![Question 3 [4 points] Suppose the model is: Y B1+B2Xu. What is the nonlinear regression algorithm to estimate the model (i.e.](http://img.homeworklib.com/questions/59d7ec30-020a-11ec-a246-f938f6a795e9.png?x-oss-process=image/resize,w_560)
Homework Answers
The model can be estimated by Ordinary Least Square (OLS) method. Under OLS, linearity is judged on the basis of parameters not on the basis of variables. The steps for estimation of the parameters are as follows:
Setting hypothesis for parameters
Testing the hypothesis
Checking ‘F’ test value for overall significance of the model
Ensuring the assumptions of OLS: (1) error terms (
) is to be
normally distributed (2) The error terms has a constant variance
(3) all independent variable are uncorrelated
Estimate the value of Parameters.
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Question 3 [4 points] Suppose the model is: Y B1+B2Xu. What is the nonlinear regression algorithm...
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 + Blog(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) = 8 + B,X + 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 = B1+ B2X + B3X²+u. The estimate...
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 4 (15p): Nonlinear estimation a. In a nonlinear BoBiXi+B2X?+ b. Consider the model Y =...
Question 4 (15p): Nonlinear estimation a. In a nonlinear BoBiXi+B2X?+ b. Consider the model Y = AK"Lb. How can this model be estimated consistently given data Y.Ki c. How can we detect nonlinearities in Stata using regressions or plots? How can a study of residuals r regression Y,-A +AX + β2x? + th, how do we interpret the coefficients? What is the marginal effect of an increase in X,? and L,? indicate nonlinearities? Show if possible using relevant formulas.
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...
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...
Q4.. [40 points] Consider the multiple linear regression model given by y - XB -+ s,...
Q4.. [40 points] Consider the multiple linear regression model given by y - XB -+ s, where y and e are vectors of size 8 × 1, X ls a matrix of size 8 x 3 and Disa vector of sze 3 × 1. Also, the following information are available e = 22 y -2 and XTy 3 1. [10 points) Estimate the regression coefficients in the model given above? 2. [4 points] Estimate the variance of the error term...
Use nonlinear regression to estimate α4 and β4 based on the following data. y= α4Xe^(β4X) x...
Use nonlinear regression to estimate α4 and β4 based on the following data. y= α4Xe^(β4X) x 0.1 0.2 0.4 0.6 0.9 1.3 1.5 1.7 1.8 y 0.75 1.25 1.45 1.25 0.85 0.55 0.35 0.28 0.14 If you were to use linear regression to find α4 and β4, how would you make the model linear? Plot the data points, the fit to the data using linear and nonlinear regression. What method produces the better estimate
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...
Question 2: Suppose that we wish to fit a regression model for which the true regression...
Question 2: Suppose that we wish to fit a regression model for which the true regression line passes through the origin (0,0). The appropriate model is Y = Bx + €. Assume that we have n pairs of data (x1.yı) ... (Xn,yn). a) From first principle, derive the least square estimate of B. (write the loss function then take first derivative W.r.t coefficient etc) b) Assume that e is normally distributed what is the distribution of Y? Explain your answer...
Question 1 (4 points) 1. [1 point) Suppose the regression model is logarithmic: log(Y) = B1 + Blog(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) = 8 + B,X + 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 = B1+ B2X + B3X²+u. The estimate...
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 4 (15p): Nonlinear estimation a. In a nonlinear BoBiXi+B2X?+ b. Consider the model Y = AK"Lb. How can this model be estimated consistently given data Y.Ki c. How can we detect nonlinearities in Stata using regressions or plots? How can a study of residuals r regression Y,-A +AX + β2x? + th, how do we interpret the coefficients? What is the marginal effect of an increase in X,? and L,? indicate nonlinearities? Show if possible using relevant formulas.
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...
Q4.. [40 points] Consider the multiple linear regression model given by y - XB -+ s, where y and e are vectors of size 8 × 1, X ls a matrix of size 8 x 3 and Disa vector of sze 3 × 1. Also, the following information are available e = 22 y -2 and XTy 3 1. [10 points) Estimate the regression coefficients in the model given above? 2. [4 points] Estimate the variance of the error term...
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...
Question 2: Suppose that we wish to fit a regression model for which the true regression line passes through the origin (0,0). The appropriate model is Y = Bx + €. Assume that we have n pairs of data (x1.yı) ... (Xn,yn). a) From first principle, derive the least square estimate of B. (write the loss function then take first derivative W.r.t coefficient etc) b) Assume that e is normally distributed what is the distribution of Y? Explain your answer...
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