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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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…
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
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?

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