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Hint: For (C) we proved that
2. Changing Units Suppose we estimate a standard OLS regression...
2. Changing Units Suppose we estimate a standard OLS regression equation on data X and Y...
2. Changing Units Suppose we estimate a standard OLS regression equation on data X and Y and have the standard formulas: 3, L2=(X - X)(Y - Ý) 1=1(X; - X)2 Bo =Ỹ – BX Now suppose that Xi = 1+1.6Z; for some Zi. I.e., suppose that X; were generated by trans- forming some Zi. a) Show that: X = do +ajz for some do, ai (that you need to solve for). b) Plug in the expression from (a) into (X;...
(e) Suppose that we reject the null hypothesis, what does that imply about OLS estimatron of the ...
(e) Suppose that we reject the null hypothesis, what does that imply about OLS estimatron of the regression equation of ve? (Hint: does this problem affect unbiasedness or c ciency of OLS estimators?) (d) (10 pts bonus) Solve the problem by completely specifying the regression model. 630 pts) Suppose & is the residual of the following regression (a) If we are also running the regression what OLS assumption of time series data we suspect is violated (what time series prob-...
2. Suppose we have the simple regression model Y =a+8X:+E, and their OLS coefficient estimators a...
2. Suppose we have the simple regression model Y =a+8X:+E, and their OLS coefficient estimators a and b. Answer the following questions. (a) Suppose we multiply X, by 1/2 for all i and do the OLS estimation again using X as the regressor (the independent variable). What will be your new estimators, denoted by ă (intercept) and b (slope)? Compare them with the original OLS estimators a and b, respectively (b) Compare Var[b] and Var[b]. Are they the same or...
f and g 1. Consider the standard bivariate regression: Y = Bo + B,X, + a)...
f and g
1. Consider the standard bivariate regression: Y = Bo + B,X, + a) What is the above function called? b) What are Y, X, X, Bo, and B, called? Graph an example of the function along with some fake data points (X,Y) and label each of the parts. c) Suppose that we estimate the above function using a sample of data and the ordinary least squares method (OLS). Write down the sample regression function. d) What is...
Suppose we have a regression model (x, > 0) with n samples of i.i.d. data 0, Varuir] 2, and (a) O...
Suppose we have a regression model (x, > 0) with n samples of i.i.d. data 0, Varuir] 2, and (a) Obtain the OLS estimator β0Ls for β (b) Obtain the optimal WLS estimator ws for B
Suppose we have a regression model (x, > 0) with n samples of i.i.d. data 0, Varuir] 2, and (a) Obtain the OLS estimator β0Ls for β (b) Obtain the optimal WLS estimator ws for B
Suppose you want to estimate the model but, unfortunately, you don't observe Y. Instead, a mismeasured...
Suppose you want to estimate the model
but, unfortunately, you don't observe Y. Instead, a mismeasured
version of Y is available, . (e.g. people may not
report their true earnings, but their incomes with some error).
We assume that = Y + V where V is a
measurement error which satisfies
Cov (Y,V ) = 0
Cov (U,V ) = 0:
Given that Y is not observed, you go ahead an estimate the
regression
= 0 + 1X +
(a)...
please show all steps thank you 4. (10 marks) Let βο and βι be the intercept and slope from the regression of y on xi, u...
please show all steps thank
you
4. (10 marks) Let βο and βι be the intercept and slope from the regression of y on xi, using n observations Let c1 and c2, with c#0, be constants. Let ß0 and ßl be the intercept and slope from the regression ofciyi on c2xi. Show that ßi-(c1/c2) B\ and Bo -cißo, thereby verifying the claims on units of measurement in Section 2-4. [Hint: Plug the scaled versions of x and y into A-s....
1. Suppose the true conditional mean function is but by mistake, a researcher ran least square...
1. Suppose the true conditional mean function is but by mistake, a researcher ran least square regression without the X term as in Assume cou (Xi , U) 0, E [Xn] O and E [x?-I . Is his/her estimate consistent for β,? If not, show which OLS assumption fails and discuss potential solutions. 2. Assume the structural equation is where E [u:|X0. It was discovered that we observe Xi with a measurement error wi instead of the real value X,...
1. Suppose the true conditional mean function is but by mistake, a researcher ran least square...
1. Suppose the true conditional mean function is but by mistake, a researcher ran least square regression without the X term as in Assume cou (Xi, U)-0, E Xil]-o and E [x?]-: i. Is his/her estimate consistent for β? If not, show which OLS assumption fails and discuss potential solutions. 2. Assume the structural equation is where E [111x,-0. It was discovered that we observe Xi with a measurement error wi instead of the real value Xi It is known...
