Homework Answers
Optimistic disposition is in the unobservable u, which is correlated with income causes OLS estimators for a regression to be biased.
Explanation: When there is some variable present in u which is correlated with the income, then slope parameter will have some extra effect with the sole effect of income. It will make the value of estimators different from the true population slope value.
Omit the intercept when its true value is not zero.
Explanation: If intercept is omitted even when true value is not zero, then functional form is not correct and slope parameter will have some extra effect with the sole effect of income. It will make the value of estimators different from the true population slope value.
Answer: Option (D) i.e., Both (b) and (c)
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2. Which of the following will cause OLS estimators for a regression Happiness = a +...
1. For a simple linear regression BMI = a + BIncome+u. Suppose you have a random...
1. For a simple linear regression BMI = a + BIncome+u. Suppose you have a random sample. Which of the following statement is true? a) OLS estimators are unbiased but inefficient when BMI does not vary much in the sample. b) OLS estimators are biased when the error u captures perseverance and self- control, and you believe that people who are perseverant and have more self- control tend to have higher income. C) OLS estimators are biased when Income does...
1. If OLS estimators satisfy asymptotic normality, it implies that a. they are approximately normally distributed b. th...
1. If OLS estimators satisfy asymptotic normality, it implies that a. they are approximately normally distributed b. they are approximately normally distributed in samples with less than 10 observations large enough sample sizes c. they have a constant mean equal to zero and variance equal to d. they have a constant mean equal to one and variance equal to o 2 In a multiple regression model, the OLS estimator is consistent if a. there is no correlation between the dependent...
2. Suppose we have the simple regression model Y =a+8X:+E, and their OLS coefficient estimators a...
2. Suppose we have the simple regression model Y =a+8X:+E, and their OLS coefficient estimators a and b. Answer the following questions. (a) Suppose we multiply X, by 1/2 for all i and do the OLS estimation again using X as the regressor (the independent variable). What will be your new estimators, denoted by ă (intercept) and b (slope)? Compare them with the original OLS estimators a and b, respectively (b) Compare Var[b] and Var[b]. Are they the same or...
Which of the following problems will cause OLS estimates of β1 to be biased? Including an...
Which of the following problems will cause OLS estimates of β1 to be biased? Including an irrelevant X5 variable Failing to include an independent variable that is not correlated with Y Failing to include an independent variable that is correlated with Y only Failing to include an independent variable that is correlated with Y and X1 Not only does X cause Y, but Y causes X.
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...
Which of the following statements is true? Group of answer choices A.an unbiased estimator is consistent...
Which of the following statements is true? Group of answer choices A.an unbiased estimator is consistent if its variance goes to zero as the sample size gets large. B.a biased estimator is consistent if its bias goes to zero as the sample size gets large. C. a consistent estimator is biased in small samples. D.all unbiased estimators are consistent. E. all consistent estimators are unbiased.
Correlation and Regression a) Determine the value of a (as a function of n and y),...
Correlation and Regression a) Determine the value of a (as a function of n and y), which minimizes S function given below. Prove your answer with all the details. s=30,-a)? b) Consider the following two models: Modell:Y, = B. +B,X, + u Model2:Y,= 2, + QX: +e; where Ñ =X; -X (i) Are the OLS estimators of constant terms for both models identical? Are their variances the same? Prove your answer. Are the OLS estimators of slope terms for both...
Question 1: Which of the following would generally cause the variance of the OLS estimator of...
Question 1: Which of the following would generally cause the variance of the OLS estimator of the slope in a regression model to be larger? 1) smaller variance of the error term 2) a larger sample size 3) smaller variance of the independent variable 4) larger variance of Xi ------------------------------------------------------------------------------------------------------------------------------ Question 2: Which of the following is the best description of the sampling distribution of the OLS estimator under the least squares assumptions? 1) it is a Student's t distribution...
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...
12. Suppose you are interested in studying the relationship between education and wage. More specifically, suppose...
12. Suppose you are interested in studying the relationship between education and wage. More specifically, suppose that you believe the relationship to be captured by the following linear regression model, Wago-Po + ?| Education + u Suppose further that you estimate the unknown population linear regression model by OLS What is the difference between ? 1 and ?? o A. Both, ?? and ?' , are OLS estimators of true parameters of the population regression line. OB. ?' is a...
1. For a simple linear regression BMI = a + BIncome+u. Suppose you have a random sample. Which of the following statement is true? a) OLS estimators are unbiased but inefficient when BMI does not vary much in the sample. b) OLS estimators are biased when the error u captures perseverance and self- control, and you believe that people who are perseverant and have more self- control tend to have higher income. C) OLS estimators are biased when Income does...
1. If OLS estimators satisfy asymptotic normality, it implies that a. they are approximately normally distributed b. they are approximately normally distributed in samples with less than 10 observations large enough sample sizes c. they have a constant mean equal to zero and variance equal to d. they have a constant mean equal to one and variance equal to o 2 In a multiple regression model, the OLS estimator is consistent if a. there is no correlation between the dependent...
2. Suppose we have the simple regression model Y =a+8X:+E, and their OLS coefficient estimators a and b. Answer the following questions. (a) Suppose we multiply X, by 1/2 for all i and do the OLS estimation again using X as the regressor (the independent variable). What will be your new estimators, denoted by ă (intercept) and b (slope)? Compare them with the original OLS estimators a and b, respectively (b) Compare Var[b] and Var[b]. Are they the same or...
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...
Correlation and Regression a) Determine the value of a (as a function of n and y), which minimizes S function given below. Prove your answer with all the details. s=30,-a)? b) Consider the following two models: Modell:Y, = B. +B,X, + u Model2:Y,= 2, + QX: +e; where Ñ =X; -X (i) Are the OLS estimators of constant terms for both models identical? Are their variances the same? Prove your answer. Are the OLS estimators of slope terms for both...
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...
12. Suppose you are interested in studying the relationship between education and wage. More specifically, suppose that you believe the relationship to be captured by the following linear regression model, Wago-Po + ?| Education + u Suppose further that you estimate the unknown population linear regression model by OLS What is the difference between ? 1 and ?? o A. Both, ?? and ?' , are OLS estimators of true parameters of the population regression line. OB. ?' is a...
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