Which of the following is an example of a dynamic regression model? OY = Bo + B1Xit + B2X2# + Ut OY: = Bo + B1Xit + ut OY = Bo + B1Xt + B2X1t–1 + Ut OY: = Bo + B1Xit + B2X2t + B3X3¢ + Ut
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- 1. For a regression model y = XB + u where u is N(0, o?1), y is nx1 matrix, X is nxp matrix, B is px1 matrix and u is nx1 matrix, a. derive the estimators B using the method of least squaresExpedia wants to use regression analysis to build a model for airfare tickets prices in the states: Ticket prices = 30 + B1*Miles + E where Miles is measured in hundreds Coefficients 169.50 5.90 Intercept Miles (in hundreds) Which of the following is true? Standard Error 1.34 0.09 4 t Stat 126.85 61.28 P-value 0.000 0.002 If Miles increases by 1, then we predict ticket price to go up by $5.9. O If ticket price goes up by $1, then we predict Miles to go up by 590 miles. O If ticket price goes up by $100, then we predict Miles to go up by 590 miles. If Miles increases by 100, then we predict ticket price to go up by $5.9.1. Consider a linear regression model y = XB + € with E(e) = 0. The bias of the ridge estimator of 3 obtained by minimizing Q(B) = (y — Xß)¹ (y — Xß) + r(BTB), for some r > 0, is ——(X²X + r1)-¹8 1 (X¹X +rI)-¹3 r -r(XTX+rI) ¹8 r(X¹X+r1) ¹3
- 2. Consider a two variable regression model, which satisfies all the Gauss Markov assumptions except that the error variance is proportional to X² i.e.E(u?) = o²X? Y₁ = B₁ + B₂X₁ + Ui How would you obtain the best linear unbiased estimates from the above regression.Consider the regression model Yi = β0 + β1X1i + β2X2i + β3(X1i * X2i) +ui. a. ΔY>/ΔX1 = β1 + β3X2 (effect of change in X1, holding X2 constant).b. ΔY/ΔX2 = β2 + β3X1 (effect of change in X2, holding X1 constant).c. If X1 changes by ΔX1 and X2 changes by ΔX2, then ΔY =(β1+β3X2)ΔX1 + (β2 + β3X1)ΔX2 + β3ΔX1ΔX2.Styles 6. The following two regression models are Probit and Logit respectively: Pr(Y=1|X)=(Bo+Bi xXr+Bzx X2) Pr(Y=1|X)=F(Bu + B₁ × Xs + B₂ × X2) (a) what functions do and F represent? (b) How do Probit, and Logit ensure that the predicted probabilities are always between 0 and 1? (c) Sketch a graph of the Y= $(Z) function. (Z on the horizontal axis, Y on the vertical axis) (d) What estimation method is used to estimate the coefficients in a Probit/Logit model? (e) What are the two measures of fit for models with binary dependent variables? Focus 88 B E
- Consider a data set with 15 observations and consider a multiple linear regression model with 7 in-dependent variables. Assume you have estimated the model and you find that SST = 1,325 and SSR = 794.consider a regression model Yi=B1+B2Xi+ui and you estimated B2hat =0.3. This implies that a unit change x is prdicted to(2)What would the consequence be for a regression model if theerrors were not homoscedastic?
- Consider a multiple regression model: Y = Bi + B2X + B3W + B4Z + u, where Y is a dependent variable, X, W, and Z, are regressors, and u is a disturbance term. Suppose X = 2W + Z. Then the following is true: O The model suffers from nonlinearity in parameters O None of the presented possible answers are correct. O The model suffers from the lack of degrees of freedom O The model suffers from perfect collinearity O The model suffers from autocorrelationConsider the following regression model and corresponding output for a dataset with n = 104 observations: y=ß₁+ß2x2+ß³¸*¸+4 3 4x4+u Variable β Std. Error t P>|t| X2 -0.012 0.006 -2.289 0.022 X3 0.596 0.014 41.139 0.000 X4 0.52 1.06 Constant 8.860 1.766 5.017 0.000 What is the marginal effect of x4 on y? (approximate at least to 3 decimal places)Define coefficients of the Linear Regression Model?