Homework Answers
Ans . Assumption 4 of The classical linear regression model is , that the variance of ui's given the value of X is constant or homosedastic , i.e. of equal variance or equal spread of ui at each xi . When assumption 4 is voilated than it means that there is heteroscedasticity.
The old estimators are unbaised and consistent in the presence of Heteroscedasticity, but they are not efficient.
So B^1 will not be unbaised when assumption 4 is voilated is a false statement .
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5. Consider the case, the value of B1 will not be unbiased when Assumption 4 is...
Question 1 Consider the simple regression model (only one covariate): y= BoB1 u Let B1 be the OLS estimator of B1. a) W...
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...
(a) When you toss an unbiased coin five times, what is the probability that you will...
(a) When you toss an unbiased coin five times, what is the probability that you will obtain exactly 3 heads, and 2 tails? (b) In (a), what is the probability that you will obtain exactly 3 heads, and 2 tails, in that order? (c) When you spin an unbiased die, there are six possible outcomes. What is the probability that you spin an unbiased die once, and you get both a 2, and a 6? What is the probability that in one...
Consider the following slope estimator: b=2i=1 Yi Suppose the true model is ki + Bo +...
Consider the following slope estimator: b=2i=1 Yi Suppose the true model is ki + Bo + Bicite and the model satisfies the Gauss-Markov conditions. Answer the following questions: (a) What assumption in addition to the Gauss-Markov assumptions is required to estimate the model? (b) Show that in general, b is a biased estimator of B1. (c) Outline the special condition(s) under which b is an unbiased estimator of B1.
Q2: a. Derive indifference curve in case if both the commodities are “bad”. Explain your b....
Q2: a. Derive indifference curve in case if both the commodities are “bad”. Explain your b. answer logically? What happens to the shapes of indifference curve if (i) a consumer's preferences are not “Transitive”? (ii) If an assumption of "No-satiation” is violated? c. Explain the meaning of MRS. What is the meaning of MRS of good 1 for 2 is - 2.5?
We already know that when the homogeneity of variances assumption is violated in Independent-Samples t-Test you...
We already know that when the homogeneity of variances assumption is violated in Independent-Samples t-Test you rely on the Levene's Test. What is the test (or ratio) that we fall on when the homogeneity of variances assumption is violated in ANOVA? In addition to theoretical understanding, through your explanation of this topic you should show an understanding of the practical use of it in SPSS as well.
It's 5 multiple-choice questions of applicated economic, can someone help me? Thank you so much! Assume...
It's 5 multiple-choice questions of applicated economic, can
someone help me? Thank you so much!
Assume that the variable Y is actually determined by the following equation Y; = Bo + B1X1,i+ B2X2,i + Uj additionally assume that corr(X1, X2) = p. The usual assumptions for a linear model hold in this case. You are interested in estimating B1. To accomplish this you collect a sample of the variables Y and X1 and estimate the following model Y; = Yo...
5. Consider the following regression: where EUX] = 0 (remember that this is a stronger assumption...
5. Consider the following regression: where EUX] = 0 (remember that this is a stronger assumption than our usual assumption that EIXU-0). Suppose Y is binary. (a) What is PY 1X? (b) What is Var[U|X]? Is it reasonable to assume that U is homoskedastic? (c) Is it possible for the fitted value of Y to lie outside [0, 1]?
5. Consider the orthonormal basis B = {b, bs.bu) = {* B= {b1,b2, -11 !} for...
5. Consider the orthonormal basis B = {b, bs.bu) = {* B= {b1,b2, -11 !} for R3 Orthonormal just means b; · b; is 0 unless i = j, in which case it is 1. [ 21 (a) Let v= | -1 . Caculate the dot products: a=v.bi, b=v.b2, c=v.b3. (1) Show that lolo = [:] (c) Will this always work?
Consider the following one variable regression for the demand estimation: quantity demanded = Bo + Biprice...
Consider the following one variable regression for the demand estimation: quantity demanded = Bo + Biprice 4 u What do you expect to be the sign of B7? (1 point) Would the estimates of Bibe unbiased? (1 point) why? (2 point) (Hint: think about what is in the error term, and what assumption for the unbiasedness of OLS estimator is violated) What should be the true sign of B, ? (1 point) Why it is different from the estimated sign...
Consider the simple regression model yi= B1+B2xi2+ei . Suppose N=5 and the values of xi2 are...
Consider the simple regression model yi= B1+B2xi2+ei . Suppose N=5 and the values of xi2 are (1,2,3,4,5). Let the true values of the parameters be B1=1 , B2=1 . Let the true random error values, which are never known in reality, be ei= (1,-1,0,6,-6) . a) Calculate the values of yi b) Compute the OLS estimates of the parameter c) Compute the least squares residuals, e1 , e2 , e3 , e4 , e5 . What's their sum? d) It...
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...
Consider the following slope estimator: b=2i=1 Yi Suppose the true model is ki + Bo + Bicite and the model satisfies the Gauss-Markov conditions. Answer the following questions: (a) What assumption in addition to the Gauss-Markov assumptions is required to estimate the model? (b) Show that in general, b is a biased estimator of B1. (c) Outline the special condition(s) under which b is an unbiased estimator of B1.
Q2: a. Derive indifference curve in case if both the commodities are “bad”. Explain your b. answer logically? What happens to the shapes of indifference curve if (i) a consumer's preferences are not “Transitive”? (ii) If an assumption of "No-satiation” is violated? c. Explain the meaning of MRS. What is the meaning of MRS of good 1 for 2 is - 2.5?
It's 5 multiple-choice questions of applicated economic, can
someone help me? Thank you so much!
Assume that the variable Y is actually determined by the following equation Y; = Bo + B1X1,i+ B2X2,i + Uj additionally assume that corr(X1, X2) = p. The usual assumptions for a linear model hold in this case. You are interested in estimating B1. To accomplish this you collect a sample of the variables Y and X1 and estimate the following model Y; = Yo...
5. Consider the following regression: where EUX] = 0 (remember that this is a stronger assumption than our usual assumption that EIXU-0). Suppose Y is binary. (a) What is PY 1X? (b) What is Var[U|X]? Is it reasonable to assume that U is homoskedastic? (c) Is it possible for the fitted value of Y to lie outside [0, 1]?
5. Consider the orthonormal basis B = {b, bs.bu) = {* B= {b1,b2, -11 !} for R3 Orthonormal just means b; · b; is 0 unless i = j, in which case it is 1. [ 21 (a) Let v= | -1 . Caculate the dot products: a=v.bi, b=v.b2, c=v.b3. (1) Show that lolo = [:] (c) Will this always work?
Consider the following one variable regression for the demand estimation: quantity demanded = Bo + Biprice 4 u What do you expect to be the sign of B7? (1 point) Would the estimates of Bibe unbiased? (1 point) why? (2 point) (Hint: think about what is in the error term, and what assumption for the unbiasedness of OLS estimator is violated) What should be the true sign of B, ? (1 point) Why it is different from the estimated sign...
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