Implement a simple linear regression model using Python without using any machine learning libraries like scikit-learn. Your model should take a dataset of input features X and corresponding target values y, and it should output the coefficients w and b for the linear equation y =wX + b
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- Consider a plot of a model of the form Y i = B 0 +B1T i + B2(X 1i-C) + e i. Which of the following is true? A. B2 is the bump at the cutoff B. B2 is the slope of the line C. B1 is the slope of the line D. B0 is the bump at the cutoffLogistic regression aims to train the parameters from the training set D = {(x(i),y(i)), i 1,2,...,m, y ¤ {0,1}} so that the hypothesis function h(x) = g(0¹ x) 1 (here g(z) is the logistic or sigmod function g(z) can predict the probability of a 1+ e-z new instance x being labeled as 1. Please derive the following stochastic gradient ascent update rule for a logistic regression problem. 0j = 0j + a(y(¹) — hz(x)))x; ave. =Assume 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…
- Prog&Numrecal analysis MATLAB**In bivariate regression, the regression coefficient will be equal to rXY when:A machine learning model is learning parameters w₁ and w₂. It turns out that for the latest data inputted, the error function is: E=(w₁-1)²+(W₂-1)² The current values of the parameters are w₁-2 and w₂=0.9. Gradient descent is applied to update the parameters. Which statement is true? 7 0 w1 2 W2 3 4 0 W2 W1 decreases and decreases, change in w₁ is bigger. W₁ decreases and w₂ increases, change in w₂ is bigger. W₁ decreases and w₂ increases, change in w₁ is bigger. W₁ decreases and w₂ increases, both by the same amount. 18 16 14 12 10 8 6 4 HH +++ 2