![7. Consider the one-way analysis of variance model where €ij ~ N(0,02) are independent. Let rni Tm 1 Xs, and X= where n Σ.nl n (a) Show that rn i-1 (b) Show that n-m is an unbiased estimator of σ2. (Recall that if W ~ χ2(r) then E(W)-r). [4]](http://img.homeworklib.com/questions/f734a100-6f16-11ea-a9bf-ad73e41e6e8b.png?x-oss-process=image/resize,w_560)
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7. Consider the one-way analysis of variance model where €ij ~ N(0,02) are...
Exercise 1 Consider the regression model through the origin y.-β1zi-ci, where Ei ~ N(0,o). It is ...
Exercise 2b please!
Exercise 1 Consider the regression model through the origin y.-β1zi-ci, where Ei ~ N(0,o). It is assumed that the regression line passes through the origin (0, 0) that for this model a: T N, is an unbiased estimator of o2. a. Show d. Show that (n-D2 ~X2-1, where se is the unbiased estimator of σ2 from question (a). Exercise2 Refer to exercise 1 a. Show that is BLUE (best linear unbiased estimator) b. Show that +1 has...
1. Consider the simple linear regression model: Ү, — Во + B а; + Ei, where 1, . . , En are i.i.d. N(0,02), for i1,2,......
1. Consider the simple linear regression model: Ү, — Во + B а; + Ei, where 1, . . , En are i.i.d. N(0,02), for i1,2,... ,n. Let b1 = s^y/8r and bo = Y - b1 t be the least squared estimators of B1 and Bo, respectively. We showed in class, that N(B; 02/) Y~N(BoB1 T;o2/n) and bi ~ are uncorrelated, i.e. o{Y;b} We also showed in class that bi and Y 0. = (a) Show that bo is...
please don't copy. thx Question 1. Consider the model Yij = Mi + Rij, Rij~N(0,02), i...
please don't copy. thx
Question 1. Consider the model Yij = Mi + Rij, Rij~N(0,02), i = 1,2;j = 1,2, ..., Ni. 222(Y1j-81+)? Part A. Show that Sị is an unbiased estimator of o2. Part B. Show that the pooled estimate of o2 is unbiased. n1-1
Problem 1: Consider the model Y = BO + Bi X+e, where e is a N(0,02)...
Problem 1: Consider the model Y = BO + Bi X+e, where e is a N(0,02) random variable independent of X. Let also Y = Bo + B1X. Show that E[(Y - EY)^3 = E[(Ỹ – EY)^3 + E[(Y – Y)1.
please don't copy, thx Question 2. Consider the model Yij = uị + Rij, Rij~N(0,02), i...
please don't copy, thx
Question 2. Consider the model Yij = uị + Rij, Rij~N(0,02), i = 1,2; j = 1,2, ..., Ni. Part A. Determine using least squares the parameter estimates. Part B. State the estimate of variance in the model. Part C. Clearly show that that ūı = 71+ is an unbiased estimator of Mz. Part D. The average grade of 32 Nano Engineering students in STAT 353 is 75% with a standard deviation of 5%. The average...
3. Consider the linear model: Yİ , n where E(Ei)-0. Further α +Ari + Ei for...
3. Consider the linear model: Yİ , n where E(Ei)-0. Further α +Ari + Ei for i 1, assume that Σ.r.-0 and Σ r-n. (a) Show that the least square estimates (LSEs) of α and ß are given by à--Ỹ and (b) Show that the LSEs in (a) are unbiased. (c) Assume that E(e-σ2 Yi and E(49)-0 for all i where σ2 > 0. Show that V(β)--and (d) Use (b) and (c) above to show that the LSEs are consistent...
in a Bayesian view. Consider the prior π(a)-1 for all a e R Consider a Gaussian linear model Y = aX+ E Determine whether each of the following statements is true or false. π(a) a uniform prior. (1) (...
in a Bayesian view. Consider the prior π(a)-1 for all a e R Consider a Gaussian linear model Y = aX+ E Determine whether each of the following statements is true or false. π(a) a uniform prior. (1) (a) True (b) False L(Y=y14=a,X=x) (2) π(a) is a jeffreys prior when we consider the likelihood (where we assume xis known) (a) True (b)False Y-XB+ σε where ε E R" is a random vector with Consider a linear regression model E[ε1-0, E[eErJ-1....
4. (24 marks) Suppose that the random variables Yi,..., Yn satisfy Y-B BX,+ Ei, 1-1, , n, where βο and βι are parameters, X1, ,X, are con- stants, and e1,... ,en are independent and identically distr...
4. (24 marks) Suppose that the random variables Yi,..., Yn satisfy Y-B BX,+ Ei, 1-1, , n, where βο and βι are parameters, X1, ,X, are con- stants, and e1,... ,en are independent and identically distributed ran- dom variables with Ei ~ N (0,02), where σ2 is a third unknown pa- rameter. This is the familiar form for a simple linear regression model, where the parameters A, β, and σ2 explain the relationship between a dependent (or response) variable Y...
