Answered: Let y = X3 + e, where with N = 10 and p… | bartleby

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 62CR

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4.5. Let y = XB+E, where &~ N(0,0²IN), and 3 is a p-dimensional vector,
with N= 10 and p = 3. Given y'y = 58, and given the following normal
equations,
431 +232-233
281 +232 +83
-281 +8₂ +683
4
7
9,
find the least squares estimates of 3 and o2. What are the estimates of
B1, B2, B3, B1 - B2, and B₁ + B3 ?

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EXER 5.1: Given the observations (1,1), (2,3), (4,5), find the least squares estimates for m and b for the best fit line y=mx+b.
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Using the least squares approximation, the best fit an exponential curve y = ea(x-b) to the given data: (2, 7), (3, 17), (5, 49), (6, 71), defined by the form a) Y = Cx² + Bx + A b) Y = Bx + A c) Y = Cx² + A d) None of the above
Q.2: The population of the germs grown in a specific lab environment has been measured to be 600, 700, and 1000 at times t 0, 1, and 2 hours. Find the curve which gives the best least squares fit to the given population points. Find the coefficients C and D of the best curve. Also proceed to find the error vector that would demonstrate the measurement error / tolerance in population sizem.
A certain experiment produces the data (3,7.6), (4,5.2), and (5, - 0.1). Describe the model that produces a least-squares fit of these points by a function of the form y = A cos x+B sin x. E1 The model is y =XB + e, where y = X=.B = and e= E2 (Type an exact answer.)
A certain experiment produces the data (1,7.9), (2,5.4), and (3, –.9) · Describe the model that produces a least-squares fit of these points by a function of the form y = A cos x + B sin x
Given that []=[]+[Ca] x Measurements give [y₁ y₂]=[3_4]. Find the least-squares estimate for x. Use a sketch in the y₁, y2 plane to indicate the geometrical interpretation.
A certain experiment produces the data (1,7 2), (2,5.2), and (3, - 0.5). Describe the model that produces a least-squares fit of these points by a function of the form y A cos x B sin x The model is y = XB + e, where y = %3D V and e = eE, (Type an exact answer.)
Find the least-squares line y = Bo + Bjx that best fits the data (-2,0), (–1,0), (0, 2), (1,4), and (2, 4), assuming that the first and last data points are less reliable. Weight them half as much as the three interior points.
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For each of the sets of data that follows, use the least squares approximation to find the best fits with both (i) a linear function and (ii) a quadratic function. Compute the error E in both cases. (a) {(-3, 9), (−2, 6), (0, 2),(1, 1)} (b) {(1, 2), (3,4), (5, 7), (7, 9), (9, 12)} (c) {(−2, 4), (−1, 3), (0, 1), (1,−1), (2,−3)}

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