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Question5 15 points) In the class we workd with the model Y-X ?+c, where ( ....
3. Consider a linear model with only categorical predictors, written in matrix form as y = Xißi +6, Now suppose we add...
3. Consider a linear model with only categorical predictors, written in matrix form as y = Xißi +6, Now suppose we add some continuous predictors, resulting in an expanded model y X + ε. Now consider a quantity tTß, where t-M 切is partitioned according to the categorical and continuous predictors. Show that if t s stimable in the first model, then tB is estimable in the second model. If you write X [X1|X2], you may assume that r(X) (X (X2)....
3. Suppose the following data has been obtained for the linear model Y Bo+ x 14 2 1 4 0 22 (a) Fi...
a,b,c,d
3. Suppose the following data has been obtained for the linear model Y Bo+ x 14 2 1 4 0 22 (a) Find the OLS estimators βο and A using the non-matrix method. (b) Find the OLS estimators using the matrix method. (c) Find the coefficient of determination. (d) Find the standard error of
3. Suppose the following data has been obtained for the linear model Y Bo+ x 14 2 1 4 0 22 (a) Find the OLS...
2. In the regression model Y-Χβ+ E, Xis a fixed n x k matrix of rank...
2. In the regression model Y-Χβ+ E, Xis a fixed n x k matrix of rank k S11, E(c)-0 and E(es')-σ2Ω where Ω is a known non-singular matrix. The GiLS estimator of B is given by the formula Consider the following data 16 31 2 3 51 4 10 Assuming that Ay a) b) Calculate the GLS estimate of β in the model Y,Xß + ε Calculate the OLS estimate c) Compare it the two estimates and comment on efficiency.
The linear regression model in matrix format is Y Xe, with the usual definitions. Let E(elX)- 0 a...
The linear regression model in matrix format is Y Xe, with the usual definitions. Let E(elX)- 0 and γ1 0 0 0 Y2 00 01 0 00 .0 0 0 00N 0 0 0'YN 0 0 0YNL Notice that as a covariance matrix, Σ is symmetric and nonnegative definite. ) Derive Var (BoLSX). (ii) Let A: = CY be any other linear unbiased estimator where C, is an N × K function of X. Prove Var (β|X) > (X'Σ-1X)-1.
The...
The standard linear regression model is: y = Xw+e, where X is an nxd matrix of...
The standard linear regression model is: y = Xw+e, where X is an nxd matrix of predictor vari- ables, y is an n-dimensional vector of response variables, and e N (0,021) is an n-dimensional vector of model errors. (a) What is the PDF of y in terms of X,w, o?? N(0,p1). (b) Let the PDF from part (a) be denoted as fylw). Suppose also in this case that w Write an expression for the joint PDF of w and y...
Multivariate linear model Use vector notation to express the Consider the dataset below where a multivariate linear model b and c are three predictors and y is the desired response. 0 9 5 2 What are...
Multivariate linear model Use vector notation to express the Consider the dataset below where a multivariate linear model b and c are three predictors and y is the desired response. 0 9 5 2 What are X and Y in the MMSE exact solution w = (XTX)- XTY? 4 55 10 A multivariate linear model for the response will be expressed as
Multivariate linear model Use vector notation to express the Consider the dataset below where a multivariate linear model...
3. Let R3 be equipped with the inner product (x, y) = AX Ay, where A...
3. Let R3 be equipped with the inner product (x, y) = AX Ay, where A is the matrix shown below: TO -4 21 A = 3 2. LO 0 5) a.) (5 points) Let v = (1,-1,3). Find || V ||. UN b.) (5 points) Let x = (2,3,0) and y = (-3,2,1). Are x and y orthogonal in this inner product space? Justify your answer
3. Let R be equipped with the inner product (x,y) = AX Ay, where A is...
3. Let R be equipped with the inner product (x,y) = AX Ay, where A is the matrix shown below: TO-4 21 A = 3 2 LO 0 5) a.) (5 points) Let v = (1,-1,3). Find || V || 1 b.) (5 points) Let x = (2,3,0) and y = (-3,2,1). Are x and y orthogonal in this inner product space? Justify your answer
Need help with stats true or false questions Decide (with short explanations) whether the following statements are true or false a) We consider the model y-Ao +A(z) +E. Let (-0.01, 1.5) be a 95% con...
Need help with stats true or false questions
Decide (with short explanations) whether the following statements are true or false a) We consider the model y-Ao +A(z) +E. Let (-0.01, 1.5) be a 95% confidence interval for A In this case, a t-test with significance level 1% rejects the null hypothesis Ho : A-0 against a two sided alternative. b) Complicated models with a lot of parameters are better for prediction then simple models with just a few parameters c)...
