Determine the clamped-clamped splines that fit the data
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Determine the clamped-clamped splines that fit the data
3. The set of the following data points...
3. The set of the following data points is given days x 14 22 30 y...
3. The set of the following data points is given days x 14 22 30 y 320 490 540 38 380 (a) Determine the natural cubic splines that fit the data. (b) Determine the clamped-clamped splines that fit the data (e) Determine the interpolated value of y for x = 27 both from (a) and (b). (d) Plot of the data points and the interpolating polynomials.
To be done by hand 3. The set of the following data points is given days...
To be done by hand
3. The set of the following data points is given days X 14 22 490 30 38 540 380 у 320 (a) Determine the natural cubic splines that fit the data. (b) Determine the clamped-clamped splines that fit the data (c) Determine the interpolated value of y for r = 27 both from (a) and (b). (d) Plot of the data points and the interpolating polynomials.
Please answer everything fully and show steps! 3. The set of the following data points is...
Please answer everything fully and show steps!
3. The set of the following data points is given days 14 22 30 38 46 X 320 490540 500 480 (a) Determine the natural cubic splines that fit the data (b) Determine the interpolated value of y for r 27.5 (c) Plot of the data points and the interpolating polynomials
3. The set of the following data points is given days 14 22 30 38 46 X 320 490540 500 480 (a)...
1. Fit cubic splines to the following data (1) using natural end condition and estimate f(4.0)...
1. Fit cubic splines to the following data
(1) using natural end condition and estimate f(4.0) with the
cubic spline.
(2) using clamped end condition with f1’=-2.5, f5’=3.0 and
estimate f(4.0) with the cubic spline.
(3) using “not-a-knot” end condition and estimate f(4.0) with
the cubic spline.
4 2 9.0 7.0 5.0 2.5 1.0 Xi 2.5 0.5 2.5 1.0 fi 2,5 er
4 2 9.0 7.0 5.0 2.5 1.0 Xi 2.5 0.5 2.5 1.0 fi 2,5 er
9. Which of the following methods can interpolate a set of data points with a function...
9. Which of the following methods can interpolate a set of data points with a function that is differentiable at each data point? Linear Splines LU Decomposition Power Method . Bisection Method Cubic Splines 10. Assume that you have a nonlinear spring, with spring force given by F() k2 You can computework done over a displacement of x = a to x = b, by performing the integration, OF(x)dz. What will be the error incurred if Simpson's rule is used...
Example 1: Least Squares Fit to a Data Set by a Linear Function. Compute the coefficients of the ...
Example 1: Least Squares Fit to a Data Set by a Linear Function. Compute the coefficients of the best linear least-squares fit to the following data. x2.4 3.6 3.64 4.7 5.3 y| 33.8 34.7 35.5 36.0 37.5 38.1 Plot both the linear function and the data points on the same axis system Solution We can solve the problem with the following MATLAB commands x[2.4;3.6; 3.6;4.1;4.7;5.3]; y-L33.8;34.7;35.5;36.0;37.5;38.1 X [ones ( size (x)),x); % build the matrix X for linear model %...
3. Normal equations for n points to fit the line y = mx + c: ri 72 yi Problem 1 The data points i...
3. Normal equations for n points to fit the line y = mx + c: ri 72 yi Problem 1 The data points in the table are given. -2.4 | -5.0 20.81.5 0.3 2.5 1.9 6.4 3.2 11.0 3 Total (a) Fit the best line - to the points (b) Fit the best line y- mr + c to the points (c) Plot the data points and the best fit lines in (a) and (b). Which of the lines is...
8. If the data set shown below were used to fit the following simple regression model,...
8. If the data set shown below were used to fit the following simple regression model, y = Bo + Bix te, which of the following equations would result in the smallest SSE? a) y=2x V X b) y=2 + x 3 2 c) y = 3 + 0.5 4 2 d) All of the above 52
1. Consider the following data set and the Minitab output. Derive (ie., calculate) each number that has a superscri...
1. Consider the following data set and the Minitab output. Derive (ie., calculate) each number that has a superscript next to it in the upper right-hand comer.. Show all of your work in complete detail. Data Display x Y Row 1 3 14 5 16 7 20 4 2 3 5 13 8 19 23 24 5 6 9 7 10 14 22 9 20 38 10 22 39 Descriptive Statistics: X, Y Variable N NMean SE Mean StDev Minimum...
(a) Sketch the line that appears to be the best fit for the given points. (b)...
