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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(A) The linearity between two variables X and Y, in pairs, defined as X=[4,2,3,5,2,4] and Y=[6,4,6,8,5,10] is equal to? (B)An outbreak of certain illness was attributed to ice creams produced at a certain factory. Scientists measured the level of the illness causing factor in 10 randomly sampled batches of ice cream. The levels were: 0.583, 0.242, 0.129, 0.691, 0.231, 0.693, 0.619, 0.392, 0.418. What is the estimated interval of population mean at 0.05 level of significance? (C) The population standard deviation for the age of a certain University students is 13 years. If we want to be 90% confident that the sample mean age is within 3 years of the true population mean age of the University students, then how many randomly selected students must be surveyed?
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…
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(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.
3. The yield of a particular crop is a random variable whose value is considered to be a linear function of the temperature. The following data of corresponding values of temperature and yield is found: Temperature in C o 25 50 75 Yield in grams 100 14 38 54 76 95 a) Identify the independent and dependent variable from Yield and Temperature b) Develop the Simple Linear Regression to find out the linear relationship between yield and temperature Page 1 of 2 Interpret the regression coefficients (o and B,) obtained from your developed model. d) Predict the expected yield when temperature at 65°C c)
2. Suppose you are to fit a linear model which is forced to have an intercept equal to 5, of the form given by: Y₁ = 5 + B₁X₁ + &; for i = 1,2,.., n where & has mean 0 and variance o² for any value of X. a) Derive the least squares estimator, ₁ of the slope ₁. b) Find E(₁) and o² (B₁). c) Derive the maximum likelihood estimator, ₁ of the slope ₁. Is it the same as the least squares estimator? d) What is the estimator of the variance of the random error term? e) Prove whether or not it is still true that Σ₁ e₁ = 0.
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…
J 1
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.

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