Q.8
In a regression model, the assumptions of the method of least squares include: [I] Relationship between x and y is linear [II] the values of X are fixed (non-random) [III] the error terms must be correlated with each other [IV] X is independent of Y [V] the error term is normal and is identically and independently distributed about the mean of zero [VI] the error term is normal but non random
a. I, II, V |
b. II, III, VI |
c. III, IV, V |
d. I and VI |
e. All are assumptions of OLS |
In a regression model, the assumptions of the method of least squares include: [I] Relationship between x and y is linear [II] the values of X are fixed (non-random) [III] the error terms must be correlated with each other [IV] X is independent of Y [V] the error term is normal and is identically and independently distributed about the mean of zero [VI] the error term is normal but non random
Answer: Option (a)
Q.8 In a regression model, the assumptions of the method of least squares include: [I] Relationship...
6. This problem considers the simple linear regression model, that is, a model with a single covariate r that has a linear relationship with a response y. This simple linear regression model is y = Bo + Bix +, where Bo and Bi are unknown constants, and a random error has normal distribution with mean 0 and unknown variance o' The covariate a is often controlled by data analyst and measured with negligible error, while y is a random variable....
What are the pitfalls of simple linear regression? True or False for each Lacking an awareness of the assumptions of least squares regression. Not knowing how to evaluate the assumptions of least squares regressions. Not knowing the alternatives to least squares regression if a particular assumption is violated. Using a regression model without knowledge of the subject matter. Extrapolating outside the relevant range of the X and Y variables. Concluding that a significant relationship identified always reflects a cause-and-effect relationship.
Which of the following is not one of the least squares assumptions used in Stock and Watson to show that the OLS estimators are unbiased and consistent and have approximately a normal distribution in large samples? 1) large outliers are unlikely 2) the error term is homoskedastic, i.e., Var(ui ∣ X=x) does not depend on x 3) the sample (Xi,Yi),i=1,…,n constitutes an i.i.d. random sample from the population joint distribution of X and Y 4) the conditional mean of the...
In the context of multiple regression, define the n X n matrix M =- X(X'X)-'X'. (i) Show that M is symmetric and idempotent. (ii) Prove that m, the diagonals of the matrix M, satisfy 0 sm s 1 for t = 1, 2, ..., n. (iii) Consider the linear model y = XB + u satisfies the Gauss-Markov Assumptions. Let û be the vector of OLS residuals. Show that Eſûù' x) = oʻM (iv) Conclude that while the errors {u:...
In the context of multiple regression, define the n X n matrix M =- X(X'X)-'X'. (i) Show that M is symmetric and idempotent. (ii) Prove that m, the diagonals of the matrix M, satisfy 0 sm s 1 for t = 1, 2, ..., n. (iii) Consider the linear model y = XB + u satisfies the Gauss-Markov Assumptions. Let û be the vector of OLS residuals. Show that Eſûù' x) = oʻM (iv) Conclude that while the errors {u:...
0/1 pts Question7 To obtain the slope estimator using the least squares principle, you divide the sample covariance of X and Y by the sample variance of X sample covariance of X and Y by the sample variance of Y sample variance of X by the sample covariance of X and Y sample variance of X by the sample variance of Y 0/1 pts Incorrect Question8 Question 8 The standard error of the regression (SER) is defined as follows 1-R2...
I. 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 [Xa] = 0 and E [x7-1. 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 (uiX]-0. It was discovered that we observe X, with a measurement error w instead of the real value...
are the assumptions behind any multiple regression model? (b). For a multiple regression model Y-Bo + βιΧ. + β2X2 +β3Xs + € where is the error term, to represent the relationship between Y and the four X- variables. We got the following results from the data: Source Sum of Squares degrees of freedom mean squares Regression 1009.92 Residual Total 2204.94 34 And also you are given: Variable X1 Σ.tx-xr 123.74 72.98 12.207 -Pr values -11.02 5.13 X2 X3 Y-intercept is...
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...
Q. 21 The assumptions of the simple linear regression model include: a. the errors are normally distributed b. the error terms have a constant variance c. the errors have a mean of zero d. All of the above e. a and c only