Consider the multiple regression model y = X3 + €, with E(€)=0 and var(€)=oʻI. Problem 1...
Consider the multiple regression model y = X3 + €, with E(€)=0 and var(€)=oʻI. Problem 1 Gauss-Mrkov theorem (revisited). We already know that E = B and var() = '(X'X)". Consider now another unbiased estimator of 3, say b = AY. Since we are assuming that b is unbiased we reach the conclusion that AX = I (why?). The Gauss-Markov theorem claims that var(b) - var() is positive semi-definite which asks that we investigate q' var(b) - var() q. Show...
3. Consider a linear model with only categorical predictors, written in matrix form as y = Xißi +6, Now suppose we add some continuous predictors, resulting in an expanded model y X + ε. Now consider a quantity tTß, where t-M 切is partitioned according to the categorical and continuous predictors. Show that if t s stimable in the first model, then tB is estimable in the second model. If you write X [X1|X2], you may assume that r(X) (X (X2)....
a,b,c,d
3. Suppose the following data has been obtained for the linear model Y Bo+ x 14 2 1 4 0 22 (a) Find the OLS estimators βο and A using the non-matrix method. (b) Find the OLS estimators using the matrix method. (c) Find the coefficient of determination. (d) Find the standard error of
3. Suppose the following data has been obtained for the linear model Y Bo+ x 14 2 1 4 0 22 (a) Find the OLS...
2. In the regression model Y-Χβ+ E, Xis a fixed n x k matrix of rank k S11, E(c)-0 and E(es')-σ2Ω where Ω is a known non-singular matrix. The GiLS estimator of B is given by the formula Consider the following data 16 31 2 3 51 4 10 Assuming that Ay a) b) Calculate the GLS estimate of β in the model Y,Xß + ε Calculate the OLS estimate c) Compare it the two estimates and comment on efficiency.
The linear regression model in matrix format is Y Xe, with the usual definitions. Let E(elX)- 0 and γ1 0 0 0 Y2 00 01 0 00 .0 0 0 00N 0 0 0'YN 0 0 0YNL Notice that as a covariance matrix, Σ is symmetric and nonnegative definite. ) Derive Var (BoLSX). (ii) Let A: = CY be any other linear unbiased estimator where C, is an N × K function of X. Prove Var (β|X) > (X'Σ-1X)-1.
The...
The standard linear regression model is: y = Xw+e, where X is an nxd matrix of predictor vari- ables, y is an n-dimensional vector of response variables, and e N (0,021) is an n-dimensional vector of model errors. (a) What is the PDF of y in terms of X,w, o?? N(0,p1). (b) Let the PDF from part (a) be denoted as fylw). Suppose also in this case that w Write an expression for the joint PDF of w and y...
Multivariate linear model Use vector notation to express the Consider the dataset below where a multivariate linear model b and c are three predictors and y is the desired response. 0 9 5 2 What are X and Y in the MMSE exact solution w = (XTX)- XTY? 4 55 10 A multivariate linear model for the response will be expressed as
Multivariate linear model Use vector notation to express the Consider the dataset below where a multivariate linear model...
3. Let R3 be equipped with the inner product (x, y) = AX Ay, where A is the matrix shown below: TO -4 21 A = 3 2. LO 0 5) a.) (5 points) Let v = (1,-1,3). Find || V ||. UN b.) (5 points) Let x = (2,3,0) and y = (-3,2,1). Are x and y orthogonal in this inner product space? Justify your answer
3. Let R be equipped with the inner product (x,y) = AX Ay, where A is the matrix shown below: TO-4 21 A = 3 2 LO 0 5) a.) (5 points) Let v = (1,-1,3). Find || V || 1 b.) (5 points) Let x = (2,3,0) and y = (-3,2,1). Are x and y orthogonal in this inner product space? Justify your answer
Need help with stats true or false questions
Decide (with short explanations) whether the following statements are true or false a) We consider the model y-Ao +A(z) +E. Let (-0.01, 1.5) be a 95% confidence interval for A In this case, a t-test with significance level 1% rejects the null hypothesis Ho : A-0 against a two sided alternative. b) Complicated models with a lot of parameters are better for prediction then simple models with just a few parameters c)...
Consider the multiple regression model y = X3 + €, with E(€)=0 and var(€)=oʻI. Problem 1 Gauss-Mrkov theorem (revisited). We already know that E = B and var() = '(X'X)". Consider now another unbiased estimator of 3, say b = AY. Since we are assuming that b is unbiased we reach the conclusion that AX = I (why?). The Gauss-Markov theorem claims that var(b) - var() is positive semi-definite which asks that we investigate q' var(b) - var() q. Show...
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