In repeated trials of executing the code, why might the Mean Square Error (MSE) for Linear Regression sometimes be lower when employing gradient descent as opposed to the analytical solution?
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In repeated trials of executing the code, why might the Mean Square Error (MSE) for Linear Regression sometimes be lower when employing gradient descent as opposed to the analytical solution?
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- 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 functionYou trained the regression model with 100 regressors and 1000 observations in the training and another 1000 in the test sample. You found that in-sample R2 over the training sample is 70% and the out-of-sample R2 over the test sample only - 30%. (select all that apply) a) Do you think there is any problem and how would you characterize it? Can adding more regressors (if you have them) help the model? b) Which approaches you may use to solve the problem? c) What would you expect the in-sample R2 to increase or decrease after that? What about the out-of-sample (test) R2?When and why do we employ the Binomial, Poisson, and Proportional models of regression?
- 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 FalseYou are given the true labels and the predicted probabilities from logistic regression model for N test examples. Approximately compute the AUC scores for ROC and PR curves.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?
- In the simple linear regression equation ŷ = bo + b₁x, how is b₁ interpreted? it is the change in that occurs with a one-unit change in y O It is the estimated value of ŷ when x = 0 O It is the change in ŷ that occurs when bo increases O it is the change in ŷ that occurs with a one-unit change inAssume 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…Q.1 Explain the different regularization techniques used with Linear regression to handle multivariate data.
- Using the USairpollution data from the R library MVA, build a multiple linear regression model to predict the amount of SO2, which affects air pollution, from the six other explanatory variables. Provide working code in R.Say that you have the following initial settings for binary logistic regression: x = [1, 1, 3] w = [0, -2, 0.75] b = 0.5 2. Given that x's label is 1, what is the value of w_1, w_2, and w_3 at time t + 1 if the learning rate is 1? For this problem, you may ignore the issue of updating the bias term. 3. What is the value of P(y = 1 | x) given your updated weights from the previous question? 4. Given that x's label is 1, what is the value of the bias term at time t + 1 if the learning rate is 1? 5. What is the value of P(y = 1 | x) given both your updated weights and your updated bias term? 6. Given that x's label is 0, what is the value of P(y = 0| x) at time t + 1 if the learning rate is 0.1? Round your answer to the nearest 1000th as a number [0, 1].