Question 49) ListenThe misspecification of a structural population regression equation due to nonlinearities is a problem that generates inconsistency in the estimation of standarderrors.O TrueFalseQuestion 501) ListenThe Gauss-Markov assumption of zero conditional expectation of the error term in apopulation regression model implies the assumption of mean conditionalindependence.(Hint: the generalized Law of iterated expectations isE(Y | Z)=E(E(u | X, Z) | Z) for any Y, X, Z random variables)TrueFalse

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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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2. Consider the following regression model: Class Average; = Bo + B1 x 0ffice Hours; + Ui Class Average is the students' average grade in the class at the end of the term and Office Hours is the number of office hours held by the instructor over the entire term. A researcher who collects data and regresses Class Average against Office Hours finds that, surprisingly, B< 0. The OLS estimator, B, however, likely suffers from omitted variable bias because instructors who teach large introductory courses with many non-major enrollees, in which grades are relatively low, might hold more office hours than instructors who teach small upper level courses with few non-major enrollees, in which grades are relatively high. Because of this omitted variable bias, it is likely the case that B,. A) В) V A
What are the "Gauss-Markov" assumptions? Why are they important when using linear regression?
If a variable is added to a regression equation, then the adjusted R2 will increase if the t-statistic for testing the significance of the corresponding coefficient is greater than one. Is it true or false? True False QUESTION 5 Gauss-Markov theorem states, that if the model for E(YIX) is correctly specified, and the four assumptions of the multiple regression model hold, then the estimators of the parameters of the regression equation have the smallest bias among all linear and unbiased estimators of the intercept and slope coefficients. Is it true or false? True False QUESTION 6 Analysts should compare the Root MSE to the standard deviation of the dependent variable in order to judge the magnitude of the standard error of the regression, and it is true in the simple and multiple regression models. Is it true or false? O True O False
State if the following is True or false and provide a brief explanation for your answer. Consider Population modelY = Bo+ B1X1+ B2X2 + B3X3 +µ. Now consider the following statements a to c. Assumption MLR 1– 4 is satisfied if and only if:
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2.1. Discuss the basic differences between the maximum a posteriori and maximum- likelihood estimates of the parameter vector in a linear regression model.
TRUE or False 1)Logistic regression cannot be employed when the dependent variable is binary. 2)In the average linkage clustering, the distance between two clusters is defined as the average of distances between all pairs of objects, where each pair is made up of one object from each group. 3)As Monte Carlo simulation is essentially statistical sampling, the larger the number of trials used, the more precise is the result. 4)Monte Carlo simulation is an inappropriate tool to analyze cash budgets because of the inherent uncertainty of the sales forecasts on which most cash budgets are based 5)Any solution that satisfies all constraints of a problem is called a feasible solution..
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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 0.9, 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 model…
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
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…
3. Consider the following regression model: Weekly Hours = Bo + B1 × Wage + uj Weekly Hours is the average number of hours the individual worked over the course of the year and Wage is the individual's average hourly wage over the course of the year. A researcher who collects data and regresses Weekly Hours against Wage finds that B1 > 0. The OLS estimator, B, however, likely suffers from omitted variable bias because those individuals who earn high wages may be driven personalities who would work long hours no matter the wage. Because of this omitted variable bias, it is likely the case that B1_B1. A) В)

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The misspecification of a structural population regression equation due to non linearities is a problem that generates inconsistency in the estimation of standard errors. True False