The best least squares line through the 10 data points and the RMSE of the files and use it to estimate the 2010 production level.

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Answer 1

Question

Chapter 4.1, Problem 2CP

(a)

To determine

The best least squares line through the 10 data points and the RMSE of the files and use it to estimate the 2010 production level.

(b)

To determine

Find the best least squares parabola through the 10 data points and the RMSE of the files and use it to estimate the 2010 production level.

(c)

To determine

The best least squares cubic curve through the 10 data points and the RMSE of the files and use it to estimate the 2010 production level. And, explain which fit best represents the data in terms of RMSE.

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Problem 11 (a) A tank is discharging water through an orifice at a depth of T meter below the surface of the water whose area is A m². The following are the values of a for the corresponding values of A: A 1.257 1.390 x 1.50 1.65 1.520 1.650 1.809 1.962 2.123 2.295 2.462|2.650 1.80 1.95 2.10 2.25 2.40 2.55 2.70 2.85 Using the formula -3.0 (0.018)T = dx. calculate T, the time in seconds for the level of the water to drop from 3.0 m to 1.5 m above the orifice. (b) The velocity of a train which starts from rest is given by the fol- lowing table, the time being reckoned in minutes from the start and the speed in km/hour: | † (minutes) |2|4 6 8 10 12 14 16 18 20 v (km/hr) 16 28.8 40 46.4 51.2 32.0 17.6 8 3.2 0 Estimate approximately the total distance ran in 20 minutes.

- Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p − 1)/2 multiple of n, i.e. n mod p, 2n mod p, ..., p-1 2 -n mod p. Let T be the subset of S consisting of those residues which exceed p/2. Find the set T, and hence compute the Legendre symbol (7|23). 23 32 how come? The first 11 multiples of 7 reduced mod 23 are 7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8. The set T is the subset of these residues exceeding So T = {12, 14, 17, 19, 21}. By Gauss' lemma (Apostol Theorem 9.6), (7|23) = (−1)|T| = (−1)5 = −1.

Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p-1)/2 multiple of n, i.e. n mod p, 2n mod p, ..., 2 p-1 -n mod p. Let T be the subset of S consisting of those residues which exceed p/2. Find the set T, and hence compute the Legendre symbol (7|23). The first 11 multiples of 7 reduced mod 23 are 7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8. 23 The set T is the subset of these residues exceeding 2° So T = {12, 14, 17, 19, 21}. By Gauss' lemma (Apostol Theorem 9.6), (7|23) = (−1)|T| = (−1)5 = −1. how come?

Answer 2

Question

Chapter 4.1, Problem 2CP

(a)

To determine

The best least squares line through the 10 data points and the RMSE of the files and use it to estimate the 2010 production level.

(b)

To determine

Find the best least squares parabola through the 10 data points and the RMSE of the files and use it to estimate the 2010 production level.

(c)

To determine

The best least squares cubic curve through the 10 data points and the RMSE of the files and use it to estimate the 2010 production level. And, explain which fit best represents the data in terms of RMSE.

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 3

Question

Chapter 4.1, Problem 2CP

(a)

To determine

The best least squares line through the 10 data points and the RMSE of the files and use it to estimate the 2010 production level.

(b)

To determine

Find the best least squares parabola through the 10 data points and the RMSE of the files and use it to estimate the 2010 production level.

(c)

To determine

The best least squares cubic curve through the 10 data points and the RMSE of the files and use it to estimate the 2010 production level. And, explain which fit best represents the data in terms of RMSE.

Expert Solution & Answer

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Answer 4

Question

Chapter 4.1, Problem 2CP

(a)

To determine

The best least squares line through the 10 data points and the RMSE of the files and use it to estimate the 2010 production level.

(b)

To determine

Find the best least squares parabola through the 10 data points and the RMSE of the files and use it to estimate the 2010 production level.

(c)

To determine

The best least squares cubic curve through the 10 data points and the RMSE of the files and use it to estimate the 2010 production level. And, explain which fit best represents the data in terms of RMSE.

Expert Solution & Answer

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Answer 5

Chapter 4.1, Problem 2CP

(a)

To determine

The best least squares line through the 10 data points and the RMSE of the files and use it to estimate the 2010 production level.

(b)

To determine

Find the best least squares parabola through the 10 data points and the RMSE of the files and use it to estimate the 2010 production level.

(c)

To determine

The best least squares cubic curve through the 10 data points and the RMSE of the files and use it to estimate the 2010 production level. And, explain which fit best represents the data in terms of RMSE.

Answer 6

Chapter 4.1, Problem 2CP

(a)

To determine

The best least squares line through the 10 data points and the RMSE of the files and use it to estimate the 2010 production level.

Answer 7

Chapter 4.1, Problem 2CP

(a)

To determine

The best least squares line through the 10 data points and the RMSE of the files and use it to estimate the 2010 production level.

Answer 8

(b)

To determine

Find the best least squares parabola through the 10 data points and the RMSE of the files and use it to estimate the 2010 production level.

Answer 9

(b)

To determine

Find the best least squares parabola through the 10 data points and the RMSE of the files and use it to estimate the 2010 production level.

Answer 10

(c)

To determine

The best least squares cubic curve through the 10 data points and the RMSE of the files and use it to estimate the 2010 production level. And, explain which fit best represents the data in terms of RMSE.

Answer 11

(c)

To determine

The best least squares cubic curve through the 10 data points and the RMSE of the files and use it to estimate the 2010 production level. And, explain which fit best represents the data in terms of RMSE.

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 4.1 - Solve the normal equations to find the least...Ch. 4.1 - Find the least squares solutions and RMSE of the...Ch. 4.1 - Find the least squares solution of the...Ch. 4.1 - Let mn, let A be the mn identity matrix (the...Ch. 4.1 - Prove that the 2-norm is a vector norm. You...Ch. 4.1 - Let A be an nn nonsingular matrix. (a) Prove that...Ch. 4.1 - Find the best line through the set of data points,...Ch. 4.1 - Find the best line through the set of data points,...Ch. 4.1 - Find the best parabola through each data point set...Ch. 4.1 - Find the best degree 3 polynomial through each set...

The best least squares line through the 10 data points and the RMSE of the files and use it to estimate the 2010 production level.

Solution Summary: The author uses the command c=polyfit(x,y,1) to obtain the straight line which best fits the data. They calculate the Root Mean Square Error (RMSE) by considering the error as the actual value

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The best least squares line through the 10 data points and the RMSE of the files and use it to estimate the 2010 production level.

Find the best least squares parabola through the 10 data points and the RMSE of the files and use it to estimate the 2010 production level.

The best least squares cubic curve through the 10 data points and the RMSE of the files and use it to estimate the 2010 production level. And, explain which fit best represents the data in terms of RMSE.

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Chapter 4 Solutions