(a) What is meant by heteroscedasticity? What are the effects of heteroscedasticity on: (i) The OLS estimators? In parti...
(a) What is meant by heteroscedasticity? What are the effects of heteroscedasticity on:
(i) The OLS estimators? In particular, does heteroscedasticity create bias in the OLS estimators?
(ii) The variances and standard errors of the OLS estimators.
(iii) The validity of t-test and F-test of overall significance of the regression?
(b) Given:
Yi = β1 + β2 Xi + ui
Var(ui) = σ2 Xi
Show how this model can be transformed so that the disturbances have constant variance. Explain how you would obtain estimates of β1 and β2 from the transformed model.
Homework Answers
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(a) What is meant by heteroscedasticity? What are the effects of heteroscedasticity on: (i) The OLS estimators? In parti...
Answer ALL parts of this question: (a) What is meant by heteroscedasticity? What are its effects on: (i) OLS estimators...
Answer ALL parts of this question: (a) What is meant by heteroscedasticity? What are its effects on: (i) OLS estimators and their variances? (ii) The validity of t and F tests? (b) Detail 3 different formal tests for heteroscedasticity, what are the relative strengths and weaknesses of each?
(a) Distinguish between autocorrelation and heteroscedasticity and explain their implications for...
(a) Distinguish between autocorrelation and heteroscedasticity and explain their implications for the OLS estimators. (b) Briefly discuss the alternative tests, at least two in case, employed to detect the problems of autocorrelation and heteroscedasticity in the estimated regression model. (c) Using the data on consumer prices, broad money (M2) and Treasury bill rate, as given in question (1), test the quantity theory of money (QTM) as represented by: pt=β0+β1mt+β1yt+ut such that β0>;β1>0;β2<0;β1=1;β2=-1 Show the estimated regression model, together with all...
Consider the model yi = β0 +β1X1i +β2X2i +ui . We fail to reject the null...
Consider the model yi = β0 +β1X1i +β2X2i +ui . We fail to reject the null hypothesis H0 : β1 = 0 and β2 = 0 at 5% when: a) A F test of H0 : β1 = 0 and β2 = 0 give us a p value of 0.001 b) A t test of H0 : β1 = 0 give us a p value of 0.06 and a t test of H0 : β2 = 0 a p value...
4. Consider the regression model, y1B22+ BKiK+ei -.. where errors may be heteroskedastic. Choose the most incorrect sta...
4. Consider the regression model, y1B22+ BKiK+ei -.. where errors may be heteroskedastic. Choose the most incorrect statement (a) The OLS estimators are consistent and unbiased (b) We should report the OLS estimates with the robust standard errors (c) The Gauss-Markov theorem may not apply (d) The GLS cannot be used because we do not know the error variances in practice (e) We should take care of heteroskedasticity only if homoskedasticity is rejected Consider the regression model, +BKIK+et e pet-1+...
4. (24 marks) Suppose that the random variables Yi,..., Yn satisfy Y-B BX,+ Ei, 1-1, , n, where βο and βι are parameters, X1, ,X, are con- stants, and e1,... ,en are independent and identically distr...
4. (24 marks) Suppose that the random variables Yi,..., Yn satisfy Y-B BX,+ Ei, 1-1, , n, where βο and βι are parameters, X1, ,X, are con- stants, and e1,... ,en are independent and identically distributed ran- dom variables with Ei ~ N (0,02), where σ2 is a third unknown pa- rameter. This is the familiar form for a simple linear regression model, where the parameters A, β, and σ2 explain the relationship between a dependent (or response) variable Y...
1. Given data on (yi, xi) for i = 1, , n, consider the following least...
1. Given data on (yi, xi) for i = 1, , n, consider the following least square problem for a imple linear regression bo,b We assume the four linear regression model assumptions dicussed in class hold (i) Compute the partial derivatives of the objective function. (ii) Put the derived partial derivatives in (i) equal to zeros. Explain why the resulting equa tions are called normal equation'. (Hin wo n-dimesional vectors (viand (wi)- are normal-orthogonal ) if Σ-1 ui wi-0. )...
