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- For what ultimate purposes may algorithms like Nelder-Mead, Newton-Raphson or gradient-descentbe used for?a) To find the minimum of a function.b) To find all zeros of a function.c) To evaluate the derivative of a function.d) To solve a generalised regression problem1. Describe how linear regression can be used on the exponential function in a meaningful way noting that it is not a linear function. 2. Describe two different aspects between closed (bracketed) and open root-finding methods.Derive the formulas for the variance of the MLE estimators of the unknown parameters of the simple linear regression model.
- We are intrested in predicting the percentage of people commuting to work by walking given some input variables. Each observation corresponds to a different city and each input variable summarizes some characteristic of a given city, such as density, urban sprawl and average income per capita. This is 1. not a machine learning problem. Only social scientists would be interested in such a problem. 2. both a classification and a regression problem as it depends on the way one codes the output variable as either 0, 1 or a a particular number in the [0,1] interval. 3. a regression problem. The output variable is continuous. 4. a classification problem. Walking to work is a discrete variable and can only take two values: to walk to work and not to walk to worhere is myLinReg needed to solve this problem function [a,E] = myLinReg(x,y) % [a,E] = myLinReg(x,y) % calculate the linear least squares regression to data given in x,y % Input % x: column vector of measured x data to fit % y: column vector of measured y data to fit % Output % a: vector of coefficients for the linear fit y = a(1)+a(2)*x % E: error of the fit = sum of the residual square % define a as a 2 entry vector a = zeros(2,1); n = length(x); % determine number of data points if n ~= length(y) fprintf ('Error: the length of data vectors x and y must be the same\n') a(:) = realmax(); E = realmax(); % set a and E to real max return end % calculate and store sum terms Sx = sum(x); Sy = sum(y); Sxx = sum(x.*x); Sxy = sum(x.*y); % Calculate linear equation coefficients a(1) = (Sxx*Sy-Sxy*Sx)/(n*Sxx-Sx*Sx); % a0 coefficient a(2) = (n*Sxy-Sx*Sy)/(n*Sxx-Sx*Sx); % a1 coefficient % Calculate the error of the fit E = sum((y-(a(2)*x+a(1))).^2); endThat is not my question... Here's mine:- Implement this in MATLAB algorithms for: Polynomial Least Squares Regression - For polynomial curve fitting, examine 1st to 5th polynomial order and determine the right order to be used using the least value of Akaike Information Criterion and Bayesian Information Criterion. - For the final evaluation of your curve fitting functions, use the Root Mean Square Error and Mean Absolute Error as the final metrics against Data 00. - Include plots/graphs.
- Do the following: a. Explain why asymptotic bounds of functions are useful? b. Find the upper bound, lower bound, and tight bound of running time of a linear function f(n) = 6n + 3. Explain the inequalities involved.Enumerate two real-world scenarios where circular functions can be applied. Clearly discuss in each scenario how the math (circular functions) is used.Could you lend me a hand with this problem? I'm having difficulty figuring out how to approach it. Could you guide me through each step and provide a thorough explanation? question that I need with:7.10 Show that ALLDFA is in P.
- it is known that a natural. law obeys the quadratic relationship y=ax^2.what is the best line of form y=px+q that can be used to model data and minimise Mean-squared-error, if all of the data points are drawn uniformly at random from the domain [0,1]?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…Answer the given question with a proper explanation and step-by-step solution. You will be required to run Expectation Maximization for estimating parameters of a Gaussian mixture model in this example. Refer to lecture slides (Lecture E.2) for the exact formulation. You can use python or do the computations by hand. Recall that you need to use the pdf formulation for computing p(x|theta_k) Consider the following one dimensional data set: 2.3 3.2 3.1 1.6 1.9 11.5 10.2 12.3 8.6 10.9 Assume that we are interested in learning a mixture model with two components (k = 2). Let pi_k denote the probability P(z_i = k) for any i. Let (mu_1,sigma_1) be the parameters for the first Gaussian component of the mixture and (mu_2,sigma_2) be the parameters for the second Gaussian component of the mixture. Given the following initialization: pi_1 = pi_2 = 0.5, mu_1 = mu_2 = 0, and sigma_1 = sigma_2 = 1. Answer the following: a) After first M step, mu_1 = mu_2 = 6.56 b) After…