2.3.9Using the third-order Adams-Bashforth-Moultonpredictor-corrector method (that is, the second-order Adams-Bashforth formula as predictor andthe third-order Adams-Moulton formula ascorrector), compute an estimate of x(0.5) forthe initial-value problemdx= x² + t², x(0.3) = 0.1dtusing step size h = 0.05. (You will need to employanother method for the first step to start this scheme- use the fourth-order Runge-Kutta method).

Answered: 2.3.9 Using the third-order…

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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4. Monitoring oxygen consumption (y) each day during the 5-day BOD test shows the following results, which are expected to conform the equation: y = Lo(1-ekt). t (d) Y (mg/L) Perform regression analysis to fit the nonlinear equation and obtain Lo (mg/L) and k (d¹¹). 1 85 2 150 3 150 4 170 5 205
Use the data below to solve for the following: 2. Naïve method 3. Unweighted 3 month moving average 4. Weighted Moving Average (3 months, with the following weights: 0.45, 0.35, 0.20) 5. Simple Exponential Smoothing with the following parameters: Ft+1=32 and the α = .15 6. Time Series Regression Months 1 2 3 4 5 6 7 8 9 10 11 12 Firm's Actual Market share 30 32 33 34 28 33 29 27 32 33 28 33 7. Which of the following forecasting method will you use? 8. What are your basis in choosing for your forecasting techniques? Explain briefly. ONLY DO 56
Suppose you are a manager for a carnival game at the local fair. You want to estimate how many prizes you will need to have in stock to give out, based on the number of tickets purchased before the fair begins. You examine the past 24 fair openings to make your regression model, and find the following information. (x − x)² = 791.5 Σe² = = 223.1 and ŷ = 294.21 +0.186x, where is the number of tickets purchased before the fair begins, and ŷ is the predicted demand for prizes during the first day of the fair. What is the standard error of the slope of the regression line? 8.1 0.054 0.024 √
In using a double exponential smoothing method, we calculated S3 to be 2,255.6 and G3 to be 12.2. D4 is 1,916 and alpha and beta values are 0.4, and 0.53, respectively. The error for the forecast in period 4 (F4) is:
(a) According to experimental data, the intensity of scattered sunlight in the atmosphere I is inverse proportional to the wavelength in the power n, 1 = A/2". Consider the pseudo-experimental data shown in the Table where and I are presented in the normalized dimensionless variables. (b) 2 350 400 450 500 550 600 650 700 750 800 I 6.1.10 4.9-10 1.9-10 2.1-10 6.5-10 9.3-106 6.5-10 3.5-10 3.8-10° 2.5-106 Using the statistical analysis, determine the exponent n and constant A. Present the result with the determined constants in the form I(2) = A2™". (c) Present the plot 1(2) in the log-log scale. Show the data given in the table and best fit line.
4
Cascade Pharmaceuticals Company developed the following regression model, using time-series data from the past 33 quarters, for one of its nonprescription cold remedies: Y = -1.04 +0.24X₁-0.27X2 where Y = quarterly sales (in thousands of cases) of the cold remedy X₁ = Cascade's quarterly advertising (x $1,000) for the cold remedy X₂ = competitors' advertising for similar products (x $10,000) Here is additional information concerning the regression model: Sb1 = 0.052, Sb2 = 0.070, R² = 0.640, se = 1.63, F-statistic = 31.402, and Durbin-Watson (d) statistic = 0.499. Which of the independent variables (if any) appears to be statistically significant (at the 0.05 level) in explaining sales of the cold remedy? (Hint: to.05/2,33-3= 2.042.) Check all that apply. O X₁ O X₂ What proportion of the total variation in sales is explained by the regression equation? O 0.122 O 0.070 O 0.640 O 0.052 The given F-value shows that you reject the null hypothesis that neither of the independent variables…
Suppose we have a regression situation involving 3 predictor variables and an intercept, with the following model: Y = Bo + B1X1 + B2X2 + B3X3 + € where n = 15. We find the following regression output (with some values deleted). Coefficients: Estimate Std. Error (Intercept) 0.08544 0.11529 х1 x2 0.67800 1.06700 -0.85400 1.19700 x3 0.08700 2.86110 Suppose we wish to calculate a 95% confidence interval for B3 (the slope of x3), in the usual way. What is the upper bound of the interval?
1. (a) Consider the following output from a regression in R Call: 1m (formula = Y X + Z + W) Residuals: Min 10 Median 3Q -1.84572 -0.47207 -0.01262 0.54948 2.62708 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 3.32540 2.63484 1.262 0.219 0.52183 8.554 9.45e-09 *** 4.46385 -2.45113 0.05868 -41.771 1.701. Hence we use a t statistic where, under Ho. -2.45-2 0.522 As -8.531.701 then we can conclude the null hypothesis is true. =-8.53 01
3. The dependent variable of the following regression result is the log value of hourly wage. Please make your answers to the following questions. 1) What do you think is the potential problem with this regression equation? If there is a problem here, how would you solve it? 2) Heteroskedasticity robust standard errors were used in this analysis. Why do you think this analysis used heteroskedasticity robust standard errors?
B1
4. Suppose that n=100 i.i.d observations for (Y₁, X₁) yield the following results Ỹ = 32.1 +66.8X, SER=15.1, R² = 0.81 (15.1) (12.2) Another researcher is interested in the same regression, but he makes an error when he enters the data in his regression program: He enters each observation twice, so he has 200 observations. Using these 200 observations, what results will be produced by his program? Write it in the following format: Ỹ +---X, SER= (---) (---) R² =

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