(C|A,B)P(B|A)P(A). has a domain containing 10 elements. How many rows are needed to list the full joint distribution in an explicit table? B. Suppose that every random variable in the joint distribution of P(A,B,C,D,E) = P(E|C,D)P(D|C)P(C|A,B)P(B|A)P(A). has a domain containing 10 elements. How many rows in total are needed to list the conditional probability tables for your belief network representation?What does it mean to say a set of wffs Γ is p-consistent (and p-inconsistent)?