The following table gives data on output and total cost of production of a commodity in the short run To test whether the preceding data suggest the U-shaped average and marginal cost curves typically encountered in the short run, one can use the followin
The following table gives data on output and total cost of production of a
commodity in the short run. (See Example 7.4.)
Output Total cost, $
1 193
2 226
3 240
4 244
5 257
6 260
7 274
8 297
9 350
10 420
To test whether the preceding data suggest the U-shaped average and
marginal cost curves typically encountered in the short run, one can use
the following model:
Yi = β1 + β2Xi + β3X2
i...
I want to solve the branches e and f Please, I would like to solve the...
I want to solve the branches e and f
Please, I would like to solve the last two subsections
of the question
A researcher is analysing the impact of smoking during pregnancy on infant health. Using a survey of 2000 infants, data on birth weights, smoking and family income produce the following OLS estimates: bwght =116.97 -0.46cigs; + 0.09faminc + lli (Model 1) (1.05) (0.09) (0.02) where bwght is weight at birth measured in ounces, cigs is the average number...
Consider the multiple linear regression (MLR) model that satisfies the classical assumptions: Yi = Bo +...
Consider the multiple linear regression (MLR) model that satisfies the classical assumptions: Yi = Bo + B1Xil +...+Bkxik + Ui estimated by OLS/MOM. Let the estimators beßo, Ŝ1,..., ØK. Question 1 (1 point) The p-value for undertaking a hypothesis test is the smallest significance level for which we reject a null hypothesis that is correct. True False Question 2 (1 point) To test Ho: B3 = 34 vs H1 : B3 – B4 > 0, we form the test statistic...
4. Consider the regression model, y1B22+ BKiK+ei -.. where errors may be heteroskedastic. Choose the most incorrect statement (a) The OLS estimators are consistent and unbiased (b) We should report the OLS estimates with the robust standard errors (c) The Gauss-Markov theorem may not apply (d) The GLS cannot be used because we do not know the error variances in practice (e) We should take care of heteroskedasticity only if homoskedasticity is rejected Consider the regression model, +BKIK+et e pet-1+...
4. (24 marks) Suppose that the random variables Yi,..., Yn satisfy Y-B BX,+ Ei, 1-1, , n, where βο and βι are parameters, X1, ,X, are con- stants, and e1,... ,en are independent and identically distributed ran- dom variables with Ei ~ N (0,02), where σ2 is a third unknown pa- rameter. This is the familiar form for a simple linear regression model, where the parameters A, β, and σ2 explain the relationship between a dependent (or response) variable Y...
1. Given data on (yi, xi) for i = 1, , n, consider the following least square problem for a imple linear regression bo,b We assume the four linear regression model assumptions dicussed in class hold (i) Compute the partial derivatives of the objective function. (ii) Put the derived partial derivatives in (i) equal to zeros. Explain why the resulting equa tions are called normal equation'. (Hin wo n-dimesional vectors (viand (wi)- are normal-orthogonal ) if Σ-1 ui wi-0. )...
I want to solve the branches e and f
Please, I would like to solve the last two subsections
of the question
A researcher is analysing the impact of smoking during pregnancy on infant health. Using a survey of 2000 infants, data on birth weights, smoking and family income produce the following OLS estimates: bwght =116.97 -0.46cigs; + 0.09faminc + lli (Model 1) (1.05) (0.09) (0.02) where bwght is weight at birth measured in ounces, cigs is the average number...
Consider the multiple linear regression (MLR) model that satisfies the classical assumptions: Yi = Bo + B1Xil +...+Bkxik + Ui estimated by OLS/MOM. Let the estimators beßo, Ŝ1,..., ØK. Question 1 (1 point) The p-value for undertaking a hypothesis test is the smallest significance level for which we reject a null hypothesis that is correct. True False Question 2 (1 point) To test Ho: B3 = 34 vs H1 : B3 – B4 > 0, we form the test statistic...
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