In running a regression model with heteroscedastic errors, the estimators given by Weighted Least Squares (WLS) are BLUE. However, we should still use OLS method with heteroskedasticity-robust standard errors because a) this remedial method is simpler. b) the Gauss-Markov theorem holds. c) the exact form of the conditional variance is rarely known in practice. d) many econometric softwares do not have a command for weighted least squares.

In running a regression model with heteroscedastic errors, the estimators given by Weighted Least Squares (WLS) are BLUE. However, we should still use OLS method with heteroskedasticity-robust standard errors because a) this remedial method is simpler. b) the Gauss-Markov theorem holds. c) the exact form of the conditional variance is rarely known in practice. d) many econometric softwares do not have a command for weighted least squares.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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In running a regression model with heteroscedastic errors, the estimators given by Weighted Least Squares (WLS) are BLUE. However, we should still use OLS method with heteroskedasticity-robust standard errors because this remedial method is simpler. the Gauss-Markov theorem holds. the exact form of the conditional variance is rarely known in practice. many econometric softwares do not have a command for weighted least squares
What are the "Gauss-Markov" assumptions? Why are they important when using linear regression?
Even though the disturbance term in the classical linear regression model is not normallydistributed, the ordinary least square estimators are still unbiased. Why?
Do part iv
17) Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 41 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.9, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 90000 and the sum of squared errors (SSE) is 10000. From this information, what is the number of degrees of freedom for the t-distribution used to compute critical values for hypothesis tests and confidence intervals for the individual…
8)Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 11 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.86, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 86000 and the sum of squared errors (SSE) is 14000. From this information, what is MSE/MST? .5000 NONE OF THE OTHERS .2000 .3000 .4000
9)Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 11 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.79, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 79000 and the sum of squared errors (SSE) is 21000. From this information, what is the adjusted R-square? .8 .7 NONE OF THE OTHERS .6 .5
Problem 3. Please answer the following questions succinctly. Most of them can be answered with a couple of short sentences. Use math formulas whenever possible, defining symbols if their meaning is not obvious from context. (i) In linear regression, what are the standard assumptions that underlie the (strict) validity of the various P-values (from T-tests or F-tests)? (ii) Here is a summary (using the R function lm) from fitting mpg as an affine function of hp and wt based on the same dataset used in the 282B lectures. (The summary was edited a little bit.) Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 49.3509798 0.8550704 57.716 < 2e-16 -0.0203692 0.0030737 -6.627 1.16e-10 -0.0050162 0.0003059 -16.398 < 2e-16 hp wt Residual standard error: 3.291 on 384 degrees of freedom Multiple R-squared: 0.6607, Adjusted R-squared: 0.6589 F-statistic: 373.9 on 2 and 384 DF, p-value: < 2.2e-16 (a) Explain what each of the 4 components of the line pertaining to hp means. (Be very…
Explain why you would or wouldn’t agree with each of the following statements: (a) In the presence of autocorrelation, least-square estimate will be biased (b) If the pairwise correlations among predictors are all close to 0, then, there exists no collinearity; (c) If we center the predictors, VIF would change; (d) AIC can be used to select the models which are not nested with each other; (e) With the same data, the model selected by R-square is the same as the model selected by RMS; (f) For multinomial logistic regression with response variables with k categories, we need to model k logit equations; (g) Odds ratio is between 0 and 1.
Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 11 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.72, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 72000 and the sum of squared errors (SSE) is 28000. From this information, what is MSE/MST? (a) .4000 (b) .3000 (c) .5000 (d) .2000 (e) NONE OF THE OTHERS
The textbook suggests an "entity-demeaned" procedure to avoid having to specify a potentially large number of binary variables for the estimation of fixed effects regression models. The idea of the "entity-demeaned" procedure was introduced as a computationally convenient and simplifying procedure. Since there are also time fixed effects, in principle, you could use the "time-demeaned" procedure. Using the following equation Yit = Bo + B1Xit + B3S†+ uit, Show how B1 can be estimated by the OLS regression using "time-demeaned" variables.
Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 21 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.8, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 80000 and the sum of squared errors is (SSE) 20000. From this information, what is the value of the hypothesis test statistic for evidence that the true value of the coefficient of the second explanatory unknown exceeds 5? (a) 4 (b) 3…