Consider the following regression modelY=B+B₁X₁+B₂X₂ + u1 1220where E[u | X₁, X₂1]=0. Suppose X₁ and X are highly (but not perfectly) correlated. Then,12a.OLS estimators are biased.b.OLS estimators are not consistent.C.OLS estimators will have large standard errors.d.One of X1, X2 or the constant should be dropped.e.30 cannot be interpreted as the population intercept.

Given that Y=β0+β1x1+β2x2+u E(u/X1,X2)=0X1 and X2 are highly correlatedWe have to choose correct…

Answered: Consider the following regression model…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider the following regression model, Y;=B1 + B2X12+ … + BxX ik+ e, where Ele,x,]= 0 and Var(e,|x,) depends on the value of Xj, i.e., Var(e,|x,) = 02. Choose the correct statement. O a. To get around the problem, we often assume that e, is normally distributed. O b. To fix the problem, we need to have an instrumental variable. O C. This problem implies that errors are correlated with one of (x/2, ..., X): O d. If we assume Varle,lx)= o², the confidence interval is not valid. O e. None of the above is correct.
Consider the OLS regression equation: ŷ = 0 + Â₁×1 + B₂X2 + Â33. If the R² is close to zero, it implies O x3 is not highly correlated with X₁ O B3 is likely to be biased O B3 is likely to be unbiased O that we expect the estimate of B3 to be noisy.
The linear correlation between an independent (x) and dependent (y) variable A. Is the foundation for simple (bivariate) regression B. Does not indicate a causal relationship, though one might exist C. Can be direct, inverse, or nonexistent D. Can be used to predict the value of y for any observed value of x E. All of the above F. None of the above
22. In a regression model involving 45 observations, the following estimated regression equation was obtained . Y =29+18X 1 +43X 2 +87X 3 +15X 4 For this model SSR = 400 and SST = 1000 The MSR for the above model is A. 10 B. None C. 100 D. 150 E. 40
1. When estimating the parameters of a linear regression model, the OLS estimator is a scalar value and the OLS estimate is a random variable. 2. For a linear regression model including only an intercept, the OLS estimator of that intercept is equal to the sample mean of the independent variable. 3. If the error term in a linear regression model is normally distributed, then the distribution of the OLS estimator, conditional on explanatory variables, is also normal. 4. The value of the coefficient of determination, R2 of Model 1: In yi = a + Bx; + E; (M1) is different from the value of R2 of the Model 2: Yi = a+ Bx; + Ei. (M2) 5. Consider an earnings function In wage = 0.6 + 0.16 · educ estimated on a sample of n = 1000 individuals. The standard error of the estimated slope coefficient equals 0.11. This allows us to interpret the estimated slope coefficient as: ceteris paribus expected returns to schooling are 16%.
Suppose we carry out a linear regression analysis with the following model: Y = Bo + B1X1 + .. + BrXr + € where k = 8. n = 195. We find SSReg = 231.4, and SSTotal = 972.5. Before collecting the data, we knew that we'd like to test the null hypothesis that Bi = B2 = 63 = 0. If we run a regression model leaving the predictors associated with these slopes out of the model, we find SSReg = 74.1 and SSTotal = 972.5. What is the value of the appropriate Fstatistic to test this null hypothesis (that these 3 slopes are 0)?

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