Find the line y = mx + b that best approximates the data points (0, 0), (1, 2), (2, 1) in the sense of least squares.Express the answer by giving mx + b, using syntax like (-1/3)*x-5 .

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Answered: Find the line y = mx + b that best…

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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The least squares fit line for the points (1,-0.3), (2,-0.4), and (3, 0.7) has form ŷ = mx + b. First, let f be the sum of the square errors between the predicted values ŷ and y-values for the three points. f(m, b) = Minimize this function to find the m and b of the least square line, then write down equation of least squares line. y= Submit Question
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It is possible to find a linear equation that has a smaller Sum of Squared Errors (SSE) than the line based on the Method of Least Squares Equation. True False
Consider the following. (-8, 0) y = -5 y 6 4 (0, 2) (a) Find the least squares regression line. 5 (8,6) (b) Calculate S, the sum of the squared errors. Use the regression capabilities of a graphing utility to verify your results.
The least squares fit line for the points (3, 3.1), (2,2.3), and (1, 2.1) has form ŷ = mx + b. First, let f be the sum of the square errors between the predicted values ŷ and y-values for the three points. f(m, b) = Minimize this function to find the m and b of the least square line, then write down equation of least squares line. y
If we have a series of experimental data of 2 variables A and B, with both sets of data related by the expression: A = B + C, where C is a constant. If by plotting A against B we obtain a straight line with a theoretical slope m and ordinate at the origin C, and by applying the least squares method we could determine C. But, as the previous expression can be transformed into B = A - C, we could also plot B against A and obtain C from the ordinate at the origin with a changed sign. Should the same value of C be obtained by both methods?(A). Yes, because the step from "A = B + C" to "B = A - C" is an exact algebraic transformation(B). Only in the case where A and B are equal(C). Only in the case where the errors of A and B are high, since the least squares method compensates for them(D). The most normal thing is that the same value is not obtained
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Find the best-fitting least-squares linear and quadratic approximations to the data set{(1,2),(3,4),(5,7),(7,9),(9,12)}.
Find the least squares fit solution for paramters a & b of function: y = a/(x^2+b) Express the result for a & b in terms of the data (xi, yi), i=1,...,n
In a study, nine tires of a particular brand were driven on a track under identical conditions. Each tire was driven a particular controlled distance (measured in thousands of miles) and the tread depth was measured after the drive. Tread depth is measured in "mils." Here, 1 mil is 0.001 inch. The equation of the least-squares regression line is: y-hat 360.64 - 11.39x Also, r = 0.9762. For every 1,000 miles driven, the decrease in tread depth (in mils) can be estimated as: 246.74 mils. 11.39 mils. 275.6 mils. O 360.64 mils.
Which of the following best describes the least-squares line fit to the data shown in the plot? (i) bo = 0, bị =-1 (ii) bo = -3, b₁ = 1 (iii) bo-5, b₁ = 2 (iv) bo = −3, bị =-1 (v) bo = 0, b₁ = -3 2 X
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 Climatology Report No. 77-3 of the Department of Atmospheric Science, Colorado State University, showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in Colorado locations. A Minitab printout provides the following information. Predictor Constant Elevation Coef 315.00 -29.166 SE Coef 28.31 3.511 I 11.24 -8.79 P 0.002 0.003 S = 11.8603 R-Sq = 96.44 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. (c) The printout gives the value of the…

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