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Question 1. Consider the model Yij = Mi + Rij, Rij~N(0,02), i...
please don't copy, thx Question 2. Consider the model Yij = uị + Rij, Rij~N(0,02), i...
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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...
Just b) please 7. Consider the one-way analysis of variance model where €ij ~ N(0,02) are...
Just b) please
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]
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...
2. Consider the simple linear regression model: where e1, .. . , es, are i.i.d. N (0, o2), for i= 1,2,... , n. Suppose...
2. Consider the simple linear regression model: where e1, .. . , es, are i.i.d. N (0, o2), for i= 1,2,... , n. Suppose that we would like to estimate the mean response at x = x*, that is we want to estimate lyx=* = Bo + B1 x*. The least squares estimator for /uyx* is = bo bi x*, where bo, b1 are the least squares estimators for Bo, Bi. ayx= (a) Show that the least squares estimator for...
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...
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 2. Consider the one-way layout ANOVA model, where we assume that Yij = μί-cij,に1, . . . , I and J 1, . . . ,J,...
Problem 2. Consider the one-way layout ANOVA model, where we assume that Yij = μί-cij,に1, . . . , I and J 1, . . . ,J, where μί's are fixed unknown with zero mean treatment means and eiy's are random errors , al such that Σ-lai -0 and E[Yj-μ + ai,1- Show that there exists unique numbers μ, ai, a. b. Show that the null hypothesis Ho : μ,-...- μι is equivalent to Ho : 01 ,-. . .-a1-0...
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.
A simple linear regression model is given as follows Yi = Bo + B1Xi+ €i, for...
A simple linear regression model is given as follows Yi = Bo + B1Xi+ €i, for i = 1, ...,n, where are i.i.d. following N (0, o2) distribution. It is known that x4 n, and x = 0, otherwise. Denote by n2 = n - ni, Ji = 1 yi, and j2 = 1 1. for i = 1, ... ,n1 < n2 Lizn1+1 Yi. n1 Zi=1 1. Find the least squares estimators of Bo and 31, in terms of...
1. Consider a regression model Yi = x;ß +ei, i = 1,...,n. You estimate this model...
1. Consider a regression model Yi = x;ß +ei, i = 1,...,n. You estimate this model using the OLS estimator. (a) Present and discuss assumptions for the OLS estimation.
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...
Just b) please
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]
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...
2. Consider the simple linear regression model: where e1, .. . , es, are i.i.d. N (0, o2), for i= 1,2,... , n. Suppose that we would like to estimate the mean response at x = x*, that is we want to estimate lyx=* = Bo + B1 x*. The least squares estimator for /uyx* is = bo bi x*, where bo, b1 are the least squares estimators for Bo, Bi. ayx= (a) Show that the least squares estimator for...
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...
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 2. Consider the one-way layout ANOVA model, where we assume that Yij = μί-cij,に1, . . . , I and J 1, . . . ,J, where μί's are fixed unknown with zero mean treatment means and eiy's are random errors , al such that Σ-lai -0 and E[Yj-μ + ai,1- Show that there exists unique numbers μ, ai, a. b. Show that the null hypothesis Ho : μ,-...- μι is equivalent to Ho : 01 ,-. . .-a1-0...
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.
A simple linear regression model is given as follows Yi = Bo + B1Xi+ €i, for i = 1, ...,n, where are i.i.d. following N (0, o2) distribution. It is known that x4 n, and x = 0, otherwise. Denote by n2 = n - ni, Ji = 1 yi, and j2 = 1 1. for i = 1, ... ,n1 < n2 Lizn1+1 Yi. n1 Zi=1 1. Find the least squares estimators of Bo and 31, in terms of...
1. Consider a regression model Yi = x;ß +ei, i = 1,...,n. You estimate this model using the OLS estimator. (a) Present and discuss assumptions for the OLS estimation.
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