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u iegression result presented in this 9.13. Consider the following model: Y; = B1 + B2...
Question 1 (4 points] 1. [1 point] Suppose the regression model is logarithmic: log(Y) = B1 + B2 log(X) +u. The estimat...
Question 1 (4 points] 1. [1 point] Suppose the regression model is logarithmic: log(Y) = B1 + B2 log(X) +u. The estimate of B2 is 0.035. What is the interpretation of this coefficient? 2. (1 point] Suppose the regression model is semi-logarithmic: log(Y) = Bi + B2X + u. The estimate of B2 is 0.035. What is the interpretation of this coefficient? 3. [1 point] Suppose the regression model has quadratic term: Y = Bi+B2X + B3 X2 +u. The...
Question 10 1 pts In the Chow test regression model y = B1 -+ 81d+ B2x + d2d. x + u , what would it mean if 2 0 ? O The...
Question 10 1 pts In the Chow test regression model y = B1 -+ 81d+ B2x + d2d. x + u , what would it mean if 2 0 ? O The average values of x are equal in both groups. O The marginal effect of x on y is equal in both groups. O For individuals with d 1, x has no effect on y. O If x 0, both groups have the same expected value for y.
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2.4 We have defined the simple linear regression model to be y =B1 + B2x+e. Suppose...
2.4 We have defined the simple linear regression model to be y =B1 + B2x+e. Suppose however that we knew, for a fact, that ßı = 0. (a) What does the linear regression model look like, algebraically, if ßı = 0? (b) What does the linear regression model look like, graphically, if ßı = 0? (c) If Bi=0 the least squares "sum of squares" function becomes S(R2) = Gyi - B2x;)?. Using the data, x 1 2 3 4 5...
Q2. Suppose you are given the following Cob-Douglas Production Y; = B1X2 X3 exp(ui) for i...
Q2. Suppose you are given the following Cob-Douglas Production Y; = B1X2 X3 exp(ui) for i = 1, 2, ...,n, where B1, B2 and Bzare population parameters and the Ui are IID (0,02). Note that: Y; routput, X2i =labor input, Xzi =capital input, exp = base of the natural logarithm. (a) Transform the above non-linear model, Yį = B2X2 X : exp(ui) to a linear model (b) How do you the interpret B2? (c) How do you the interpret By?...
Question 1 Consider the simple regression model (only one covariate): y= BoB1 u Let B1 be the OLS estimator of B1. a) W...
Question 1 Consider the simple regression model (only one covariate): y= BoB1 u Let B1 be the OLS estimator of B1. a) What are the six assumptions needed for B1 to be unbiased, have a simple expression for its variance, and have normal distribution? (3 points) b) Under Assumptions 1-6, derive the distribution of B1 conditional on x\,..., xn. (3 points) In lecture we described how to test the null hypothesis B1 bo against the alternative hypothesis B1 bo, where...
linear stat modeling & regression 1) Consider n data points with 3 covariates and observations {xn, ^i2, xi3,yid; i,,n, and you fit the following model, y Bi+Br2+Br+e that is yi A) +Ari,1 +Ari...
linear stat modeling & regression
1) Consider n data points with 3 covariates and observations {xn, ^i2, xi3,yid; i,,n, and you fit the following model, y Bi+Br2+Br+e that is yi A) +Ari,1 +Ari,2 +Buri,3 + єї where є,'s are independent normal distribution with mean zero and variance ơ2 . H the vectors of (Y1, . . . ,Yn). Assume the covariates are centered: Σίχί,,-0, k = 1,2,3. ere, n = 50, Let L are Assume, X'X is a diagonal matrix...
1. In the simple regression model y = + β1x + u, suppose that E (u)...
1. In the simple regression model y = + β1x + u, suppose that E (u) 0. Letting oo-E(u), show that the model can always be rewrit ten with the same slope, but a new intercept and error, where the new error has a zero expected value 2. The data set BWGHT contains data on births to women in the United States. Two variables of interest are the dependent variable, nfan birth weight in ounces (bught), and an explanatory variable,...
2. Consider the following model: y = XB + u where y is a (nx1) vector...
2. Consider the following model: y = XB + u where y is a (nx1) vector containing observations on the dependent variable, B = Bi , B X is a (n x 3) matrix. The first column of X is a column of ones whilst the second and third columns contain observations on two explanatory variables (x and x2 respectively). u is (n x 1) vector of error terms. The following are obtained: 1234.7181 1682.376 7345.581 192.0 259.6 1153.1) X'X...
QUESTION 8 Consider a linear model to explain monthly beer consumption: beer = Bo + Biinc...
QUESTION 8 Consider a linear model to explain monthly beer consumption: beer = Bo + Biinc + B2price + B3educ + B4female + u, E(ulinc, price, educ, female) = 0 and Var(ulinc, price, educ, female) = o inc. Which of the following transformed equation has a homoscedastic error term? a. beer = Bo + B1inc + B2price + B3educ + B4female + u b.beer/inc= Bo(1/inc) + B1(1/inc) + B2(price/inc-) + B3(educ/inc?) + B4(female/inc?) + (u/inc) OC beer/inc = Bo(1/inc) +...
