Homework Answers
1. True
An estimator of a given parameter is said to be unbiased if its expected value is equal to the true value of the parameter.
2. True
The unbiasedness property of OLS in Econometrics is the basic minimum requirement to be satisfied by any estimator.
3. True
4. True,
The sample size matters alot. When sample size increases, we have more data so the estimates are more accurate and the model is more robust.
If any doubt ask
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(1) True or False: Please specify your reasons. (i) An estimator is unbiased, if its expected...
Question 19 3 pts The ordinary least squares estimator of a slope coefficient is unbiased means...
Question 19 3 pts The ordinary least squares estimator of a slope coefficient is unbiased means if repeated samples of the same size are taken, on average the OLS estimates will be equal to the true slope parameter O the mean of the sampling distribution of the slope coefficient is zero. O the estimated slope coefficient will always be equal to the true parameter value. the estimated slope coefficient will get closer to the true parameter value as the size...
4. (10 marks) Classify each statement by circling TRUE or FALSE. i) A scatterplot is not...
4. (10 marks) Classify each statement by circling TRUE or FALSE. i) A scatterplot is not an attribute. TRUE FALSE ii) An unbiased estimator is always preferable to a biased estimator. TRUE FALSE iii) The observed significance level measures evidence against the null hypothesis. TRUE FALSE iv) The Horvitz-Thompson estimator is unbiased given a probability sampling design. TRUE FALSE v) When sampling with replacement the sample average is a Horvitz-Thompson estimate. TRUE FALSE vi) We can quantify the sampling error...
1. Select all true statements about sample mean and sample median. A) When the population distribution...
1. Select all true statements about sample mean and sample median. A) When the population distribution is skewed, sample mean is biased but sample median is an unbiased estimator of population mean. B) When the population distribution is symmetric, both mean and sample median are unbiased estimators of population mean. C) Sampling distribution of sample mean has a smaller standard error than sample median when population distribution is normal. D) Both mean and median are unbiased estimators of population mean...
1. Answer to following with "True" or "False". Explain your answers briefly. (if false, explain what...
1. Answer to following with "True" or "False". Explain your answers briefly. (if false, explain what happen instead also) (a) Suppose that we observe a random variable Y that depend on another observed value x, through the relationYo+By+ewhere Bo,ßı and x are (b) We can reduce a by pushing the critical regions further into the tails of the (c) Decrease in the probability of the type II error always results in an increase in constants ande N(0,1). Then Y N(O,(Po+Bix)-)...
1. Suppose the true conditional mean function is but by mistake, a researcher ran least square...
1. Suppose the true conditional mean function is but by mistake, a researcher ran least square regression without the X term as in Assume cou (Xi, U)-0, E Xil]-o and E [x?]-: i. Is his/her estimate consistent for β? If not, show which OLS assumption fails and discuss potential solutions. 2. Assume the structural equation is where E [111x,-0. It was discovered that we observe Xi with a measurement error wi instead of the real value Xi It is known...
Which of the following statements is true? (a) If the calculated value of F statistic is...
Which of the following statements is true? (a) If the calculated value of F statistic is higher than the critical value, we reject the alternative hypothesis in favor of the null hypothesis. (b) The F statistic is always nonnegative as SSR, is never smaller than SSRur. (C) Degrees of freedom of a restricted model is always less than the de- grees of freedom of an unre- stricted model. (d) The F statistic is more flexible than the t statistic to...
For observations {Y, X;}=1, recall that for the model Y = 0 + Box: +e the...
For observations {Y, X;}=1, recall that for the model Y = 0 + Box: +e the OLS estimator for {00, Bo}, the minimizer of E. (Y: - a - 3x), is . (X.-X) (Y-Y) and a-Y-3X. - (Xi - x) When the equation (1) is the true data generating process, {X}- are non-stochastic, and {e} are random variables with B (ei) = 0, B(?) = 0, and Ele;e;) = 0 for any i, j = 1,2,...,n and i j, we...
QUESTION 1 Consider the following OLS regression line (or sample regression function): wage =-2.10+ 0.50 educ...
