Consider a probit model with an interaction term: Pr(y = 1|2) = (Bo+ Bi1+B202+ Bar1 x 2) %3D %3D a. What is marginal effect of r1? b. Now suppose B (1,-2, 3,-1) find the marginal effect of r if a = 0 and %3D 22 = 0. c. Now suppose B = (1,-2, 3,-1) find the marginal effect of r, if 0 and %3D T2 = 1. d. Now suppose B = (1,-2, 3,-1) find the marginal effect of a if r = 1 and %3D %3D 2 = 0. e. Now suppose B = (1,-2, 3,-1) find the marginal effect of a1 if a = 1 and %3D 2 = 1.
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![Consider a probit model with an interaction term:
Pr(y = 1|r) = (Bo + B1r1+ B2r2 + Bza1 x r2)
a. What is marginal effect of r1?
b. Now suppose B = (1, -2,3,-1) find the marginal effect of r if r1 = 0 and
%3D
%3D
22 = 0.
c. Now
suppose 3 = (1, –2, 3,-1) find the marginal effect of r1 if r1 = 0 and
%3D
12 = 1.
d. Now suppose B = (1,-2, 3, –1) find the marginal effect of r if r, = 1 and
%3D
%3D
I2 = 0.
e. Now suppose B = (1,-2, 3,-1) find the marginal effect of ai if ri
T2 = 1.
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- An ecologist models the interaction between the tree frog (P) and insect (N) populations of a small region of a rainforest using the Lotka-Volterra predator prey model. The insects are food for the tree frogs. The model has nullclines at N=0, N=500, P=0, and P=75. Suppose the small region of the rainforest currently has 800 insects and 50 tree frogs. In the short term, the model predicts the insect population will • and the tree frog population will At another point time, a researcher finds the region has 300 insects and 70 tree frogs. In the short term, the model predicts the insect population will * and the tree frog population willThe Simple Linear Regression model is Y = b0 + b1*X1 + u and the Multiple Linear Regression model with k variables is: Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term, Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 14 Suppose that in the model Y=b0+b1*X1+u, we add a variable that is correlated with both Y and X1. What will happen to the standard error of the OLS estimator for b1? It will go up It will go down We cannot say with the provided information It will remain unchanged QUESTION 15 Suppose you have an MLR model that includes an intercept, with 150 observations and 11 variables. If assumptions MLR1-MLR6 hold, a t-statistic for any of the…The Simple Linear Regression model is Y = b0 + b1*X1 + u and the Multiple Linear Regression model with k variables is: Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term, Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 1 In the SLR model, suppose the dependent variable (Y) represents the quantity consumed of apples in a particular area in tones, and the explanatory variable (X1) is the average price of apples in that area in £. If this model is estimated by OLS, then the estimated slope b1_hat, represents: by how many tones consumption of apples will change, if the average price of apples increases by £1 the predicted change in the consumption of apples (in…
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- The Simple Linear Regression model is Y = b0 + b1*X1 + u and the Multiple Linear Regression model with k variables is: Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term, Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 19 Suppose your estimated MLR model is: Y_hat = 11 - 0.4*X + 0.01*X2 According to this estimated model, what is the value of X that minimizes Y_hat? It is equal to -20 It is equal to -40 It is equal to 20 It is equal to 40 QUESTION 20 Suppose your estimated MLR model with two explanatory variables, log(X1) and X2, is: Y_hat= 10 – 10*log(X1) + 0.04*X2 Which of the following statements about the interpretation of the coefficient of log(X1)…The Simple Linear Regression model is Y = b0 + b1*X1 + u and the Multiple Linear Regression model with k variables is: Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term, Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 7 In the MLR model, the assumption of ‘linearity in parameters’ is violated if: one of the slope coefficients appears as a power (e.g. Y = b0 + b1*(X1^b2) + b3*X2 + u) the model includes the reciprocal of a variable (e.g. 1/X1) the model includes a variable squared (e.g. X1^2) the model includes a variable in its logarithmic form (i.e. log(X1) ) QUESTION 8 In the MLR model, the assumption of 'no perfect collinearity'…The Simple Linear Regression model is Y = b0 + b1*X1 + u and the Multiple Linear Regression model with k variables is: Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term, Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 13 In the MLR model, what do we mean by Heteroskedasticity? That the error term depends on the values of the explanatory variables That all the explanatory variables have different variance That the variance of the error term is a function of the explanatory variables That the variance of the error term is constant QUESTION 14 Suppose that in the model Y=b0+b1*X1+u, we add a variable that is correlated with both Y and X1. What will happen…
- The Simple Linear Regression model is Y = b0 + b1*X1 + u and the Multiple Linear Regression model with k variables is: Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term, Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 4 Suppose we have an SLR model, where the dependent variable (Y) represents ‘how satisfied someone is with his/her life, from 0 to 100’ (the higher the value, the higher the satisfaction with life), and the explanatory variable (X1) represents ‘personal annual income in £1,000’. The estimated OLS regression line is: Yhat = 33.2 + 0.74*X1. According to this model, what is the predicted life satisfaction, for someone with…The Simple Linear Regression model is Y = b0 + b1*X1 + u and the Multiple Linear Regression model with k variables is: Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term, Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 25 In the MLR model, with 150 observations and 5 explanatory variables, suppose you want to test the null hypothesis, H0: b3=0, b4=0 We also know that the RSS of the unrestricted model is 563, while the RSS of a model that excludes the variables associated with the 2 coefficients under the null hypothesis is 577. Given this information what is the F-statistic for this hypothesis? It is around -1.79 It is around 1.75 It is around -1.75 It is…Consider a linear model to explain monthly beer consumption: beer = Bo + Biinc + Bzprice + Bzeduc + Bafemale + u E(ulinc, price, educ, female) = 0 Var(ulinc, price, educ, female) = o²inc². Write the transformed equation that has a homoskedastic error term.
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