2. Calculate the following quantities using least-squares (give coefficients to three decimal places):(a) The least-squares solution to the inconsistent system x+3y=9, 3r+ y = 5, x+y=2.(b) The least-squares line y = mx +b approximating the points {(4,7), (11, 21), (15,29), (19,35), (30,49)}.(c) The least-squares quadratic y = ar²+bx+c approximating the points {(-2,22), (-1,11), (0,4), (1,3), (2, 13)}.

(a) To find the least squares solution to the inconsistent system. x+3y=93x+y=5x+y=2 (b) To find the…

Answered: 2. Calculate the following quantities…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Internet Audience At the end of a certain year, the four companies with the largest number of home Internet users in the United States were Microsoft, Time Warner, Yahoo, and Google, with a combined audience of 284 million users. Taking x to be the Microsoft audience in millions, y the Time Warner audience in millions, z the Yahoo audience in millions, and u the Google audience in millions, it was observed that zu = x + y = and xy + zu = 44. How large was the audience of each of the four companies at the end of that year? Microsoft Time Warner Yahoo Google 3(x - y) + 8 50 + z + u
Suppose you want to interpolate the points (−1, 0), (0, 6), (1, 0) and (2, 0) by a polynomial. (a) What will the degree of the interpolating polynomial be? Write down the linear system. Solve the system to get the polynomial. Find the interpolated value at t = 1/2. (b) Write down directly the Lagrange basis interpolation. Simplify the polynomial to get the same answer as (a).
In the least-squares line = 5 – 9x, what is the value of the slope?When x changes by 1 unit, by how much does y change? When x increases by 1 unit, y decreases by 9 units. When x decreases by 1 unit, y decreases by 9 units. When x increases by 1 unit, y decreases by −9 units. When x increases by 1 unit, y increases by 9 units.
5. a. Find the line of best fit through these points using the least squares method and the pseudo inverse. Plot the result (The best fit line and the five points should be on the graph). Ax b. Given the following five points in the (x, y) plane: (-4,-7), (-2,-3), (0, 2), (1, 3), (5,9) = Show how the slope and y-intercept of your line are related to the solution of Pb, where A can be factored to QR and P = QQ¹.
The function h is a quadratic function whose graph is a translation 7 units left and 9 units up of the parent function Ax)=x". What is the equation of h in vertex form and in the form y = ax² +bx+c? a Ob O C Od y = (x + 7)² +9; y = x² +14x+49 y =(x-7)² +9; y=x²-14x+58 y = (x+7)² +9; y=x² +14x+58 y =(x-7)² +9; y = x² - 14x+49
14) The equation of the least squares regression line between the dose of medication in mg (x) and the patients' systolic blood pressure (y) is... ŷ = -10x + 170 a) Use the regression line to estimate the systolic blood pressure for a patient taking 4 mg of medication. b) If we want to have a systolic blood pressure of 110, use the regression line to estimate the appropriate dose.
Each month for several months, the average temperature in °C (x) and the number of pounds of steam (y) consumed by a certain chemical plant were measured. The least-squares line computed from the resulting data is y = 245.82 + 1.11x. a) Predict the number of pounds of steam consumed in a month where the average temperature is 65°C. Round the answer to two decimal places. b) If two months differ in their average temperatures by 5°C, by how much do you predict the number of pounds of steam consumed to differ? Round the answer to two decimal places.
In a study to predict temperature from air pressure in a piston-cylinder device, 19 measurements were made of temperature in °F (y) and air pressure in psi (x). Three models were fit: the linear model y = Bo + B,x + ɛ, the quadratic model y = Bo + Bix + B2x² + ɛ, and the cubic model y = Bo + B,x + B2x? + Bx3 + E. The residuals and fitted values for each model are presented in the following table. Plot the residuals versus the fitted values for each model. For each model, state whether the model is appropriate, and explain. %3D Quadratic Model Fit Linear Model Cubic Model Residual Fit Residual Residual Fit -56.2 125.6 11.2 58.2 3.3 66.1 -34.0 153.1 -7.4 126.5 -6.7 125.7 8.4 179.8 4.9 183.4 9.2 179.0 21.4 207.2 -3.6 232.2 0.9 227.8 28.6 234.7 -8.2 271.5 -5.9 269.2 46.9 260.9 8.1 299.7 7.3 300.5 47.2 288.1 15.7 319.6 12.1 323.2 8.5 314.4 -7.0 329.8 -11.7 334.6 -7.1 342.0 4.0 330.9 1.0 333.9 -47.1 139.3 -1.3 93.6 -4.1 96.4 -1.6 166.2 9.1 155.5 12.1 152.5 38.0 220.9 5.9 253.0 9.5 249.4…
Find the best fit polynomial of degree 1 approximating the data of the system of equations P(0) = 0, P(1) = 1, and P(2) = 4. y = 2x + 3 y =2x 3 y = 3x + 2 - X 2 0 0 0 0 y= HIM
It is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let x be the number of fouls more than (i.e., over and above) the opposing team. Let y be the percentage of times the team with the larger number of fouls wins the game. x 1 2 5 6 y 48 41 33 26 Find the equation of the least-squares line = a + bx. (Round your answers to four decimal places.) = + x
а. Complete the table. (or just write answers) Xi Yi 2 2 3 4 Totals E x; = E yi = Exf = Σχy Find SSxy, SSXX B1. x, y, and fo- Write the equation of the least squares line. b. C. d) What will be y if x=10
Four points have these coordinates: 3 4 4 4 3 y Use the least-squares line to predict the value of ywhen x= 3.5. اختر احدى الدجابات 0.6 O 5.5 О 35 3.4

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