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- Find A+ and use it to compute the minimal length least squares solution to Ax = b.The following data were collected to determine therelationship between two processing variables and thehardness of a certain kind of steel: AnnealingHardness Copper content temperature(Rockwell 30-T) (percent) (degrees F)y x1 x278.9 0.02 1,00055.2 0.02 1,20080.9 0.10 1,00057.4 0.10 1,20085.3 0.18 1,00060.7 0.18 1,200Fit a plane by the method of least squares, and use it toestimate the average hardness of this kind of steel when the copper content is 0.14 percent and the annealing tem-perature is 1,100◦F.Find the orthogonal trajectories of the family of circles passing through the points (1, −2) and (1, 2).
- Find the least squares approximation g(x) = a0 + a1x of f (x) = ex, 0 ≤ x ≤ 1.A certain experiment produces the data (0, 1),(−1, 2),(1, 0.5),(2, −0.5). Find values for a, b, and c which describe the model that produces a least squares fit of the points by a function of the form f(x) = ax2 + bx + c.Using least-squares regression, find a straight line that best fits the data in Table 1 below. xi yi 0.2 8.2 0.4 8.4 0.6 8.5 0.8 8.6 1.0 8.8 1.2 8.7 b. Using table 1 above, find the second-degree Lagrange interpolating polynomial that goes through the first three data points, and use it to find the interpolated value at xi = 0.48.
- Write down the Lagrangian, and hence find the two stationary points of the problem below and Find the Bordered Hessian for this problem, evaluate the required leading principalminors for both solutions. Hence show that one solution is a local maximum and the other is indefinite.Calculate the error using error correction learning rule where inputs are x1 = 1.7, x2 = 0.3, x3 = 0.15 and synaptic weights are w1 = -1, w2 = 1.7, w3 = 2, bias = -15 and desired output dk = 17.Below you are given a partial Excel output based on a sample of 25 observations. Coefficients Standard ErrorIntercept 145 29x1 20 5x2 –18 6x3 4 4 The critical t value obtained from the table to test an individual parameter at the 5% level is _____. a. 2.074 b. 2.069 c. 2.080 d. 2.06
- The joint pmf of X and Y is f(x, y) = 1/6, 0 ≤ x+y ≤ 2, where x and y are nonnegative integers. Compute Cov(X, Y) and determine the correlation coefficient.Find the Wronskian and determine whether the given set of functions is linearly independent on the interval (-∞, ∞)In Exercise, find A+ and use it to compute the minimal length least squares solution to Ax = b.