Which of the following is NOT an assumption of the multiple regression model? Select one: a....
Which of the following is NOT an assumption of the multiple regression model? Select one:
a. E(ei)=0 E ( e i ) = 0
b. The values of each xik are not random and are not exact linear functions of the other explanatory variables.
c. cov(yi,yj)=cov(ei,ej)=0;(i≠j) c o v ( y i , y j ) = c o v ( e i , e j ) = 0 ; ( i ≠ j ) d. var(yi)=var(ei)=σ2i
Homework Answers
Answer :
(c) cov(yi,yj)=cov(ei,ej)=0;(i≠j) c o v ( y i , y j ) = c o v ( e i , e j ) = 0 ; ( i ≠ j )
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Which of the following is NOT an assumption of the multiple
regression model? Select one:
a....
(b) (1 mark) In the multiple regression model, the assumption of no perfect collinearity is best...
(b) (1 mark) In the multiple regression model, the assumption of no perfect collinearity is best described as: i. The explanatory variables will not be correlated at all. ii. The explanatory variables will have correlation coefficients close to one. iii. None of the explanatory variables will be an exact linear combination of the other explanatory variables. iv. The dependent variable will not be correlated with the explanatory variables.
5) Consider the simple linear regression model N(0, o2) i = 1,...,n Let g be the...
5) Consider the simple linear regression model N(0, o2) i = 1,...,n Let g be the mean of the yi, and let â and ß be the MLES of a and B, respectively. Let yi = â-+ Bxi be the fitted values, and let e; = yi -yi be the residuals a) What is Cov(j, B) b) What is Cov(â, ß) c) Show that 1 ei = 0 d) Show that _1 x;e; = 0 e) Show that 1iei =...
under the assumptions of the linear regression model and cov(Ei,Ej) 0 prove that CON(W,Y):0 under the assumptions of the linear regression model and cov(Ei,Ej) 0 prove that CON(W,Y):0
under the assumptions of the linear regression model and cov(Ei,Ej) 0 prove that CON(W,Y):0
under the assumptions of the linear regression model and cov(Ei,Ej) 0 prove that CON(W,Y):0
Model Assumptions: Question: • Assumption MLR.1 (Linear in the Parameters): The model in the population can...
Model Assumptions:
Question:
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Regression analysis
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1.3. Use the statistical model Yi Bo1Xi+ € to show that ei ~NID(0, o2) implies each of the following: (a) E(Y)Bo B1X, (b) 2(Y2, and (c) Cov(Y,Y)= 0,...
6. This problem considers the simple linear regression model, that is, a model with a single...
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....
Consider the following simple linear regression model: y=Po+P1x Po and B1 are Multiple Choice 41 the...
Consider the following simple linear regression model: y=Po+P1x Po and B1 are Multiple Choice 41 the response variables the random error terms the unknown parameters the explanatory variables 11 of 30 Prev Next
Simple linear regression model Assumptions: AI E[u] 0 for all i, i1, .., n On average,...
Simple linear regression model Assumptions: AI E[u] 0 for all i, i1, .., n On average, random component is zero Model runs through expected values of Yand Y A2 E[uaij]-0 for all i and j where i /j COV(IIİlh)- Unobserved component not related across observations E[14"]= for all i All observations have random component dravn from a distribution with the same variance σ2 , f(0,02) A3 var(11i)-σ (Homoskedasticitv) A4 E[Alli] = 0 for all i Random component and covariate not...
(b) (1 mark) In the multiple regression model, the assumption of no perfect collinearity is best described as: i. The explanatory variables will not be correlated at all. ii. The explanatory variables will have correlation coefficients close to one. iii. None of the explanatory variables will be an exact linear combination of the other explanatory variables. iv. The dependent variable will not be correlated with the explanatory variables.
5) Consider the simple linear regression model N(0, o2) i = 1,...,n Let g be the mean of the yi, and let â and ß be the MLES of a and B, respectively. Let yi = â-+ Bxi be the fitted values, and let e; = yi -yi be the residuals a) What is Cov(j, B) b) What is Cov(â, ß) c) Show that 1 ei = 0 d) Show that _1 x;e; = 0 e) Show that 1iei =...
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Model Assumptions:
Question:
• Assumption MLR.1 (Linear in the Parameters): The model in the population can be written as y = Bo + B1X + ... + BkXk+u where Bo, B1, ..., Bk are the unknown parameters of interest and u unobserved random error. Assumption MLR.2 (Random Sampling): We have a random samp n observations, {(Xi1, X12, ..., Xik, Yi) : 1 = 1,2,...,n}, following the population model in Assumption MLR.1. Assumption MLR.3 (No Perfect Collinearity): In the sample, none...
1. A simple regression model is given by Y81B2X+ e for t 1, (1) ,n errors e with Var (e) a follow AR(1) model where the regression et pet-1 + , t=1...n where 's are uncorrelated random variables with constant variance, that is, E()0, Var (v) = , Cov (, ,) 0 for t Now given that Var (e) = Var (e1-1)= , and Cov (e-1, v)0 (a) Show that (b) Show that E (ee-1)= p. (c) What problem(s) will...
Regression analysis
1.3. Use the statistical model Yi Bo1Xi+ € to show that ei ~NID(0, o2) implies each of the following: (a) E(Y)Bo B1X, (b) 2(Y2, and (c) Cov(Y,Y)= 0, i i' For Parts (b) and (c), use the following definitions of variance and covariance o2(Y Y E(Y)]} Cov(Yi, Y) E{[Y-E(Y)Y- E(Y)]
1.3. Use the statistical model Yi Bo1Xi+ € to show that ei ~NID(0, o2) implies each of the following: (a) E(Y)Bo B1X, (b) 2(Y2, and (c) Cov(Y,Y)= 0,...
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Consider the following simple linear regression model: y=Po+P1x Po and B1 are Multiple Choice 41 the response variables the random error terms the unknown parameters the explanatory variables 11 of 30 Prev Next
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