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Suppose the true regression model is 1 of 3 Now, consider the following advice: "When the...
1. Consider the following simple regression model: y = β0 + β1x1 + u (1) and the following multiple regression model: y = β0 + β1x1 + β2x2 + u (2), where x1 is the variable of primary interest to explain y. Which of the following statements is correct? a. When drawing ceteris paribus conclusions about how x1 affects y, with model (1), we must assume that x2, and all other factors contained in u, are uncorrelated with x1. b....
Question 14 3 pts Suppose that you estimate a multiple regression model, but that you inadvertently omit an explanatory variable that is correlated with the dependent variable. In this case, the coefficients on the included variables will always be unbiased, but the standard errors and test statistics will be biased. there is no effect on the coefficients of the included variables since the omitted variable has been omitted. the coefficients on the included variables will always be biased. the coefficients...
Consider the following simple regression model: a. Suppose that OLS assumptions 1 to 4 hold true. We know that homoskedasticity assumption is statedas: Var[UjIx] = σ2 for all i Now, suppose that homoskedasticity does not hold. Mathematically, this is expressed as In other words, the subscript i in σ12 means that the conditional variance of errors for each individual i is different. Under heteroskedasticity, we can derive the expression for the variance of Var(B) as SST Where SSTx is the...
Theoretical questions: Regression without intercept(40 pts) In this question, we consider a two-variable regression model when there is no intercept in the model: There is no intercept zo in the model. Suppose we have n different samples. Then answer the following questions: (a) Write the design matrix X for our model, using the subscript notation we introduce in class.(10 pts) (b) Write the explicit solution of βί and ß2, in terms of Σ'al ril, Ση! x2, Σ¡al 2ilxi2Σ aily, and...
Suppose that you estimate a multiple regression model, but that you inadvertently omit an explanatory variable that is correlated with the dependent variable. In this case, the coefficients on the included variables will always be unbiased, but the standard errors and test statistics will be biased. the coefficients on the included variables will always be biased. there is no effect on the coefficients of the included variables since the omitted variable has been omitted. the coefficients on the included variables...
Question 14 3 pts Suppose that you estimate a multiple regression model, but that you inadvertently omit an explanatory variable that is correlated with the dependent variable. In this case, the coefficients on the included variables will always be biased. the coefficients on the included variables will always be unbiased, but the standard errors and test statistics will be biased. there is no effect on the coefficients of the included variables since the omitted variable has been omitted. the coefficients...
Suppose that the true linear regression model in a given situation is Now, assume that the researcher mistakenly believes that the true model is , and that he estimates this model, accordingly. Prove that his (OLS) estimator of will be biased.
1. Consider the following linear regression model: (a) Which assumptions are needed to make the B, unbiased estimators for the B, (b) Explain how one can test the hypothesis that A +As = 0 by means of a t-test. (c) Explain how one can test the hypothesis that A-A-0. Indicate the relevant test statistic. (d) Suppose that ri is an irrelevant explanatory variable in the population model and that you estimate the model including both and r2. What are the...
1. Consider the following unobserved effects regression model: Suppose that the idiosyncratic error u, t 1,..,T are serially correlated with constant variance σ2. Show that the correlation between adjacent differences, Δυ" and Δυ,-l is -0.5. Therefore under the ideal FE assumptions, first differencing induces negative serial correlation of a known value. [Note:
a,b,c,d 4. Suppose we run a regression model Y = β0+AX+U when the true model is Y-a0+ α1X2 + V. Assume that the true model satisfies all five standard assumptions of a simple regression model discussed in class. (a) Does the regression model we are running satisfy the zero conditional mean assumption? (b) Find the expected value of A (given X values). (e) Does the regression model we are running satisfy homoscedasticity? d) Find the variance of pi (given X...