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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Q1 When regressing number of crimes committed by an individual against years of education you omit the relevant variable innate ability. Then, the estimated coefficient for education is going to be: A downwards biased B. upwards biased C. biased, but we cannot say in which direction D. not biased Q2 You estimate the equation: Y=6.2+0.41X. After finding heteroscedasticity, you run a second equation: Y/X=0.39+6.31/X. What is the effects of X on Y based on your preferred specification? A. A 1 unit change in X increases Y by 6.31 units. B. A 1 unit change in X increases Y by 0.39 units C. A 1 unit change in X increases Y by 6.31%. D. A 1 unit change in X increases Y by 39% Q 3 Which of the following are advantages of the use of panel data over pure cross- sectional or pure timeseries modelling? (i) The use of panel data can increase the number of degrees of freedom and therefore the power of tests (ii) The use of panel data allows the average value of the dependent…
Consider the following population linear regression model of individual food expenditure: Y = 50 + 0.5X + u, where Y is weekly food expenditure in dollars, X is the individual’s age, and 50+0.5X is the population regression line. Suppose we generate artificial data for 3 individuals using this model. This artificial sample, which consists of 3 observations, is shown in the following table: Answer the following questions. Show your working. (a) What are the values of V1 and V4? (b) Suppose we know that in this artificial sample, the sample covariance between X and Y is 150, and the sample variance of X is 100. Compute the OLS regression line of the regression of Y on X. (Hint: Assume these summary statistics and the OLS regression line continue to hold in parts (c)-(e).) (c) What are the values of V5 and V7?
Table 4.18 shows estimated effects for a fitted logistic regression model with squamous cell esophageal cancer (1 = yes, 0 = no) as the response variable Y. Smoking status (S) equals 1 for at least one pack per day and 0 other- wise, alcohol consumption (A) equals the average number of alcoholic drinks consumed per day, and race (R) equals 1 for blacks and 0 for whites. A. To describe the race-by-smoking interaction, construct the prediction equation when R = 1 and again when R = 0. Find the fitted YS conditional odds ratio for each case. Similarly, construct the prediction equation when S = 1 and again when S = 0. Find the fitted YR conditional odds ratio for each case. Note that, for each association, the coefficient of the cross-product term is the difference between the log odds ratios at the two fixed levels for the other variable. B. In Table 4.18, explain what the coefficients of R and S represent, for the coding as given above. What hypotheses do the P -values refer to for…
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
The US government is interested in understanding what predicts death rates. They have a set of data that includes the number of deaths in each state, the number of deaths resulting from vehicle accidents (VEHICLE), the number of people dying from diabetes (DIABETES), the number of deaths related to the flu (FLU) and the number of homicide deaths (HOMICIDE). Your run a regression to predict deaths and get the following output: At α = .10, which variable(s) is/are significant predictors of deaths?
A study of a high-pressure inlet fogging method for a gas turbine engine analyzed a complete second-order model for y, heat rate (kilojoules per kilowat per hour) of a gas turbine as a function of two quantitative variables
A study investigating the relationship between a country's annual gross domestic product x (in trillions of dollars) and carbon dioxide emissions y(in millions of metric tons) yielded r = 0.87, se = 141.9 , and the regression equation y-hat = 199.5x + 56.0. For each additional trillion dollars in %3D gross domestic product, carbon dioxide emissions increases by about 0.87 million metric tons, on average increases by about 199.5 million metric tons, on average changes by an amount that cannot be determined from the information given O increases by about 141.9 million metric tons, on average increases by about 56.0 million metric tons, on average
Consider the simple linear regression model Wage = Bo + B1*Age + U. The error term U can capture the followings, with the exception of O A. possible measurement error in Wage. O B. the temperature in London Ontario tomorrow. O C. possible model misspecification, such as the nonlinear effect of Age on Wage. O D. other variables that affect the dependent variable, such as previous work experience.
12-6. A regression model is to be developed for predicting the ability of soil to absorb chemical contaminants. Ten obser- vations have been taken on a soil absorption index (y) and two regressors: x₁ = amount of extractable iron ore and x₂ = amount of bauxite. We wish to fit the model y = Bo + B₁ x₁ + B₂x₂ + €. Some necessary quantities are: 1.17991 -7.30982 E-3 7.3006 E-4 (X'X)¹ = -7.30982 E-3 7.9799 E-5 -1.23713 E-4, 7.3006 E-4 -1.23713 E-4 4.6576 E-4 220 X'y = 36,768 9,965 (a) Estimate the regression coefficients in the model specified. (b) What is the predicted value of the absorption index y when x₁ = 200 and x₂ = 50?
A fitted linear regression model is (y=10+2x ). If x = 0 and the corresponding observed value of y = 9, the residual at this observation is:
3

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