2. Suppose we have the simple regression model Y =a+8X:+E, and their OLS coefficient estimators a...
15. Suppose that the population model is y-βο + Ax + u Another way to deal with endogeneity ofr s to employ the Two-stage Least Squared Estimator. In the first stage, we estimate x = π。+ π12+ u and obtain its prediction x and run the regression y = β° + Ax + u in the second stage. Which of the following is correct regarding therelationship between the 2SLS and IV estimators? (a) The 2SLS estimator is exactly the same...
(e) Suppose that we reject the null hypothesis, what does that imply about OLS estimatron of the regression equation of ve? (Hint: does this problem affect unbiasedness or c ciency of OLS estimators?) (d) (10 pts bonus) Solve the problem by completely specifying the regression model. 630 pts) Suppose & is the residual of the following regression (a) If we are also running the regression what OLS assumption of time series data we suspect is violated (what time series prob-...
please help! Following is a simple linear regression model: y = a + A + & The following results were obtained from some statistical software. R2 = 0.523 Syx (regression standard error) = 3.028 n (total observations) = 41 Significance level = 0.05 = 5% Variable Interecpt Slope of X Parameter Estimate 0.519 -0.707 Std. Err. of Parameter Est 0.132 0.239 Note: For all the calculated numbers, keep three decimals. Write the fitted model (5 points) 2. Make a prediction...
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...
Suppose we have a regression model Yi = bXi + Ei where Y = X = 0 and there is no intercept in the model. Consider a slope estimator ĥ - E(X;)2(Y;) 2(x;)2 Show whether this will yield an unbiased estimate of b or not.
Question 1 Consider the simple regression model (only one covariate): y= BoB1 u Let B1 be the OLS estimator of B1. a) What are the six assumptions needed for B1 to be unbiased, have a simple expression for its variance, and have normal distribution? (3 points) b) Under Assumptions 1-6, derive the distribution of B1 conditional on x\,..., xn. (3 points) In lecture we described how to test the null hypothesis B1 bo against the alternative hypothesis B1 bo, where...
Question 5. Given sample data (x, y), and sample size n. We fit the simple regression model: and estimate the least square estimators (a) Suppose A,-1, ß,-2, and x-1. Compute у. b) Suppose S and sry 0.5, compute the R2. Question 5. Given sample data (x, y), and sample size n. We fit the simple regression model: and estimate the least square estimators (a) Suppose A,-1, ß,-2, and x-1. Compute у. b) Suppose S and sry 0.5, compute the R2.
1. In the simple regression model y = + β1x + u, suppose that E (u) 0. Letting oo-E(u), show that the model can always be rewrit ten with the same slope, but a new intercept and error, where the new error has a zero expected value 2. The data set BWGHT contains data on births to women in the United States. Two variables of interest are the dependent variable, nfan birth weight in ounces (bught), and an explanatory variable,...
Exercise 4.11 Consider the regression model Y Po PX+u Suppose that you know Bo 1. Derive the formula for the least squares estimator of p The least squares objective function is OA. n (v2-bo-bx?) i-1 Ов. O B. n (M-bo-bX) /# 1 n Click to select your answer and then click Check Answer. Exercise 4.11 OA n Σ (--B,χ?) O B. E (Y-bo-b,X)2 j= 1 n Σ (Υ-Βo-bΧ) 3. j= 1 D. n Σ (Υ-0-b,) i- 1 Click to select...
Suppose we have a regression model (x, > 0) with n samples of i.i.d. data 0, Varuir] 2, and (a) Obtain the OLS estimator β0Ls for β (b) Obtain the optimal WLS estimator ws for B Suppose we have a regression model (x, > 0) with n samples of i.i.d. data 0, Varuir] 2, and (a) Obtain the OLS estimator β0Ls for β (b) Obtain the optimal WLS estimator ws for B