10. (a) Perform a qualitative analysis on the following slightly different competitionmodel:dydtdxdtO Search= x(1- x - y)= y(0.5-0.25y-0.75x)(b) Based on your work, in the long-term, if both populations start out at non-zerovalue, will one population drive the other into extinction or will the populationsbe able to coexist?11. (a) Use Euler's method to estimate x(0.3) for the differential equationdxdtC= 2(1-x)with initial condition x(0) = 2. Use a time step of 0.1.(b) Calculate the actual value of x(0.3) based on your solution in Problem 2.IRE R O

Given the competition model described by the system of differential equations…

Answered: Perform a qualitative analysis on the…

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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Can you show an example similar to this problem part A - but not this problem - of how to calculate an exact percentage change?
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�=−1.04+0.24�1−0.27�2 where Y� = quarterly sales (in thousands of cases) of the cold remedy X1�1 = Cascade's quarterly advertising (× $1,000) for the cold remedy X2�2 = competitors' advertising for similar products (× $10,000) Here is additional information concerning the regression model: sb1=0.042�b1=0.042, sb2=0.070�b2=0.070, R2=0.720�2=0.720, se=1.63��=1.63, F-statistic=31.402F-statistic=31.402, and Durbin-Watson (d) statistic=0.499Durbin-Watson (d) statistic=0.499. Which of the independent variables (if any) appears to be statistically significant (at the 0.05 level) in explaining sales of the cold remedy? (Hint: t0.05/2,33 - 3=2.042�0.05/2,33 - 3=2.042.) Check all that apply. X1�1 X2�2 What proportion of the total variation in sales is explained by the regression…
Consider a competitive market in which price adjusts to excess demand or supply and firms enter and exit the industry if profits or losses are being made. Price adjusts to excess demand according to dp 0.5(qº – q$) dt Where qº = 30 – 2p is the demand function, qº = 2N is the supply function, p is price, N is the number of firms in the industry and a is the speed of adjustment coefficient. The number of firms adjust according to dN 5 (p 10) dt Derive a system of differential equation to represent this information. Solve the system.
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…
Consider the linear regression model Y; = Bo + B1 X¡ + U¡ for each i in $10,000) and Y; represents the home size (measured in square feet). We run an OLS regression and get: 1,..., n withn = 1,000. X; represents the annual income of individual i (measured Bin = 43.2, SE(§ „) = 10.2, Bon = 700, SE(Bom) = 7.4. Suppose that we want to test Ho : B1 O against H1 : ß1 # 0 at 1% significance level. Assuming that the sample size is large enough, which one of the following is true about the p-value of this test? 43.2 The p-value can be computed as P(-| ), where is the standard Normal CDF 10.2 а. b. None of the answers 43.2 The p-value can be computed as (- ), where O is the standard Normal CDF 10.2 С. 43.2 d. The p-value can be computed as 20(-- ), where O is the standard Normal CDF 10.2
Plzz give the answer of all questions
Proposed Method: 1. Simple linear regression 2. One sample t-test Regression equation: y; = B0 + B1z; + € i = 1(1)30 Where y; Quarterly sales data from the ith gas station z; the size of the population of cars in the ith gas station B0 and B1 are unknown parameters which are to be estimated by the model. Null hypothesis: HO: B1 = 0 Alternative Hypothesis: H1: B1 + 0 1 forgot how to do this because its been a while since doing a statistics class
Please all solve the problem
Q13) assume the final regression equation from the stepwise regression analysis of the dependent variable cost (C) and the 10 potential independent variables is as follows: C = -5000 + 75 D + 0.4 S - 130 PT + 100 NE Given that the final model is valid, interpret the coefficient of S: On average, with each additional MWe of net capacity, the construction cost _____ while keeping other variables constant. A) decreases by $0.4 B) increases by $400,000 C) increases by $0.4 D) decreases by $400,000
Assume there is a positive linear correlation between the variable R (Return rate in percent of a financial investment) and the variable t (age in years of the investment) given by the regression equation R= 2.3t + 4.8 A. Without further information, can we assume there is a cause-and-effect relationship between the return rate and the age of the investment? B. If the investment continues to grow at a constant rate, what is the expeted return rate when the investment is 7 years old? C. If the investment continues to grow at a constant rate, how old is the investment when the return rate is 30%?
Suppose we have data on dependent variable y and explanatory variables x 1 and x_2, all measured in units. We estimate the following linear regression: Number of cbs = E( 2, 1656) Prob > ? R-squared Adj R-squared 1659 1123.68 0.0000 0.5757 %3D 0.5752 Coef. Std. Err. P>It| x_1 I x_2 1 cons I 1.003119 .68 80123 .2408667 .0252676 .0253665 .077143 39.70 27.12 3.12 0.000 0.000 0.002 Which of the following statements is correct? Select one: a. We can conclude that there is no nonlinear effect of x 2 on y. b. An increase of 1% in x_1 increases y by 0.3119%, when x 2 remains constant. c. The estimated level of y for someone with x_1 equal to 10 and x_2 equal to 8 is 15.535. d. The estimated level of y for someone with x_1 equal to 10 and x 2 equal to 8 is 15.776,

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