What is mathematical model ?Analytical (exact) and numerical solutionError concept: Round-off error 3.7 The derivative of f(x) = 1/(1 – 3x²) is given by%3D6x(1 – 3x?)?-Do you expect to have difficulties evaluating this function atx = 0.577? Try it using 3- and 4-digit arithmetic with chopping. 3.8 (a) Evaluate the polynomialy = x' - 7x2 + 8x – 0.35at x = 1.37. Use 3-digit arithmetic with chopping. Evaluate thepercent relative error.(b) Repeat (a) but express y asy = ((x – 7)xr + 8)x – 0.35-Evaluate the error and compare with part (a).

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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You are asked to estimate the model wage=B1+B2 EDU+ B3 EDU? where wage is the hourly wage ($) and EDU is the number of years of education. OLS results from a sample of 1000 university graduates are reported below: Wage=9.79-1.20 EDU+0.089 EDU2; R-square%-D0.23 se (2.67) (0.40) (0.09) Test the hypothesis that the expected effect of an extra year of education on hourly wage of an individual with 12 years of education is $1 against the alternative that it is less than $1 at 5% significance level (show all work). You are given the se(b2+2"b3 EDU)=D 0.045 Paragraph BI II
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Timber yield is approximately equal to the volume of a tree, however, this value is difficult to measure without first cutting the tree down. Instead, other variables, such as height and diameter, may be used to predict a tree's volume and yield. Below is data on diameter (inches), height (feet), and volume (cubic feet) diameter height volume 18 80 51.5 8.3 70 10.3 11.2 75 19.9 13.3 86 27.4 12.9 85 33.8 11.7 69 21.3 20.6 87 77 11.4 76 21.4 17.9 80 58.3 13.7 71 25.7 16 72 38.3 10.7 81 18.8 10.8 83 19.7 16.3 77 42.6 12 75 19.1 13.8 64 24.9 10.5 72 16.4 17.3 81 55.4 11 75 18.2 11.4 76 21 8.8 63 10.2 14.2 80 31.7 Develop a regression model to use diameter and height to predict volume. Report the adjusted R-squared. Blank 1. Fill in the blank, read surrounding text.
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The next four questions (29 to 32) refer to the following: To most Canadians, earthquakes are viewed as rare occurrences, but they are actually quite common. In just one month in 2001, Natural Resources Canada recorded 215 earthquakes that affected Canada from B.C. to Nunavut to Newfoundland. We would like to determine whether there is a linear relationship between the location of an earth- quake X (measured in degrees latitude north of the equator) and the magnitude of the earthquake Y (measured on the Richter scale). The explanatory and response variables are measured for a sample of 13 earthquakes. The equation of the least squares regression line is ŷ = -3.05+ 0.10x. The ANOVA table is showm below: ге Source of Variation df Sum of Squares Mean Square F Regression Error Total 1.40 25.10

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3.7 The derivative of f(x) = 1/(1 – 3x²) is given by %3D 6x (1 — Зх?)2 - Do you expect to have difficulties evaluating this function at x = 0.577? Try it using 3- and 4-digit arithmetic with chopping.