State whether the following statements are correct or not in the context of regression analysis, and...
State whether the following statements are correct or not in the context of regression analysis, and explain why:
a. The sum of OLS residuals is zero.
b. The OLS estimator of b0 of the regression equation y = b0 + u is the sample mean of y.
Homework Answers
a.
Correct.
Reason: OLS method provides mean value of Y for a given X i.e. E(Y|X). When all deviations are summed up, errors are summed up in following way:
Sum(ei) = Sum(Y - E(Y|X)) = 0
b.
Correct.
As I presented in part a, conditional means of Y are calculated when X is present.
In this case (absence of X), only unconditional mean of Y is calculated which is also known as sample mean.
Add Answer to:
State whether the following statements are correct or not in the
context of regression analysis, and...
Consider the following regression equation with the ususal assumptions of the Linear Regression Model. State whether the following are True or False. Give reasons for your answer. The OLS Sample regression equation passes through the point of sample mean
Consider the following regression equation with the ususal assumptions of the Linear Regression Model. State whether the following are True or False. Give reasons for your answer.i) The OLS Sample regression equation passes through the point of sample means ii) The sum of the estimated () equals the sum of the observed ; or the sample mean of the estimated () equals the sample mean of the observed .iii) The OLS residuals (i = 1, …, N) are uncorrelated with...
3. In the multiple regression model shown in the previous question, which one of the following st...
3. In the multiple regression model shown in the previous question, which one of the following statements is incorrect: (b) The sum of squared residuals is the square of the length of the vector ü (c) The residual vector is orthogonal to each of the columns of X (d) The square of the length of y is equal to the square of the length of y plus the square of the length of û by the Pythagoras theorem In all...
QUESTION 1 If a t-test is performed in the context of a multiple regression model and...
QUESTION 1 If a t-test is performed in the context of a multiple regression model and the null hypothesis cannot be rejected, this means that A. the independent variable for which the test has been performed has a significant relationship with the dependent variable. B. the independent variable for which the test has been performed has no significant relationship with the dependent variable. C. all independent variables have a significant relationship with the dependent variable. D. no independent variable has...
Q3. [10 points [Serial Correlation Consider a simple linear regression model with time series dat...
Q3. [10 points [Serial Correlation Consider a simple linear regression model with time series data: Suppose the error ut is strictly exogenous. That is Moreover, the error term follows an AR(1) serial correlation model. That where et are uncorrelated, and have a zero mean and constant variance a. 2 points Will the OLS estimator of P be unbiased? Why or why not? b. [3 points Will the conventional estimator of the variance of the OLS estimator be unbiased? Why or...
1. Consider the following simple regression model: y = β0 + β1x1 + u (1) and...
1. Consider the following simple regression model: y = β0 + β1x1 + u (1) and the following multiple regression model: y = β0 + β1x1 + β2x2 + u (2), where x1 is the variable of primary interest to explain y. Which of the following statements is correct? a. When drawing ceteris paribus conclusions about how x1 affects y, with model (1), we must assume that x2, and all other factors contained in u, are uncorrelated with x1. b....
Select all of the following statements that are true about linear regression analysis of quantitative variables....
Select all of the following statements that are true about linear regression analysis of quantitative variables. If the purpose of our regression model is prediction, it does not matter which variables we define as the explanatory and response variable. The observed values of Y will fall on the estimated regression line, while the predicted values of Y will vary around the regression line. The purpose of linear regression is to investigate if there exists a linear relationship between a response...
The correct answer is A Please explain Which of the following statements is incorrect about the...
The correct answer is A Please explain
Which of the following statements is incorrect about the regression y = Be + Bix +u, if we assume E(ulx) = 0? A. The OLS estimates of ßo and ß1 are inconsistent. B. The OLS estimates of Bo and ß1 are unbiased. C. Bias(31)=E(8) -3. D. Dividing all of the x observations by 10 does not affect the t test significance of B1.
In the context of regression analysis, which of the following statements is true? Select one: a....
In the context of regression analysis, which of the following statements is true? Select one: a. When a dataset includes an influential point, the data must come from a nonlinear population model. b. All outlying data points have high influence. c. All data points with high leverage have high influence. d. None of the above
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...
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...
3. In the multiple regression model shown in the previous question, which one of the following statements is incorrect: (b) The sum of squared residuals is the square of the length of the vector ü (c) The residual vector is orthogonal to each of the columns of X (d) The square of the length of y is equal to the square of the length of y plus the square of the length of û by the Pythagoras theorem In all...
QUESTION 1 If a t-test is performed in the context of a multiple regression model and the null hypothesis cannot be rejected, this means that A. the independent variable for which the test has been performed has a significant relationship with the dependent variable. B. the independent variable for which the test has been performed has no significant relationship with the dependent variable. C. all independent variables have a significant relationship with the dependent variable. D. no independent variable has...
Q3. [10 points [Serial Correlation Consider a simple linear regression model with time series data: Suppose the error ut is strictly exogenous. That is Moreover, the error term follows an AR(1) serial correlation model. That where et are uncorrelated, and have a zero mean and constant variance a. 2 points Will the OLS estimator of P be unbiased? Why or why not? b. [3 points Will the conventional estimator of the variance of the OLS estimator be unbiased? Why or...
Select all of the following statements that are true about linear regression analysis of quantitative variables. If the purpose of our regression model is prediction, it does not matter which variables we define as the explanatory and response variable. The observed values of Y will fall on the estimated regression line, while the predicted values of Y will vary around the regression line. The purpose of linear regression is to investigate if there exists a linear relationship between a response...
The correct answer is A Please explain
Which of the following statements is incorrect about the regression y = Be + Bix +u, if we assume E(ulx) = 0? A. The OLS estimates of ßo and ß1 are inconsistent. B. The OLS estimates of Bo and ß1 are unbiased. C. Bias(31)=E(8) -3. D. Dividing all of the x observations by 10 does not affect the t test significance of B1.
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...
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...
Most questions answered within 3 hours.
-
1-The Electrons in a beam are moving at 2.7×108 m/s in an
electric field of 15000...
asked 3 minutes ago -
A gas tank is a vertical cylinder. It has a radius of 1m, a
height of...
asked 29 minutes ago -
Accent Software faces the following conditions. All of these
support Accent’s use of a market-penetration pricing...
asked 1 hour ago -
A mathematically inclined friend emails you the following
instructions: "Meet me in the cafeteria the first...
asked 1 hour ago -
A monopoly sells in two countries . The demand curves in the two
countries are p1...
asked 2 hours ago -
A .15kg rubber ball is bounced off a wall. Before hitting the
wall, the ball moves...
asked 3 hours ago -
A manufacturing company preparing to build a new plant is
considering three potential locations for it....
asked 3 hours ago -
B. If compound Y has approximately the same values of solubility
in toluene as compound X,...
asked 3 hours ago -
Oscar Inc. has inventory in Japan valued at 39,051,000 Yen one
year ago. One year ago...
asked 4 hours ago -
If Canada suffered from "fundamental disequilibrium," and its
government choose not to devalue its currency, a...
asked 4 hours ago -
4. How many input & output Key Value Pairs are passed into,
and emitted out of...
asked 4 hours ago -
Why would your heart not function well if constructed of
skeletal muscle? What is the particular...
asked 4 hours ago