Homework Answers
1. Here ß2 is estimated to be 0.035.
The given is a log linear model. It's states that for every unit change in log(x), log(y) changes by 0.035 on an average.
This equation can be solved using the OLS method. ẞ2 measures the elasticity of Y with respect to X. This is also called a constant elasticity model as ß2 is fixed
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Question 1 (4 points) 1. [1 point) Suppose the regression model is logarithmic: log(Y) = B1...
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 1 1. [1 point] Suppose the regression model is logarithmic: log(Y ) = β1 +...
Question 1 1. [1 point] Suppose the regression model is logarithmic: log(Y ) = β1 + β2 log(X) + u. The estimate of β2 is 0.035. What is the interpretation of this coefficient? 2. [1 point] Suppose the regression model is semi-logarithmic: log(Y ) = β1 + β2X + u. The estimate of β2 is 0.035. What is the interpretation of this coefficient? 3. [1point]Supposetheregressionmodelhasquadraticterm: Y =β1+β2X+β3X2+u. The estimate of β2 is 0.035. What is the interpretation of this coefficient?...
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...
4. (60%) Consider the following linear regression model s XIXJ YB1+B2X u, i 1,2.. .n Suppose...
4. (60%) Consider the following linear regression model s XIXJ YB1+B2X u, i 1,2.. .n Suppose the following sample is observed. 6 X 2 10 8 4 Y 3 4 5 6 2 4.8 3.Y 4c (1) Find the OLS estimates for B, and B2. (2) Compute the estimate of Var(u). (3) What are the variances of the OLS estimates? (4) Compute the coefficient of determination. (5) Show the relationship between r2 and Dxy (6) Compute the correlation coefficient pxy...
Question 3 [4 points] Suppose the model is: Y B1+B2Xu. What is the nonlinear regression algorithm...
Question 3 [4 points] Suppose the model is: Y B1+B2Xu. What is the nonlinear regression algorithm to estimate the model (i.e., list the steps to estimate the coefficients)?
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.
Question...
Question 5 A researcher proposes the following alternative method of estimating the slope of a simple regression model...
Question 5 A researcher proposes the following alternative method of estimating the slope of a simple regression model Y; = B1 B2X; u. First, compute: Y Y Y Xi X X* = by solving Then, obtain 2 min (x The researcher claims that 3; = B2, where 2 is the OLS estimator. Do you agree disagree? or Question 6 Consider the following model: What is the OLS estimator for 6,? What does this imply for the R2 of the regres-...
sve v anu i, respectively. 7. Regression without any regressor. Suppose you are given the model:...
sve v anu i, respectively. 7. Regression without any regressor. Suppose you are given the model: Y = pi + uj. Use OLS to find the estimator of Bi. What is its variance and the RSS? Does the estimated By make intuitive sense? Now consider the two-variable model Y = B1 + B2X; +ui. Is it worth adding X, to the model? If not, why bother with regression analysis?
1. Consider the following regression model: Y; = Bo + B1 * Xi + Ei S&x=21...
1. Consider the following regression model: Y; = Bo + B1 * Xi + Ei S&x=21 SSTx = 10, SST = 90, R2 = 0.6 n = 11 x= 10, y = 30 Where y = output in pounds and x is the amount of labor used measured in hours. a. Estimate a 95% confidence interval for ß, . What is the interpretation of this confidence interval?
Q4. You analyze the non-linear relationships of two financial securities by fitting both a linear and a quadratic function with EXCEL linear model ret_A = a + b1 * ret_B + error Coefficients...
Q4. You analyze the non-linear relationships of two financial securities by fitting both a linear and a quadratic function with EXCEL linear model ret_A = a + b1 * ret_B + error Coefficients Standard Error of coefficients A 0.0000 0.0006 b1 -1.978 0.025 and Nonlinear model ret_A = a + b1 * ret_B + b2 * ret_B2 + error variable Coefficients Standard Error of coefficients a 0.0000 0.0006 b1 -1.850 0.0245 b2 4.45 0.382 Calculate the t-stat for the coefficient...
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...
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...
4. (60%) Consider the following linear regression model s XIXJ YB1+B2X u, i 1,2.. .n Suppose the following sample is observed. 6 X 2 10 8 4 Y 3 4 5 6 2 4.8 3.Y 4c (1) Find the OLS estimates for B, and B2. (2) Compute the estimate of Var(u). (3) What are the variances of the OLS estimates? (4) Compute the coefficient of determination. (5) Show the relationship between r2 and Dxy (6) Compute the correlation coefficient pxy...
Question 3 [4 points] Suppose the model is: Y B1+B2Xu. What is the nonlinear regression algorithm to estimate the model (i.e., list the steps to estimate the coefficients)?
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...
Question 5 A researcher proposes the following alternative method of estimating the slope of a simple regression model Y; = B1 B2X; u. First, compute: Y Y Y Xi X X* = by solving Then, obtain 2 min (x The researcher claims that 3; = B2, where 2 is the OLS estimator. Do you agree disagree? or Question 6 Consider the following model: What is the OLS estimator for 6,? What does this imply for the R2 of the regres-...
sve v anu i, respectively. 7. Regression without any regressor. Suppose you are given the model: Y = pi + uj. Use OLS to find the estimator of Bi. What is its variance and the RSS? Does the estimated By make intuitive sense? Now consider the two-variable model Y = B1 + B2X; +ui. Is it worth adding X, to the model? If not, why bother with regression analysis?
1. Consider the following regression model: Y; = Bo + B1 * Xi + Ei S&x=21 SSTx = 10, SST = 90, R2 = 0.6 n = 11 x= 10, y = 30 Where y = output in pounds and x is the amount of labor used measured in hours. a. Estimate a 95% confidence interval for ß, . What is the interpretation of this confidence interval?
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