1. Given a table of datax |0115 3we want to find a linear functiony = co +c1xthat best fits the data in the least squares sense.(a) (3 points) Write down a linear system Ac = y for the vector c =of coefficients.C1(b) (4 points) Find the best least squares fit by a linear function to the data by computingthe least squares solution of the linear system in part (a).

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Answered: 1. Given a table of data a | 0|1|2 y…

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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A collector of antique clocks sold at auction believes that the price received for the clocks may be modeled as a linear function of the age of the clocks and the number of bidders at the auction. After a preliminary study and collection of 32 observations, the collector came up with the following second-order model: y = BO+B₁x₁+B₂x₂ + ß3 x1x2 +B4x² +ɛ, where y: price of a clock; x₁: age of a clock; x2: the number of bidders. Considering the output below and by setting a = 0.05, answer the following questions. The regression equation is Price = 262 +2.26 Age + 14.2 Bidder + 1.13 AgeBid 4.20 Bid^2 Predictor Constant -261.7 2.260 14.21 Age Bidder AgeBid Bid^2 S = 84.512 Coef SE Coef 1.1301 -4.196 Analysis of Variance Source 404.4 2.052 R-Sq= 96.0% Variable Age Bidder AgeBid Bid^2 60.83 0.23 5.17 0.000 0.219 1.344 -3.12 0.004 R-Sq (adj) DF Regression 4 4606950 Residual Error 27 192840 Total 31 4799790 SS T P -0.65 0.523 1.10 0.280 0.817 a. Is the model useful as a whole? Apply an…
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Sand is being dumped from a hopper railcar at a rate of 40 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal to each other (both are growing larger as more sand is dumped). How fast is the base diameter increasing when the base is 18 feet long? Round your answer to three decimal places. ft/min
Find the null space associated with the equations: 2x+z+w = 0 7x-6y-z-w-v = 0 -5x+4y+w = 0
Let s be a person's annual salary (in thousands of dollars) after she has worked for t years at a company. Some pairs of values of t and s are shown in the table below. t (years) 0 1 3 6 s (thousands of dollars) 54 57 63 72 a) Create a scattergram of the data. b) Draw in a linear model on the same grid. c) Use your graph to estimate when the person's salary will be $66 thousand. (Show your work on the graph.) d) What is the s-intercept of the model? Interpret it in terms of this application.

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1. Given a table of data a | 0|1|2 y 153 we want to find a linear function y = 0 +c1x that best fits the data in the least squares sense. (a) (3 points) Write down a linear system Ac = y for the vector c = of coefficients.