Assignment 1: Bivariate Regression ECO 321 DUE Thursday, February 20 at the beginning of class. You...
Assignment 1: Bivariate Regression ECO 321 DUE Thursday, February 20 at the beginning of class. You must submit a hard copy of the assignment. 1. Consider the standard bivariate regression Y B + B,X, + a) Suppose that we estimate the above function using a sample of data and the ordinary least square method (OLS). Write down the sample regression function b) Name each of the components in part (a). Then graph an example of the function along with some...
2. Changing Units Suppose we estimate a standard OLS regression equation on data X and Y and have the standard formulas: 3, L2=(X - X)(Y - Ý) 1=1(X; - X)2 Bo =Ỹ – BX Now suppose that Xi = 1+1.6Z; for some Zi. I.e., suppose that X; were generated by trans- forming some Zi. a) Show that: X = do +ajz for some do, ai (that you need to solve for). b) Plug in the expression from (a) into (X;...
(e) Suppose that we reject the null hypothesis, what does that imply about OLS estimatron of the regression equation of ve? (Hint: does this problem affect unbiasedness or c ciency of OLS estimators?) (d) (10 pts bonus) Solve the problem by completely specifying the regression model. 630 pts) Suppose & is the residual of the following regression (a) If we are also running the regression what OLS assumption of time series data we suspect is violated (what time series prob-...
2. Suppose we have the simple regression model Y =a+8X:+E, and their OLS coefficient estimators a and b. Answer the following questions. (a) Suppose we multiply X, by 1/2 for all i and do the OLS estimation again using X as the regressor (the independent variable). What will be your new estimators, denoted by ă (intercept) and b (slope)? Compare them with the original OLS estimators a and b, respectively (b) Compare Var[b] and Var[b]. Are they the same or...
f and g
1. Consider the standard bivariate regression: Y = Bo + B,X, + a) What is the above function called? b) What are Y, X, X, Bo, and B, called? Graph an example of the function along with some fake data points (X,Y) and label each of the parts. c) Suppose that we estimate the above function using a sample of data and the ordinary least squares method (OLS). Write down the sample regression function. d) What is...
Suppose we have a regression model (x, > 0) with n samples of i.i.d. data 0, Varuir] 2, and (a) Obtain the OLS estimator β0Ls for β (b) Obtain the optimal WLS estimator ws for B
Suppose we have a regression model (x, > 0) with n samples of i.i.d. data 0, Varuir] 2, and (a) Obtain the OLS estimator β0Ls for β (b) Obtain the optimal WLS estimator ws for B
Suppose you want to estimate the model
but, unfortunately, you don't observe Y. Instead, a mismeasured
version of Y is available, . (e.g. people may not
report their true earnings, but their incomes with some error).
We assume that = Y + V where V is a
measurement error which satisfies
Cov (Y,V ) = 0
Cov (U,V ) = 0:
Given that Y is not observed, you go ahead an estimate the
regression
= 0 + 1X +
(a)...
please show all steps thank
you
4. (10 marks) Let βο and βι be the intercept and slope from the regression of y on xi, using n observations Let c1 and c2, with c#0, be constants. Let ß0 and ßl be the intercept and slope from the regression ofciyi on c2xi. Show that ßi-(c1/c2) B\ and Bo -cißo, thereby verifying the claims on units of measurement in Section 2-4. [Hint: Plug the scaled versions of x and y into A-s....
1. Suppose the true conditional mean function is but by mistake, a researcher ran least square regression without the X term as in Assume cou (Xi , U) 0, E [Xn] O and E [x?-I . Is his/her estimate consistent for β,? If not, show which OLS assumption fails and discuss potential solutions. 2. Assume the structural equation is where E [u:|X0. It was discovered that we observe Xi with a measurement error wi instead of the real value X,...
1. Suppose the true conditional mean function is but by mistake, a researcher ran least square regression without the X term as in Assume cou (Xi, U)-0, E Xil]-o and E [x?]-: i. Is his/her estimate consistent for β? If not, show which OLS assumption fails and discuss potential solutions. 2. Assume the structural equation is where E [111x,-0. It was discovered that we observe Xi with a measurement error wi instead of the real value Xi It is known...
Assignment 1: Bivariate Regression ECO 321 DUE Thursday, February 20 at the beginning of class. You must submit a hard copy of the assignment. 1. Consider the standard bivariate regression Y B + B,X, + a) Suppose that we estimate the above function using a sample of data and the ordinary least square method (OLS). Write down the sample regression function b) Name each of the components in part (a). Then graph an example of the function along with some...
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