In class we saw that the linear probability model is inherently heteroskedastic. Why is this the...
In class we saw that the linear probability model is inherently heteroskedastic. Why is this the case? That is, show why the variance of the error term in the LPM will necessarily be non-constant.
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In class we saw that the linear probability model is inherently
heteroskedastic. Why is this the...
Question 1 (a) (4 points) What are they key advantages of the Logit model over the...
Question 1 (a) (4 points) What are they key advantages of the Logit model over the Linear Probability Model? (b) (15 points) In class we saw that efficient estimates of the coefficients from a linear regression model can be obtained under the presence of heteroskedasticity using Generalized Least Squares (GLS). How does GLS work? That is, describe the mechanism through which GLS addresses non-constant error variances to achieve efficient estimation. (c) (5 points) Let Zi be the log-odds ratio in...
Consider the space V of continuous functions on (0, 1] with the 2-norm 12 J f2 We saw in class that V is an incompl...
Consider the space V of continuous functions on (0, 1] with the 2-norm 12 J f2 We saw in class that V is an incomplete normed linear space. (a) For a continuous function p on [0, 1], define a linear map Mp: V-V by Mpf-pf. Show that Mp is bounded and calculate its norm. (b) Is A = (Mplp E C(0,1)) a Banach algebra? Note that B(V) is necessarily incomplete, so it is not enough to prove that A is...
Recall how we saw in class that if we add a total time derivative of a...
Recall how we saw in class that if we add a total time derivative of a function g(g; t) on configuration space to the Lagrangian then the equations of motion were unaffected, i.e. the new Lagrangian gives the same Euler-Lagrange equations as the original Lagrangian L. The reason this worked was that the action only shifted by a boundary term, which doesn't affect the extremization procedure We have also seen that if q is a cyclic coordinate, meaning aL/aq0, then...
We estimate a linear probability model with PTSD as our dependent variable and the number of...
We estimate a linear probability model with PTSD as our dependent variable and the number of years on the force as our only independent variable. We get the following results: Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta (Constant) .702 .064 10.969 .000 Number of Years on Force -.043 .006 -.609 -7.167 .000 R2 = .37 with these results, answer the following questions: a. Write out the full regression equation. b. Interpret the constant. c. Interpret...
Q3. [10 points [Serial Correlation Consider a simple linear regression model with time series dat...
Q3. [10 points [Serial Correlation Consider a simple linear regression model with time series data: Suppose the error ut is strictly exogenous. That is Moreover, the error term follows an AR(1) serial correlation model. That where et are uncorrelated, and have a zero mean and constant variance a. 2 points Will the OLS estimator of P be unbiased? Why or why not? b. [3 points Will the conventional estimator of the variance of the OLS estimator be unbiased? Why or...
Consider the following BNF grammar that we saw in class: EXP ::= EXP + TERM ...
Consider the following BNF grammar that we saw in class: EXP ::= EXP + TERM | EXP - TERM | TERM TERM ::= TERM * FACTOR | TERM / FACTOR | FACTOR FACTOR ::= ( EXP ) | DIGIT DIGIT ::= 0 | 1 | 2 | 3 (a) Translate into EBNF. (b) Draw syntax diagrams. (c) What are the two requirements on a grammar for a predictive parser to be able to...
The following properties show that a model is not linear. (select one or more) 1) The...
The following properties show that a model is not linear. (select one or more) 1) The error terms do not have constant variance (heteroscedasticity) 2) The error terms are not independent 3) The model fits all but one or a few outliers 4) The error terms are not normally distributed
In the Stackelberg model we saw in class there were two firms 1 and 2. Suppose...
In the Stackelberg model we saw in class there were two firms 1 and 2. Suppose that the market demand is p(Q) = 60−Q, where as in class Q is the aggregate quantity. The const function for firm 1 is c1(q1) = 10q1 and the cost function for firm 2 is c2(q2) = q2. Firm 1 is the leader and Firm 2 is the follower. (a) Solve for the follow’s reaction function, and the leader’s maximization problem. (b) Describe the...
Consider a binary response variable y and two explanatory variables xy and x2. The following table contains the parameter estimates of the linear probability model (LPM) and the logit model, wit...
Consider a binary response variable y and two explanatory variables xy and x2. The following table contains the parameter estimates of the linear probability model (LPM) and the logit model, with the associated p-values shown in parentheses. Constant .40 -2.30 x1 x2 0.06 (0.03) 0.36 0.90 (0.03)(0.07) -0.03-0.10 (0.02) (0.01) a. At the 5% significance level, comment on the significance of the variables for both models. Logit gnificant 0 (Not significant x1 x2 b. What is the predicted probability implied...
6. This problem considers the simple linear regression model, that is, a model with a single...
6. This problem considers the simple linear regression model, that is, a model with a single covariate r that has a linear relationship with a response y. This simple linear regression model is y = Bo + Bix +, where Bo and Bi are unknown constants, and a random error has normal distribution with mean 0 and unknown variance o' The covariate a is often controlled by data analyst and measured with negligible error, while y is a random variable....
Consider the space V of continuous functions on (0, 1] with the 2-norm 12 J f2 We saw in class that V is an incomplete normed linear space. (a) For a continuous function p on [0, 1], define a linear map Mp: V-V by Mpf-pf. Show that Mp is bounded and calculate its norm. (b) Is A = (Mplp E C(0,1)) a Banach algebra? Note that B(V) is necessarily incomplete, so it is not enough to prove that A is...
Recall how we saw in class that if we add a total time derivative of a function g(g; t) on configuration space to the Lagrangian then the equations of motion were unaffected, i.e. the new Lagrangian gives the same Euler-Lagrange equations as the original Lagrangian L. The reason this worked was that the action only shifted by a boundary term, which doesn't affect the extremization procedure We have also seen that if q is a cyclic coordinate, meaning aL/aq0, then...
Q3. [10 points [Serial Correlation Consider a simple linear regression model with time series data: Suppose the error ut is strictly exogenous. That is Moreover, the error term follows an AR(1) serial correlation model. That where et are uncorrelated, and have a zero mean and constant variance a. 2 points Will the OLS estimator of P be unbiased? Why or why not? b. [3 points Will the conventional estimator of the variance of the OLS estimator be unbiased? Why or...
Consider a binary response variable y and two explanatory variables xy and x2. The following table contains the parameter estimates of the linear probability model (LPM) and the logit model, with the associated p-values shown in parentheses. Constant .40 -2.30 x1 x2 0.06 (0.03) 0.36 0.90 (0.03)(0.07) -0.03-0.10 (0.02) (0.01) a. At the 5% significance level, comment on the significance of the variables for both models. Logit gnificant 0 (Not significant x1 x2 b. What is the predicted probability implied...
6. This problem considers the simple linear regression model, that is, a model with a single covariate r that has a linear relationship with a response y. This simple linear regression model is y = Bo + Bix +, where Bo and Bi are unknown constants, and a random error has normal distribution with mean 0 and unknown variance o' The covariate a is often controlled by data analyst and measured with negligible error, while y is a random variable....
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