4. Consider the balanced one-way ANOVA model with I treatment groups, and J observations for each...
4. Consider the balanced one-way ANOVA model with I treatment groups, and J observations for each group iid where the idiosyncratic errors are ε ~N(0,02). (a) Show that SSW/o xi- (b) Show that SSB/o2 -1. (c) Show that SSW and SSB are independent. (d) What is the null distribution of SSW (11-1
4. Consider the balanced one-way ANOVA model with I treatment groups, and J observations for each group iid where the idiosyncratic errors are ε ~N(0,02). (a) Show that...
Problem 3: Absence of Intercept Consider the regression model Y, = BX,+", where , and X,...
Problem 3: Absence of Intercept Consider the regression model Y, = BX,+", where , and X, satisfy Assumptions SLR1-SLR5. Y (i) Let B denote an estimator of B that is constructed as P where Y and X as are the sample means of Y,and X,, respectively. Show that B is conditionally unbiased. Derive the least squares estimator of B. Show that the estimator is conditionally unbiased. Derive the conditional variance of the estimator. (ii) (iii) (iv) 2
Exercise 2b please!
Exercise 1 Consider the regression model through the origin y.-β1zi-ci, where Ei ~ N(0,o). It is assumed that the regression line passes through the origin (0, 0) that for this model a: T N, is an unbiased estimator of o2. a. Show d. Show that (n-D2 ~X2-1, where se is the unbiased estimator of σ2 from question (a). Exercise2 Refer to exercise 1 a. Show that is BLUE (best linear unbiased estimator) b. Show that +1 has...
1. Consider the simple linear regression model: Ү, — Во + B а; + Ei, where 1, . . , En are i.i.d. N(0,02), for i1,2,... ,n. Let b1 = s^y/8r and bo = Y - b1 t be the least squared estimators of B1 and Bo, respectively. We showed in class, that N(B; 02/) Y~N(BoB1 T;o2/n) and bi ~ are uncorrelated, i.e. o{Y;b} We also showed in class that bi and Y 0. = (a) Show that bo is...
please don't copy. thx
Question 1. Consider the model Yij = Mi + Rij, Rij~N(0,02), i = 1,2;j = 1,2, ..., Ni. 222(Y1j-81+)? Part A. Show that Sị is an unbiased estimator of o2. Part B. Show that the pooled estimate of o2 is unbiased. n1-1
Problem 1: Consider the model Y = BO + Bi X+e, where e is a N(0,02) random variable independent of X. Let also Y = Bo + B1X. Show that E[(Y - EY)^3 = E[(Ỹ – EY)^3 + E[(Y – Y)1.
please don't copy, thx
Question 2. Consider the model Yij = uị + Rij, Rij~N(0,02), i = 1,2; j = 1,2, ..., Ni. Part A. Determine using least squares the parameter estimates. Part B. State the estimate of variance in the model. Part C. Clearly show that that ūı = 71+ is an unbiased estimator of Mz. Part D. The average grade of 32 Nano Engineering students in STAT 353 is 75% with a standard deviation of 5%. The average...
3. Consider the linear model: Yİ , n where E(Ei)-0. Further α +Ari + Ei for i 1, assume that Σ.r.-0 and Σ r-n. (a) Show that the least square estimates (LSEs) of α and ß are given by à--Ỹ and (b) Show that the LSEs in (a) are unbiased. (c) Assume that E(e-σ2 Yi and E(49)-0 for all i where σ2 > 0. Show that V(β)--and (d) Use (b) and (c) above to show that the LSEs are consistent...
in a Bayesian view. Consider the prior π(a)-1 for all a e R Consider a Gaussian linear model Y = aX+ E Determine whether each of the following statements is true or false. π(a) a uniform prior. (1) (a) True (b) False L(Y=y14=a,X=x) (2) π(a) is a jeffreys prior when we consider the likelihood (where we assume xis known) (a) True (b)False Y-XB+ σε where ε E R" is a random vector with Consider a linear regression model E[ε1-0, E[eErJ-1....
4. (24 marks) Suppose that the random variables Yi,..., Yn satisfy Y-B BX,+ Ei, 1-1, , n, where βο and βι are parameters, X1, ,X, are con- stants, and e1,... ,en are independent and identically distributed ran- dom variables with Ei ~ N (0,02), where σ2 is a third unknown pa- rameter. This is the familiar form for a simple linear regression model, where the parameters A, β, and σ2 explain the relationship between a dependent (or response) variable Y...
4. Consider the balanced one-way ANOVA model with I treatment groups, and J observations for each group iid where the idiosyncratic errors are ε ~N(0,02). (a) Show that SSW/o xi- (b) Show that SSB/o2 -1. (c) Show that SSW and SSB are independent. (d) What is the null distribution of SSW (11-1
4. Consider the balanced one-way ANOVA model with I treatment groups, and J observations for each group iid where the idiosyncratic errors are ε ~N(0,02). (a) Show that...
Problem 3: Absence of Intercept Consider the regression model Y, = BX,+", where , and X, satisfy Assumptions SLR1-SLR5. Y (i) Let B denote an estimator of B that is constructed as P where Y and X as are the sample means of Y,and X,, respectively. Show that B is conditionally unbiased. Derive the least squares estimator of B. Show that the estimator is conditionally unbiased. Derive the conditional variance of the estimator. (ii) (iii) (iv) 2
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