Given that the data set below:(a) calculate the model parameters a, b and c of a second degree polynomial modely(x)-ax²+bx+c by using the least-squares method.(b) make plots of the data set and the polynomial fit in the same graph.i 12345 67 89 10 11 12 13 14 15X₁0.5 1.01.52.0 2.53.0 3.54.04.55.0 5.56.0 6.57.0-0.2 0.5 1.52.4 2.8 2.0 1.91.0 0.6 0.3 -0.2 -0.4 -0.3-1.0BYi0.0-0.5

(a) The given quadratic equation can be normalized as follows:

Answered: Given that the data set below: (a)…

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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What is the coefficient of x² term in the least-squares parabola prepared for the data in the table below? X y 1 2 2 6 3 7 4 8 5 10 6 11 7 11 8 10 9 9
Consider the intersection of a linear function f(x) = mx + b and a third degree polynomial function, P(x) = a3x3 + a2x2 + a,x + ao . Which of the following statements is false? Select one: a. It is possible that the graphs of the two functions do not intersect at all b. It is possible that the graphs of the two functions intersect in exactly one point c. It is possible that the graphs of the two functions cross in one point and touch in another without crossing d. It is possible that the graphs of the two functions intersect in exactly three points
We use the form ŷ = a + bx for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept. Data from a report showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in a state. A Minitab printout provides the following information. Predictor Coef SE Coef T P Constant 315.27 28.31 11.24 0.002 Elevation -31.812 3.511 -8.79 0.003 S = 11.8603 R-Sq = 96.8% Notice that "Elevation" is listed under "Predictor." This means that elevation is the explanatory variable x. Its coefficient is the slope b. "Constant" refers to a in the equation ŷ = a + bx. (a) Use the printout to write the least-squares equation. ŷ = + x (b) For each 1000-foot increase in elevation,…
We use the form ŷ = a + bx for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept. Data from a report showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in a state. A Minitab printout provides the following information. Predictor Coef SE Coef T P Constant 316.62 28.31 11.24 0.002 Elevation -30.516 3.511 -8.79 0.003 S = 11.8603 R-Sq = 96.2% The printout gives the value of the coefficient of determination r2. What is the value of r? Be sure to give the correct sign for r based on the sign of b. (Round your answer to four decimal places.) What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares…
Year 2008 2009 2010 2011 2012 2013 2014 2015 Index 87 40 57 64 63 57 84 106 Use quadratic regression to find a fourth-order polynomial function f(x) that models this data
Fit a linear function of the form f (t) = c0 + c1t to the data points (0, 0), (0, 1), (1, 1), using least squares. Use only paper and pencil. Sketch your solution, and explain why it makes sense.
H1.
Suppose experimental data are represented by a set of points in the plane. An interpolating polynomial for the data is a polynomial whose graph passes through every point. In scientific work, such a polynomial can be used, for example, to estimate values between the known data points. Another use is to create curves for graphical images on a computer screen. One method for finding an interpolating polynomial is to solve a system of linear equations. Find the interpolating polynomial of (SEE PICTURE)

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