QUESTION 1 Consider the following OLS regression line (or sample regression function): wage =-2.10+ 0.50 educ (1), where wage is hourly wage, measured in dollars, and educ years of formal education. According to (1), a person with no education has a predicted hourly wage of [wagehat] dollars. (NOTE: Write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading minus sign symbol, a leading zero and trailing...
Question 22 of 25 1 Points Which of the following is TRUE? i. We can evaluate...
Question 22 of 25 1 Points Which of the following is TRUE? i. We can evaluate two projects with different timing of cash flows using the IRR rule, ll. The hurdle rate of the IRR rule is arbitrary (random), H. The payback period is the time until the sum of the present value of future cash flows equals the initial investment. I. IRR rule ignores distant cash flows while the NPV rule does not O A. II, III, IV OB.Iv...
Question 19 3 pts The ordinary least squares estimator of a slope coefficient is unbiased means if repeated samples of the same size are taken, on average the OLS estimates will be equal to the true slope parameter O the mean of the sampling distribution of the slope coefficient is zero. O the estimated slope coefficient will always be equal to the true parameter value. the estimated slope coefficient will get closer to the true parameter value as the size...
4. (10 marks) Classify each statement by circling TRUE or FALSE. i) A scatterplot is not an attribute. TRUE FALSE ii) An unbiased estimator is always preferable to a biased estimator. TRUE FALSE iii) The observed significance level measures evidence against the null hypothesis. TRUE FALSE iv) The Horvitz-Thompson estimator is unbiased given a probability sampling design. TRUE FALSE v) When sampling with replacement the sample average is a Horvitz-Thompson estimate. TRUE FALSE vi) We can quantify the sampling error...
1. Answer to following with "True" or "False". Explain your answers briefly. (if false, explain what happen instead also) (a) Suppose that we observe a random variable Y that depend on another observed value x, through the relationYo+By+ewhere Bo,ßı and x are (b) We can reduce a by pushing the critical regions further into the tails of the (c) Decrease in the probability of the type II error always results in an increase in constants ande N(0,1). Then Y N(O,(Po+Bix)-)...
1. Suppose the true conditional mean function is but by mistake, a researcher ran least square regression without the X term as in Assume cou (Xi, U)-0, E Xil]-o and E [x?]-: i. Is his/her estimate consistent for β? If not, show which OLS assumption fails and discuss potential solutions. 2. Assume the structural equation is where E [111x,-0. It was discovered that we observe Xi with a measurement error wi instead of the real value Xi It is known...
Which of the following statements is true? (a) If the calculated value of F statistic is higher than the critical value, we reject the alternative hypothesis in favor of the null hypothesis. (b) The F statistic is always nonnegative as SSR, is never smaller than SSRur. (C) Degrees of freedom of a restricted model is always less than the de- grees of freedom of an unre- stricted model. (d) The F statistic is more flexible than the t statistic to...
For observations {Y, X;}=1, recall that for the model Y = 0 + Box: +e the OLS estimator for {00, Bo}, the minimizer of E. (Y: - a - 3x), is . (X.-X) (Y-Y) and a-Y-3X. - (Xi - x) When the equation (1) is the true data generating process, {X}- are non-stochastic, and {e} are random variables with B (ei) = 0, B(?) = 0, and Ele;e;) = 0 for any i, j = 1,2,...,n and i j, we...
QUESTION 1 Consider the following OLS regression line (or sample regression function): wage =-2.10+ 0.50 educ (1), where wage is hourly wage, measured in dollars, and educ years of formal education. According to (1), a person with no education has a predicted hourly wage of [wagehat] dollars. (NOTE: Write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading minus sign symbol, a leading zero and trailing...
Question 22 of 25 1 Points Which of the following is TRUE? i. We can evaluate two projects with different timing of cash flows using the IRR rule, ll. The hurdle rate of the IRR rule is arbitrary (random), H. The payback period is the time until the sum of the present value of future cash flows equals the initial investment. I. IRR rule ignores distant cash flows while the NPV rule does not O A. II, III, IV OB.Iv...
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