Consider the following data points (1,3) (2,7) (3,6) (4, 10) Use partial derivatives to obtain the...
8. (16 points) Suppose you use a quadratic curve y = ax? +b to fit the three (x,y) points (1,3), (0,-1), (-1,1). Use matrix method as described in class to find the least squares estimate of the constants a and b in the above equation. In particular, formulate the relevant normal equation, whose solution leads to the least squares estimates of a and b, and hence obtain the least squares estimate of a and b.
(4 points) 8. Use partial derivatives to perform implicit differentiation to find dy if 5x® y2 + sin (z^y) = 2y4 + 3x, where y is a differentiable function of x.
Consider the following data table: 0 2i = 0.2 0.4 f(xi) = 2 2.018 2.104 2.306 0.6 0.2 and 23=0.4 is The linear Lagrange interpolator L1,1 (2) used to linearly interpolate between data points 12 (Chop after 2 decimal places) None of the above. -2.50x+0.20 -5.00x+2.00 -5.00x+2.00 5.00x-1.00 Consider the following data table: 2 Ti = 0 0.2 0.4 0.6 f(x) = 2.018 2.104 2.306 0.2 and 23 = 0.4, the value obtained at 2=0.3 is Using Lagrange linear interpolation...
Consider the set of data points S = {(2,5),(4, 13), (5, 17), (7, 26)}. Use linear algebra to find the values of the parameters m and b for which the line y = mx + b best fits the data in the least-squares sense.
4. Consider the following data. 16 74 900 29810 (a) Suppose you would like to fit a model of the form yCes (C and k are constants) to this data. Transform the model in such a way that you can use linear least squares to determine C and k. (b) For this data set, use the following equations to find a best fit line. and (e) Use your calculation from part b) to find the model y - Cek for...
(1 point) Find the least-squares regression line ý = bp + biz through the points (-2,0),(2,7),(5,13), (8, 18), (11,27), and then use it to find point estimates y corresponding to r = 4 and 3 = 9. For x = 4, y = For x = 9,4 =
Question 2 (20 points): Consider the functions f(x, y)-xe y sin y and g(x, y)-ys 1. Show f is differentiable in its domain 2. Compute the partial derivatives of g at (0,0) 3. Show that g is not differentiable at (0,0) 4. You are told that there is a function F : R2 → R with partial derivatives F(x,y) = x2 +4y and Fy(x, y 3x - y. Should you believe it? Explain why. (Hint: use Clairaut's theorem) Question 2...
Question 4 Obtain a least squares exponential fit for the following data. Temperature, T (oF) | Solubility, S (%) 100 185 239 285 2.4 3.4 7.0 11.1 19.6
2. Consider the following function: Compute each of the following: Hint: There is probably a better way to compute these than to just mindlessly compute all ot partial derivatives in the order given 3. Is there a function f(x, y) with partial derivatives f, (z, y) = 2r + 5e" + 4y and f,(x, y) = 2y + 5e" + 2x? If so, give an example of a function with these partial derivatives. If not, say why not 2. Consider...