Q5: Given the data set below:0.0 0.50.11.01.5 2.0 2.5 3.0 3.54.0y0.6 1.1 1.8 2.4 2.2 2.0 1.5 0.7Calculate the model coefficients A, B and C of a second-degree polynomialy = Ax² + Bx + C by the least-square curve fitting.X

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Answered: Q5: Given the data set below: 0.0 0.5…

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 annual expenditure for cell phones varies by the age of an individual. The average annual expenditure E(a) (in $) for individuals of age a (in years) is given below:a: 20, 30, 40, 50, 60, 70E(a): 502, 658, 649, 627, 476, 2131. Use quadratic regression to find the model that best represents the data.2. At what age is the yearly expenditure for cell phones the greatest? Round the answer to the nearest year. YOU MUST SHOW THE WORK FOR THIS PART!
A computer engineer needs to know how the efficiency of a new computerprogram depends on the size of incoming data. Efficiency will be measuredby the number of processed requests per hour. Applying the program todata sets of different sizes with the following results. The response variableis the number of processed requests (Y) and to predict it from the size of adata set (X). Estimate the quadratic regression model and use it to find theprocessed requests when the data size is 14 GB.Data size (GB) X 6 7 7 8 10 10 15Processed requests Y 50 43 44 37 25 26 15
We are given the following training examples: (1.2, 3.2), (2.8, 8.5), (2,4.7), (0.9, 2.9), (5.1, 11) We want to apply a 3-nearest neighbor rule in order to perform regression. (a) : Predict the label (real value) at each of the following two points: 1 = 1.5 and x2 = 4.5. time we want to perform distance-weighted nearest neighbor regression. What values do we predict now for x1 = 1.5 and x2 = 4.5? (b). Instead of weighing the contribution of each of the 3 nearest neighbors equally, this
The following are Rotameter calibration data (flow rate versus Rotameter reading): 100 160 a) Fitting the calibration data to a second order polynomial using curve fitting. Rotameter Reading R 15 30 60 80 Flow rate V(L/min) 20 85.7 119.3 55 b) Calculate the flowrate (V) at rotameter reading R=70.
i. Create a quadratic model: thergh j. What is the R2 value? What does this tell you about the relationship between x and y? k. Do a scatterplot of Y1 and the data. What does that tell you about the quadratic model? 1. Store the predictions in L3 and the Residuals in L4. m. Do a scatterplot of X-values vs Residuals. When doing this plot, first Deselect Y1. Sketch the plot here. What does this tell you about the quadratic model? n. Look at the Residual plot and use the Trace Key to find the 'largest' residual (it could be positive or negative.) Go back to your Stat Editor and find the corresponding x- value, y-value and predicted y-value.
The following data is the forward-bias characteristics of a silicon diode. Fit the data with linear, cubic spline, and 4th-degree polynomial methods. Use Vp as a and Ip as y, respectively. Ip(mA) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Vp(V) 0.506 0.541 0.561 0.575 0.586 0.595 0.603 0.609 0.615 Ip(mA) 1 2 3 4 5 7 8 Vp(V) 0.620 0.655 0.675 0.690 0.702 0.711 0.719 0.726 0.733 Ip(mA) 10 11 12 13 14 15 16 17 18 VD(V) 0.739 0.743 0.749 0.753 0.757 0.762 0.766 0.769 0.773 Ip(mA) 19 20 VD(V) 0.776 0.779
Suppose you have four data points xo ... x4 as shown on the figure to the right. Note that the data are not evenly spaced. We desire f(x) to estimate the value of f(x*). 6. On the figure, DRAW what a polynomial regression of order zero would look like. Label the line as "A. 7. On the figure, DRAW what a polynomial regression of order one would look like. Label the line as "B." 8. In the space below, write the regression equation for the polynomial you would choose to estimate the value of f(x*). Leave all coefficients as unknowns. Then, DRAW how it should look on the figure. Label is as line "C." O Xo X1 x* O + x X2 X3

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Q5: Given the data set below: 0.0 0.5 0.1 0.6 1.5 2.0 2.5 3.0 3.5 1.0 4.0 1.1 1.8 2.4 2.2 2.0 1.5 0.7 y Calculate the model coefficients A, B and C of a second-degree polynomial y = Ax² + Bx + C by the least-square curve fitting. X