In a given linear regression model with given features/predictors, we can compute its coefficients (which multiply corresponding features) by using... (check all that apply; hint: exactly two are correct) confusion matrix normal equations cross-validation ROC ☐ gradient descent algorithm
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- In R, write a function that produces plots of statistical power versus sample size for simple linear regression. The function should be of the form LinRegPower(N,B,A,sd,nrep), where N is a vector/list of sample sizes, B is the true slope, A is the true intercept, sd is the true standard deviation of the residuals, and nrep is the number of simulation replicates. The function should conduct simulations and then produce a plot of statistical power versus the sample sizes in N for the hypothesis test of whether the slope is different than zero. B and A can be vectors/lists of equal length. In this case, the plot should have separate lines for each pair of A and B values (A[1] with B[1], A[2] with B[2], etc). The function should produce an informative error message if A and B are not the same length. It should also give an informative error message if N only has a single value. Demonstrate your function with some sample plots. Find some cases where power varies from close to zero to near…given the observed data (obsX,obsY), learning rate (alpha), error change threshold, and delta from the huber loss model,write a function returns theta0 and theta1 that minimizes the error. Use pseudo huber loss functionWhich statements are true about LASSO linear regression? Group of answer choices has embedded variable selection by shrinking the coefficient of some variables to exactly zero. has one hyper-parameter lambda (The regularization coefficient) which needs to be tuned if there are multiple correlated predictors lasso will select all of them adds the L2 norm of the coefficients as penalty to the loss function to penalize larger coefficients
- check the picture to understand the questions dont reject itQuestion 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…A Ridge Linear Regression adds the sum of the squared values of the coefficients to the loss function to penalize large coefficients. Group of answer choices True False
- Mary: "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?Choose an option for each of the 4 pointsAssume the following simple regression model, Y = β0 + β1X + ϵ ϵ ∼ N(0, σ^2 ) Now run the following R-code to generate values of σ^2 = sig2, β1 = beta1 and β0 = beta0. Simulate the parameters using the following codes: Code: # Simulation ## set.seed("12345") beta0 <- rnorm(1, mean = 0, sd = 1) ## The true beta0 beta1 <- runif(n = 1, min = 1, max = 3) ## The true beta1 sig2 <- rchisq(n = 1, df = 25) ## The true value of the error variance sigmaˆ2 ## Multiple simulation will require loops ## nsample <- 10 ## Sample size n.sim <- 100 ## The number of simulations sigX <- 0.2 ## The variances of X # # Simulate the predictor variable ## X <- rnorm(nsample, mean = 0, sd = sqrt(sigX)) Q1 Fix the sample size nsample = 10 . Here, the values of X are fixed. You just need to generate ϵ and Y . Execute 100 simulations (i.e., n.sim = 100). For each simulation, estimate the regression coefficients (β0, β1) and the error variance (σ 2 ). Calculate the mean of…