Use the graphical approach to classify the following Lotka-Volterra models of interspecific competitionaccording to coexistence, founder control, species 1 excludes species 2, or species 2 excludes species 1.dN1= 6N1dtN11-13N2- 0.113%3DdN2N2N14N2 1-350.2-35%3Ddt.....The given model is classified as which of the following?O A. species 2 excludes species 1B. coexistenceC. founder controlD. species 1 excludes species 2

Given system is dN1dt=6N11-N113-0.1N213dN2dt=4N21-N235-0.2N135

Answered: Use the graphical approach to classify…

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 following table contains output from a lasso fit to a linear model with d = 6 variables and n = 70 observations. Starting from the left, the columns are λ, and B1, ..., B6, i.e. each row has and the transposed column vector ẞ(λ). 0.00000 0.14473 -0.01238 -0.16257 -0.02082 -0.19404 0.08851 0.58488 0.13477 0.00000 -0.14698 -0.00910 1.12126 0.12656 0.00000 -0.13565 0.00000 7.27740 0.03425 0.00000 -0.02504 0.00000 8.69332 0.01007 0.00000 0.00000 0.00000 -0.02773 0.00000 9.29266 0.00000 0.00000 0.00000 0.00000 -0.01778 0.00000 10.52807 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -0.18503 0.08213 -0.17573 0.07534 -0.05573 0.00000 For each of the required computations below, briefly report your procedure and the required quantity. a) For each row in the table, compute s, the proportion of shrinkage defined ass = s(λ) = ||B(a)||₁/max ||B(1)||1. b) Consider λ = 8.99299. Note that λ' is the intermediate value between λ = 8.69332 and λ = 9.29266 of the 5th and 6th rows above. Using this…
(New Question) Consider the following regression equation with panel data: Yt = Bo + B1 Xt + y2 D2; + ys D3; + + Yn Dn; + uit Where X is our regressor of interest and D2; is a binary variable that equals to 1 when i=2 and O otherwise. Binary variables D3; ,. , Dn¡ are defined similarly. Which of the followings is not correct? O Assuming there's no other omitted variables, the OLS estimator for B1 is unbiased and consistent. O The equation should be estimated by OLS with clustered heteroskedasticity-robust standard errors. O The intercept for entity j (j + 1) is Vj. O The estimation of the above equation is only possible if n is not too large.
A scientist has measured quantities y, x1,and x,. She believes that y is related to x, and x2 through the equation y = ae+Px2 8, where & is a random error that is always positive. Find a transformation of the data that will enable her to use a linear model to estimate B, and B,.
Consider the following generic fixed effects model, along with a two-period (t = 1, 2), randomly sampled panel data set with dependent variable y and independent variable x: Yit = Bo + 5o d24 + B1rit + ai +Uit where Yit = value of y for individual i at timet d2; = binary variable equal to 1 in the second time period (t = 2), and o otherwise (t = 1) Cit = value of a for individual i at time t a; = unobserved (time-invariant) effect Uj = idiosyncratic error Taking the first difference of the model (that is, subtracting the regression equation for t=1 from the regression equation for t=2) yields the following first-differenced equation: Note: Let A denote the change from t=1 to t = 2. Ay; = Yi2 – Yi1= So Au; You now plan to use OLS to estimate your first-differenced equation, in order to obtain the first-differenced estimator. Suppose that ait is a binary variable equal to 1 if the individual was born male, and o otherwise. True or False: The first-differenced estimator cannot be…
Dt rt-9t 5. Suppose a theory predicts that, Pt = the slope of the following regression? a) a = 0 and ß = 1 and p = -1 b) a = 0 and ß = 1 and ¢ = 1 c) a = 0 and ß = 1 and p = 0 d) a = 0 and ß = -1 and p = 1 It = a + ß what restriction does this theory imply about Dt 31 1 2 + Pt •+ørt + Et
A doctor recorded the number of miles walked each day by patients over age 60 and the number of doctor visits in a year for 40 patients. The resulting data were used to conduct a hypothesis test to determine whether there is a linear relationship between the number of miles walked and the number of doctor visits. What are the correct hypotheses for the test?
2. Consider the multiple regression model with three independent variables, under the classical linear model assumptions MLR.1 through MLR.6: y= Bo+ B1x1 + B2x2 + B3x3 + u. You would like to test the null hypothesis Ho: B1 - 3ẞ2 = 1. a. Let B1 and B2 denote the OLS estimators of B1 and B2. Find Var(B₁ - 3B2) in terms of the variances of B₁ and B2 and the covariance between them. What is the standard error of B₁ - 3B2 ? b. Write the t statistic for testing Ho: ẞ1-3ẞ2 = 1. c. Define B1-3ẞ2 and ₁ = B₁ - 3ẞ2. Write a regression equation involving Bo, 1, B2 and B3 that allows you to directly obtain ₁ and its standard error.
Q1. Consider the following cross-sectional population regression model relating the dependent variable Y, and regressor X, : Y, = Bo + BIXI + u, where i = 1,..,n, and X, = Y, + Z.. Assume that Cov(Z,u) 0. (a) Explain why X, is an endogenous regressor. (b) Show that Z, is a relevant instrument for X;. %3D
Is there evidence to suggest the model suffers from heteroskedasticity? Yes or no.
Consider the following simple regression model Y = bo + bịX + u. Suppose Z is an omitted variable. Suppose Cov(X, u) > 0 and Cov(Z, X) > 0. Then, the OLS estimator has: O a. a downward bias. b. no bias. ou. OC. an upward bias. O d. bias of uncertain direction.
In a regression analysis involving 27 observations, the following estimated regression equation was developed. ý = 25.2 + 5.5x,1 For this estimated regression equation SST = 1,600 and SSE = 51o. (a) At a = 0.05, test whether x, is significant. State the null and alternative hypotheses. O Ho: Bo = 0 H3: Bo = 0 O Ho: B1 + 0 = 0 O Hoi Bo#0 H3: Bo = 0 O Hoi B1 = 0 H3: B1 * 0 Find the value of the test statistic. (Round your answer to two decimal places.) F = Find the p-value. (Round your an wer to three decimal places.) p-value = Is x, significant? Reject Ho. We conclude that x, is significant. Reject Ho. We conclude that x, is not significant. Do not reject H,: We conclude that x, is significant. Do not reject H,: We conclude that x, is not significant. Suppose that variables x, and x, are added to the model and the following regression equation is obtained. ý = 16.3 + 2.3x, + 12.1x, - 5.8x3 For this estimated regression equation SST = 1,600 and SSE = 100.
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