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- 4. Write a Julia function called resistance that returns the resistance distance r given the Cholesky factor U of L+ ee" and nodes i and j. rij = resistance (U, i, j)Write a function using lgwt() to calculate composite Gausian quadrature using the call I = compositeGauss_integrate(Fun,a,b,n,N) where, - Fun is the name for the function to be integrated, - a is the lower limit of integration, b is the upper limit of integration, - n is the number of points used in each Gaussian quadrature subintervals - N is the number of subintervals. Code: function[I]=compositeGauss_integrate(Fun,a,b,n,N)% Inputs:% Fun - the function being integrated% a - the lower limit of the integration% b - the upper limit of the integration% n - the number of points used in each Gaussian quadrature subintervals% N - the number of subintervals % Outputs:% I - value of integral % calculate the width of each subintervalh=(b-a)/N;% calculate the endpoints of the N subintervalsxs= ;% initialize the integral valueI=0;% for each subinterval, calculate the Gaussian point locations and the weights,% then calculate the weighted sum of the evaluated function at the% Gauss points and…Write a function reg3 that, given x and y data vectors, fits a least-squares regression function of the form y ≈ f (x) = ax + b and uses this regression function to return the estimated y value at the input xnew. For example, if x = [7, 2, 3, 4, 5]; y = [3, 2, 1, 0, 1]; xnew = 6, the output should be 1.8378
- Write a function that takes in two variables, x, and y. The function should compute the correlation coefficient( Pearson's, Spearman, and Kendall). Perform a hypothesis test on the correlation coefficient using the function cor. test() Using RstudioThis assignment is to a analyze a random experiment. Assume that you have to toss a fair coin (50% probability for each head and tail) N times, where N→ 00, When head comes up, you will be rewarded (gain) RM1, while if tail comes up, you will be penalized (loss) RM1. Write a function function sum_return coin_toss (N) that returns a row vector sum_return of length N+1. Each column i represents gained sum from i-1 number of coin tosses, i.e. sum_return (1) =0. To solve this problem, you will need both a for statement and the rand function. Try out several (minimum of 2) tries a value of N of 1000, 10000, 100000, 1000000 and plot the results. The x-axis must show the values from 0 to N. The y-axis should be limited to the maximum gain and minimum loss during each experiment. Note that as N is large, plotting N points will take a long time. Find a way on how this can be made faster.There are a number of plants in a garden. Each of the plants has been treated with some amount of pesticide. After each day, if any plant has more pesticide than the plant on its left, being weaker than the left one, it dies. You are given the initial values of the pesticide in each of the plants. Determine the number of days after which no plant dies, i.e. the time after which there is no plant with more pesticide content than the plant to its left. Example // pesticide levels Use a -indexed array. On day , plants and die leaving . On day , plant in dies leaving . There is no plant with a higher concentration of pesticide than the one to its left, so plants stop dying after day . Input Format The first line contains an integer , the size of the array .The next line contains space-separated integers . Constraints Sample Input 7 6 5 8 4 7 10 9 Sample Output 2 Explanation Initially all plants are alive. Plants = {(6,1), (5,2), (8,3), (4,4), (7,5),…
- In Python, write a function that does least squares regression. The function should take input of an X and Y data. The output should be a dict in Python with the 1) best fit values for the intercept 2) the best-fit value for the slope, 3) the sum-squared error, 4) the residuals, and 5) the p-value for the two-sided hypthesis test of the slope being zero. Each component of the dict should be labeled. Test the function with simulated data.Plot the function f(x) = x4 − 3x3 + 10x2 − x − 2 for −6 ≤ x ≤ 6.Draw the function as a solid black 2-point-wide line, and turn on the grid. Be sure to include a title and axis labels, and include the equation for the function being plotted in the title string.Count the total number of different one-to-one functions from the set {0, 1} into the set {1, 2, 3,...,n}, where n is a positive integer.
- The following table contains output from a lasso fit to a linear model with d= 5 variables and n = 65 observations. Starting from the left, the columns are X, and B₁, ..., B5, i.e. each row has X and the transposed column vector B¹(X). 0.00000 0.00000 -0.04596 0.08497 0.04129 -0.08195 -0.00764 0.22778 -0.04274 0.07868 0.03430 -0.07599 0.00000 1.96117 -0.02092 0.04606 0.00000 -0.04090 3.28220 0.00000 0.02263 0.00000 -0.02105 4.49485 0.00000 0.00375 0.00000 0.00000 4.73846 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 You will perform computations using this table and report your results. A) Compute the maximum value of the L₁ norm for vectors of coefficients attained in this table, that is compute maxx ||3¹(A)||₁ B) Consider the 2nd breakpoint from the top of the table, namely the breakpoint corresponding to A-0.22778. Compute the L₁ norm for the vector of coefficients at this point in the path, i.e. compute || (0.22778)||1 C) For the same 2nd breakpoint in the table, compute…In Python, write a function that does least squares regression. The function should take input of an X and Y data set. The output should be a dict in Python with the 1) best fit values for the intercept 2) the best-fit value for the slope, 3) the sum-squared error, 4) the residuals, and 5) the p-value for the two-sided hypthesis test of the slope being zero. Each component of the dict should be labeled. Test the function with simulated data.The following table contains output from a lasso fit to a linear model with d = 5 variables and n = 50 observations. Starting from the left, the columns are X, and B₁,..., B5, i.e. each row has X and the transposed column vector (X). 0.00000 1.20706 -0.66487 0.46392 0.19746 -0.38526 6.18304 1.05715 -0.50740 0.27952 0.00000 -0.17280 12.48795 0.91734 -0.36985 0.11063 0.00000 0.00000 16.89171 0.82829 -0.28890 0.00000 0.00000 0.00000 33.19002 0.53551 0.00000 0.00000 0.00000 0.00000 59.28000 0.00000 0.00000 0.00000 0.00000 0.00000 For each of the required computations below, briefly report your procedure and the required quantity. a) For each row in the table, compute s, the proportion of shrinkage defined as s = s(X) = ||B(A)||₁/ maxx ||B(A)||1- b) Consider X'= 25.040865. Note that X' is the intermediate value between λ = 16.89171 and λ = 33.19002 of the 4th and 5th rows above. Using this value of X', compute and report the shrunk estimator B(x'). c) Give the proportion of shrinkage s(X')…