(a)
Sketch the line that appears to be the best fit for the given
points.
(b) Find the least squares regression line. y(x)=
(c) Calculate the sum of squared error.
11. [-13.22 Points] DETAILS LARLINALG8 2.6.017. Consider the following. 5 (1,5) 4 (2, 4) 3 2 (2, 2) (3, 1) - Х - 1 2 3 4 -14 (a) Sketch the line that appears to be the best fit for the given points.
3. The set of the following data points is given days x 14 22 30 y 320 490 540 38 380 (a) Determine the natural cubic splines that fit the data. (b) Determine the clamped-clamped splines that fit the data (e) Determine the interpolated value of y for x = 27 both from (a) and (b). (d) Plot of the data points and the interpolating polynomials.
To be done by hand
3. The set of the following data points is given days X 14 22 490 30 38 540 380 у 320 (a) Determine the natural cubic splines that fit the data. (b) Determine the clamped-clamped splines that fit the data (c) Determine the interpolated value of y for r = 27 both from (a) and (b). (d) Plot of the data points and the interpolating polynomials.
Please answer everything fully and show steps!
3. The set of the following data points is given days 14 22 30 38 46 X 320 490540 500 480 (a) Determine the natural cubic splines that fit the data (b) Determine the interpolated value of y for r 27.5 (c) Plot of the data points and the interpolating polynomials
3. The set of the following data points is given days 14 22 30 38 46 X 320 490540 500 480 (a)...
1. Fit cubic splines to the following data
(1) using natural end condition and estimate f(4.0) with the
cubic spline.
(2) using clamped end condition with f1’=-2.5, f5’=3.0 and
estimate f(4.0) with the cubic spline.
(3) using “not-a-knot” end condition and estimate f(4.0) with
the cubic spline.
4 2 9.0 7.0 5.0 2.5 1.0 Xi 2.5 0.5 2.5 1.0 fi 2,5 er
4 2 9.0 7.0 5.0 2.5 1.0 Xi 2.5 0.5 2.5 1.0 fi 2,5 er
9. Which of the following methods can interpolate a set of data points with a function that is differentiable at each data point? Linear Splines LU Decomposition Power Method . Bisection Method Cubic Splines 10. Assume that you have a nonlinear spring, with spring force given by F() k2 You can computework done over a displacement of x = a to x = b, by performing the integration, OF(x)dz. What will be the error incurred if Simpson's rule is used...
Example 1: Least Squares Fit to a Data Set by a Linear Function. Compute the coefficients of the best linear least-squares fit to the following data. x2.4 3.6 3.64 4.7 5.3 y| 33.8 34.7 35.5 36.0 37.5 38.1 Plot both the linear function and the data points on the same axis system Solution We can solve the problem with the following MATLAB commands x[2.4;3.6; 3.6;4.1;4.7;5.3]; y-L33.8;34.7;35.5;36.0;37.5;38.1 X [ones ( size (x)),x); % build the matrix X for linear model %...
3. Normal equations for n points to fit the line y = mx + c: ri 72 yi Problem 1 The data points in the table are given. -2.4 | -5.0 20.81.5 0.3 2.5 1.9 6.4 3.2 11.0 3 Total (a) Fit the best line - to the points (b) Fit the best line y- mr + c to the points (c) Plot the data points and the best fit lines in (a) and (b). Which of the lines is...
8. If the data set shown below were used to fit the following simple regression model, y = Bo + Bix te, which of the following equations would result in the smallest SSE? a) y=2x V X b) y=2 + x 3 2 c) y = 3 + 0.5 4 2 d) All of the above 52
1. Consider the following data set and the Minitab output. Derive (ie., calculate) each number that has a superscript next to it in the upper right-hand comer.. Show all of your work in complete detail. Data Display x Y Row 1 3 14 5 16 7 20 4 2 3 5 13 8 19 23 24 5 6 9 7 10 14 22 9 20 38 10 22 39 Descriptive Statistics: X, Y Variable N NMean SE Mean StDev Minimum...
(a)
Sketch the line that appears to be the best fit for the given
points.
(b) Find the least squares regression line. y(x)=
(c) Calculate the sum of squared error.
11. [-13.22 Points] DETAILS LARLINALG8 2.6.017. Consider the following. 5 (1,5) 4 (2, 4) 3 2 (2, 2) (3, 1) - Х - 1 2 3 4 -14 (a) Sketch the line that appears to be the best fit for the given points.
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