Regression analysis class Find the variance stabilizing transformation g(y) for a response variableY,ifE(y) = µ and V(y)= V.Consider the linearizable functions as follows. Find new transformed variables (x*, y*,Bo or B as you need) to linearize the functions below.y =Bir1 + Bo.

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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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Mathematics of Data Management, Analyzing One and Two Variable Data
77. DISCUSS: The Least Squares Line The least squares line or regression line is the line that best fits a set of points in the plane. We studied this line in the Focus on Modeling that follows Chapter 1 (see page 174). By using calculus, it can be shown that the line that best fits the n data points (x1, yı), (X2, y2), - .. , (X, Yn) is the line y = ax + b, where the coefficients a and b satisfy the following pair of linear equations. (The notation E- x, stands for the sum of all the x's. See Section 13.1 for a complete description of sigma (E) notation.) x Ja + nb = Ey. k=1 (2:)- + (2-) » - .» k=1 Use these equations to find the least squares line for the fol- lowing data points. (1, 3), (2,5). (3, 6), (5,6). (7,9) Sketch the points and your line to confirm that the line fits these points well. If your calculator computes regression lines, see whether it gives you the same line as the formulas.
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Find the regression line associated with the set of points. (Round all coefficients to four decimal places.) HINT [See Example 2.] (3, 4), (4, 4), (5, 5) y(x) = Graph the data and the best-fit line.
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