Homework Answers
Consider the following regression model: Xi = Bo + Bixi + y; where yi is individual...
Consider the following regression model: Xi = Bo + Bixi + y; where yi is individual i's University GPA and xi is the individual's high school grades. a. What do you think is in ui? Do you think E[ulx) = 0? Suggest a variable that you think might affect University GPA that isn't included in the regression equation but should be. c. What sign of bias would you expect in an OLS regression of y on x? Briefly explain. d....
Consider the zero intercept model given by Yi = B1Xi + ei (i=1,…,n) with the ei...
Consider the zero intercept model given by Yi = B1Xi + ei (i=1,…,n) with the ei normal, independent, with variance sigma^2. For this mode (i) find the sum of (Yi –Yi-hat). (ii) find the sum of (Yi – Yi-hat)Xi. (iii) find the estimator of the error variance, sigma^2. (iv) is the estimator of the error variance biased?
Yi = Bo + BiXi + Ui, where Xi = 1 if individual i was treated...
Yi = Bo + BiXi + Ui, where Xi = 1 if individual i was treated and 0 otherwise, Bo = E[Y/C), B1 = T, and Ui = YC - E[Y;-). (a) Calculate E[ui]. (b) Calculate E[u;X]. Hint: use law of iterated expectations. (c) Using your answers to (a) and (b), calculate Cov(Xị, Ui) (d) Using your answer to (c), show that endogeneity bias is equal to selection bias in this setting, i.e., Cov(Xi, ui iz 41) = E[Y;|X; =...
Consider the linear model: Yi = α0 + α1(Xi − X̄) + ui. Find the OLS...
Consider the linear model: Yi = α0 + α1(Xi − X̄) + ui.
Find the OLS estimators of α0 and α1. Compare with the OLS
estimators of β0 and β1 in the standard model discussed in class
(Yi = β0 + β1Xi + ui).
Consider the linear model: Yį = ao + Q1(X; - X) + Ui. Find the OLS estimators of do and a1. Compare with the OLS estimators of Bo and B1 in the standard model discussed in...
Exercise 5 Consider a linear model with n = 2m in which Yi = Bo +...
Exercise 5 Consider a linear model with n = 2m in which Yi = Bo + Bici + Eigi = 1,..., m, and Yi = Bo + B2X1 + Ei, i = m + 1, ...,n. Here €1,..., En are i.i.d. from N(0,0), B = (Bo, B1, B2)' and o2 are unknown parameters, X1, ..., Xn are known constants with X1 + ... + Xm = Xm+1 + ... + Xn = 0. 1. Write the model in vector form...
Exercise5 Consider a linear model with n -2m in which yi Bo Pi^i +ei,i-1,...,m, and Here €1, ,En are 1.1.d. from N(0,ơ)...
Exercise5 Consider a linear model with n -2m in which yi Bo Pi^i +ei,i-1,...,m, and Here €1, ,En are 1.1.d. from N(0,ơ), β-(A ,A, β), and σ2 are unknown parameters, zı, known constants with x1 +... + Xm-Tm+1 + +xn0 , zn are 1, write the model in vector form as Y = Xß+ε describing the entries in the matrix X. 2, Determine the least squares estimator β of β.
Exercise5 Consider a linear model with n -2m in which...
3. Consider the linear model: Yİ , n where E(Ei)-0. Further α +Ari + Ei for...
3. Consider the linear model: Yİ , n where E(Ei)-0. Further α +Ari + Ei for i 1, assume that Σ.r.-0 and Σ r-n. (a) Show that the least square estimates (LSEs) of α and ß are given by à--Ỹ and (b) Show that the LSEs in (a) are unbiased. (c) Assume that E(e-σ2 Yi and E(49)-0 for all i where σ2 > 0. Show that V(β)--and (d) Use (b) and (c) above to show that the LSEs are consistent...
3. Consider the multiple linear regression model iid where Xi, . . . ,Xp-1 ,i are observed covariate values for observation i, and Ei ~N(0,ơ2) (a) What is the interpretation of B1 in this model? (b)...
3. Consider the multiple linear regression model iid where Xi, . . . ,Xp-1 ,i are observed covariate values for observation i, and Ei ~N(0,ơ2) (a) What is the interpretation of B1 in this model? (b) Write the matrix form of the model. Label the response vector, design matrix, coefficient vector, and error vector, and specify the dimensions and elements for each. (c) Write the likelihood, log-likelihood, and in matrix form. aB (d) Solve : 0 for β, the MLE...
Consider the simple linear regression model: Yi = Bo + Bilitei, i = 1,...,n. with the...
Consider the simple linear regression model: Yi = Bo + Bilitei, i = 1,...,n. with the least squares estimates ỘT = (Bo ß1). We observe a new value of the predictor: x] = (1 xo). Show that the expression for the 100(1 - a)% prediction interval reduces to the following: . (xo – x2 Ēo + @130 Etap 11+ntan (x; – 7)2
Exercise 7.7 Of the variables (yi, xi) only the pair (yi, xi) are observed. In this...
Exercise 7.7 Of the variables (yi, xi) only the pair (yi, xi) are observed. In this case, we say that yi is a latent variable. Suppose where ui is a measurement error satisfying Let ß denote the OLS coefficient from the regression of yi on (a) Ís β the coefficient from the linear projection of yi on z? (b) Is β consistent for β as n oo? (c as n oo. e) Find the asymptotic distribution of yn(3-8 as
Consider the following regression model: Xi = Bo + Bixi + y; where yi is individual i's University GPA and xi is the individual's high school grades. a. What do you think is in ui? Do you think E[ulx) = 0? Suggest a variable that you think might affect University GPA that isn't included in the regression equation but should be. c. What sign of bias would you expect in an OLS regression of y on x? Briefly explain. d....