3. Some computations related to a stock S(t) following the Merton-Black-Scholes Model. (a) Let S(t) =...
3. Some computations related to a stock S(t) following the Merton-Black-Scholes Model. (a) Let S(t) = S(0) exp((u - 02/2)t +oW(t)), where W(t) is a standard Brownian motion. Compute that u is the expected annual return rate, i.e., E[S(T)] = S(O)eMT, where T > 0. Is o2 the variance of S(T)/S(O)? (b) Let X be the continuously compounded annual rate of return between 0 and T, i.e., S(T) = S(0) exp(XT). Compute E(X) and Var(X) (find the distribution of X...
Question 1 (4 points] 1. [1 point] Suppose the regression model is logarithmic: log(Y) = B1 + B2 log(X) +u. The estimate of B2 is 0.035. What is the interpretation of this coefficient? 2. (1 point] Suppose the regression model is semi-logarithmic: log(Y) = Bi + B2X + u. The estimate of B2 is 0.035. What is the interpretation of this coefficient? 3. [1 point] Suppose the regression model has quadratic term: Y = Bi+B2X + B3 X2 +u. The...
Question 10 1 pts In the Chow test regression model y = B1 -+ 81d+ B2x + d2d. x + u , what would it mean if 2 0 ? O The average values of x are equal in both groups. O The marginal effect of x on y is equal in both groups. O For individuals with d 1, x has no effect on y. O If x 0, both groups have the same expected value for y.
Question...
2.4 We have defined the simple linear regression model to be y =B1 + B2x+e. Suppose however that we knew, for a fact, that ßı = 0. (a) What does the linear regression model look like, algebraically, if ßı = 0? (b) What does the linear regression model look like, graphically, if ßı = 0? (c) If Bi=0 the least squares "sum of squares" function becomes S(R2) = Gyi - B2x;)?. Using the data, x 1 2 3 4 5...
Q2. Suppose you are given the following Cob-Douglas Production Y; = B1X2 X3 exp(ui) for i = 1, 2, ...,n, where B1, B2 and Bzare population parameters and the Ui are IID (0,02). Note that: Y; routput, X2i =labor input, Xzi =capital input, exp = base of the natural logarithm. (a) Transform the above non-linear model, Yį = B2X2 X : exp(ui) to a linear model (b) How do you the interpret B2? (c) How do you the interpret By?...
Question 1 Consider the simple regression model (only one covariate): y= BoB1 u Let B1 be the OLS estimator of B1. a) What are the six assumptions needed for B1 to be unbiased, have a simple expression for its variance, and have normal distribution? (3 points) b) Under Assumptions 1-6, derive the distribution of B1 conditional on x\,..., xn. (3 points) In lecture we described how to test the null hypothesis B1 bo against the alternative hypothesis B1 bo, where...
linear stat modeling & regression
1) Consider n data points with 3 covariates and observations {xn, ^i2, xi3,yid; i,,n, and you fit the following model, y Bi+Br2+Br+e that is yi A) +Ari,1 +Ari,2 +Buri,3 + єї where є,'s are independent normal distribution with mean zero and variance ơ2 . H the vectors of (Y1, . . . ,Yn). Assume the covariates are centered: Σίχί,,-0, k = 1,2,3. ere, n = 50, Let L are Assume, X'X is a diagonal matrix...
1. In the simple regression model y = + β1x + u, suppose that E (u) 0. Letting oo-E(u), show that the model can always be rewrit ten with the same slope, but a new intercept and error, where the new error has a zero expected value 2. The data set BWGHT contains data on births to women in the United States. Two variables of interest are the dependent variable, nfan birth weight in ounces (bught), and an explanatory variable,...
2. Consider the following model: y = XB + u where y is a (nx1) vector containing observations on the dependent variable, B = Bi , B X is a (n x 3) matrix. The first column of X is a column of ones whilst the second and third columns contain observations on two explanatory variables (x and x2 respectively). u is (n x 1) vector of error terms. The following are obtained: 1234.7181 1682.376 7345.581 192.0 259.6 1153.1) X'X...
QUESTION 8 Consider a linear model to explain monthly beer consumption: beer = Bo + Biinc + B2price + B3educ + B4female + u, E(ulinc, price, educ, female) = 0 and Var(ulinc, price, educ, female) = o inc. Which of the following transformed equation has a homoscedastic error term? a. beer = Bo + B1inc + B2price + B3educ + B4female + u b.beer/inc= Bo(1/inc) + B1(1/inc) + B2(price/inc-) + B3(educ/inc?) + B4(female/inc?) + (u/inc) OC beer/inc = Bo(1/inc) +...
3. Some computations related to a stock S(t) following the Merton-Black-Scholes Model. (a) Let S(t) = S(0) exp((u - 02/2)t +oW(t)), where W(t) is a standard Brownian motion. Compute that u is the expected annual return rate, i.e., E[S(T)] = S(O)eMT, where T > 0. Is o2 the variance of S(T)/S(O)? (b) Let X be the continuously compounded annual rate of return between 0 and T, i.e., S(T) = S(0) exp(XT). Compute E(X) and Var(X) (find the distribution of X...
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