Yi = Bo + BiXi + Ui, where Xi = 1 if individual i was treated and 0 otherwise, Bo = E[Y/C), B1 = T, and Ui = YC - E[Y;-). (a) Calculate E[ui]. (b) Calculate E[u;X]. Hint: use law of iterated expectations. (c) Using your answers to (a) and (b), calculate Cov(Xị, Ui) (d) Using your answer to (c), show that endogeneity bias is equal to selection bias in this setting, i.e., Cov(Xi, ui iz 41) = E[Y;|X; =...
Consider the linear model: Yi = α0 + α1(Xi − X̄) + ui.
Find the OLS estimators of α0 and α1. Compare with the OLS
estimators of β0 and β1 in the standard model discussed in class
(Yi = β0 + β1Xi + ui).
Consider the linear model: Yį = ao + Q1(X; - X) + Ui. Find the OLS estimators of do and a1. Compare with the OLS estimators of Bo and B1 in the standard model discussed in...
Exercise 5 Consider a linear model with n = 2m in which Yi = Bo + Bici + Eigi = 1,..., m, and Yi = Bo + B2X1 + Ei, i = m + 1, ...,n. Here €1,..., En are i.i.d. from N(0,0), B = (Bo, B1, B2)' and o2 are unknown parameters, X1, ..., Xn are known constants with X1 + ... + Xm = Xm+1 + ... + Xn = 0. 1. Write the model in vector form...
Exercise5 Consider a linear model with n -2m in which yi Bo Pi^i +ei,i-1,...,m, and Here €1, ,En are 1.1.d. from N(0,ơ), β-(A ,A, β), and σ2 are unknown parameters, zı, known constants with x1 +... + Xm-Tm+1 + +xn0 , zn are 1, write the model in vector form as Y = Xß+ε describing the entries in the matrix X. 2, Determine the least squares estimator β of β.
Exercise5 Consider a linear model with n -2m in which...
3. Consider the linear model: Yİ , n where E(Ei)-0. Further α +Ari + Ei for i 1, assume that Σ.r.-0 and Σ r-n. (a) Show that the least square estimates (LSEs) of α and ß are given by à--Ỹ and (b) Show that the LSEs in (a) are unbiased. (c) Assume that E(e-σ2 Yi and E(49)-0 for all i where σ2 > 0. Show that V(β)--and (d) Use (b) and (c) above to show that the LSEs are consistent...
3. Consider the multiple linear regression model iid where Xi, . . . ,Xp-1 ,i are observed covariate values for observation i, and Ei ~N(0,ơ2) (a) What is the interpretation of B1 in this model? (b) Write the matrix form of the model. Label the response vector, design matrix, coefficient vector, and error vector, and specify the dimensions and elements for each. (c) Write the likelihood, log-likelihood, and in matrix form. aB (d) Solve : 0 for β, the MLE...
Consider the simple linear regression model: Yi = Bo + Bilitei, i = 1,...,n. with the least squares estimates ỘT = (Bo ß1). We observe a new value of the predictor: x] = (1 xo). Show that the expression for the 100(1 - a)% prediction interval reduces to the following: . (xo – x2 Ēo + @130 Etap 11+ntan (x; – 7)2
Exercise 7.7 Of the variables (yi, xi) only the pair (yi, xi) are observed. In this case, we say that yi is a latent variable. Suppose where ui is a measurement error satisfying Let ß denote the OLS coefficient from the regression of yi on (a) Ís β the coefficient from the linear projection of yi on z? (b) Is β consistent for β as n oo? (c as n oo. e) Find the asymptotic distribution of yn(3-8 as
Most questions answered within 3 hours.
-
1) There is a 5.0 μC charge at each of 3 corners of a square
(each...
asked 14 seconds ago -
A study of 420,095 cell phone users found that
134 of them developed cancer of the...
asked 3 minutes ago -
2.50 g of NH4Cl is added to 12.9 g of water. Calculate the
molality of the...
asked 6 minutes ago -
Part 1
(a) Calculate the pH at 25°C of a 0.10 M solution of a
weak...
asked 8 minutes ago -
1-Calculate the mass in grams of 2.55 moles of KCl
2- Calculate how many moles are...
asked 36 minutes ago -
Bright Sun, Inc. sold an issue of 30-year $1,000 par value bonds
to the public. The...
asked 30 minutes ago -
Bismuth-210 is beta emitter with a half-life of 5.0 days.
Part A
If a sample contains...
asked 22 minutes ago -
The income statement for the month of June, 2014 of Happy Smiles
Enterprises contains the following...
asked 35 minutes ago -
To be done in java code. 2 words are anagrams if 1 word can be
formed...
asked 33 minutes ago -
Two players take turns at removing 1 to 4 coins from an original
pile of 16...
asked 29 minutes ago -
1. Choose value for p between 0.20 and 0.80. It should have at
least two decimal...
asked 37 minutes ago -
QUESTIONS: 500 words for the question
In defining abnormality, the criteria of “deviance”, “distress”
and “dysfunction”...
asked 38 minutes ago