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Exercise 1 Suppose X is the initial matrix in a multiple regression problem. We then add...
Considering multiple linear regression models, we compute the regression of Y, an n x 1 vector,...
Considering multiple linear regression models, we compute the regression of Y, an n x 1 vector, on an n x (p+1) full rank matrix X. As usual, H = X(XT X)-1 XT is the hat matrix with elements hij at the ith row and jth column. The residual is e; = yi - Ýi. (a) (7 points) Let Y be an n x 1 vector with 1 as its first element and Os elsewhere. Show that the elements of the...
Considering multiple linear regression models, we compute the regression of Y, an n x 1 vector,...
Considering multiple linear regression models, we compute the regression of Y, an n x 1 vector, on an n x (p+1) full rank matrix X. As usual, H = X(XT X)-1 XT is the hat matrix with elements hij at the ith row and jth column. The residual is e; = yi - Ýi. (a) (7 points) Let Y be an n x 1 vector with 1 as its first element and Os elsewhere. Show that the elements of the...
linear regression 1.1 Localized Suppose we want to estimate localized linear regression by weighting the contribution...
linear regression 1.1 Localized Suppose we want to estimate localized linear regression by weighting the contribution of the data points by their distance to the query pointr,i.e. using the cost i=1 where (r)-2(is the inverse Euclidean distance between the training point and query (test) point Derive the modified normal equations for the above cost function E(r(a)). (Hint: first, rewrite the cost function in matrix/vector notation, using a diagonal matrix to represent the weights w).
2) Suppose you have multiple regression set up Ynxi XnxpBpxi Sxl and f ~ N(0nx1, σ21.). P Po X(X,...
linear statistics modeling and regression
2) Suppose you have multiple regression set up Ynxi XnxpBpxi Sxl and f ~ N(0nx1, σ21.). P Po X(X,X)-X, be the projection matrix on the column space of X. a) Show residual vector, e = (1,-P)Y. Here e is the vector of residuals ei S. b) Show that the variance of e, is 1 - Pi, where P is the i, j th entry of the matrix P c) Show that the sample covariance of...
Consider two separate linear regression models and For concreteness, assume that the vector yi co...
please help me to solve that question
Consider two separate linear regression models and For concreteness, assume that the vector yi contains observations on the wealth ofn randomly selected individuals in Australia and y2 contains observations on the wealth of n randomly selected individuals in New Zealand. The matrix Xi contains n observations on ki explanatory variables which are believed to affect individual wealth in Australia, and he matrix X2 contains n observations on k2 explanatory variables which are believed...
Please help me to solve part b and c . and please dont copy my answer in part a and then post it ...
please help me to solve part b and c .
and please dont copy my answer in part a and then post it as
an answer.
thanks
Consider two separate linear regression models and For concreteness, assume that the vector yi contains observations on the wealth ofn randomly selected individuals in Australia and y2 contains observations on the wealth of n randomly selected individuals in New Zealand. The matrix Xi contains n observations on ki explanatory variables which are believed...
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)....
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...
3. In the multiple regression model shown in the previous question, which one of the following st...
3. In the multiple regression model shown in the previous question, which one of the following statements is incorrect: (b) The sum of squared residuals is the square of the length of the vector ü (c) The residual vector is orthogonal to each of the columns of X (d) The square of the length of y is equal to the square of the length of y plus the square of the length of û by the Pythagoras theorem In all...
a. (5) From the multiple regression model we want to test the following hypothesis: Ho: β1-0...
a. (5) From the multiple regression model we want to test the following hypothesis: Ho: β1-0 and β2-β3 and β5-1 Rewrite the null hypothesis Ho in the form of RB-r using the matrix R and two vectors B and r b. (5) Consider the following wage regression result: log(wage) 3.240.06educ 0.51Female 0.01educ Female, where educ denotes years of education and Female is a dummy variable for females. What is the return to schooling for male workers? What is the return...
Considering multiple linear regression models, we compute the regression of Y, an n x 1 vector, on an n x (p+1) full rank matrix X. As usual, H = X(XT X)-1 XT is the hat matrix with elements hij at the ith row and jth column. The residual is e; = yi - Ýi. (a) (7 points) Let Y be an n x 1 vector with 1 as its first element and Os elsewhere. Show that the elements of the...
Considering multiple linear regression models, we compute the regression of Y, an n x 1 vector, on an n x (p+1) full rank matrix X. As usual, H = X(XT X)-1 XT is the hat matrix with elements hij at the ith row and jth column. The residual is e; = yi - Ýi. (a) (7 points) Let Y be an n x 1 vector with 1 as its first element and Os elsewhere. Show that the elements of the...
linear regression 1.1 Localized Suppose we want to estimate localized linear regression by weighting the contribution of the data points by their distance to the query pointr,i.e. using the cost i=1 where (r)-2(is the inverse Euclidean distance between the training point and query (test) point Derive the modified normal equations for the above cost function E(r(a)). (Hint: first, rewrite the cost function in matrix/vector notation, using a diagonal matrix to represent the weights w).
linear statistics modeling and regression
2) Suppose you have multiple regression set up Ynxi XnxpBpxi Sxl and f ~ N(0nx1, σ21.). P Po X(X,X)-X, be the projection matrix on the column space of X. a) Show residual vector, e = (1,-P)Y. Here e is the vector of residuals ei S. b) Show that the variance of e, is 1 - Pi, where P is the i, j th entry of the matrix P c) Show that the sample covariance of...
please help me to solve that question
Consider two separate linear regression models and For concreteness, assume that the vector yi contains observations on the wealth ofn randomly selected individuals in Australia and y2 contains observations on the wealth of n randomly selected individuals in New Zealand. The matrix Xi contains n observations on ki explanatory variables which are believed to affect individual wealth in Australia, and he matrix X2 contains n observations on k2 explanatory variables which are believed...
please help me to solve part b and c .
and please dont copy my answer in part a and then post it as
an answer.
thanks
Consider two separate linear regression models and For concreteness, assume that the vector yi contains observations on the wealth ofn randomly selected individuals in Australia and y2 contains observations on the wealth of n randomly selected individuals in New Zealand. The matrix Xi contains n observations on ki explanatory variables which are believed...
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)....
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...
3. In the multiple regression model shown in the previous question, which one of the following statements is incorrect: (b) The sum of squared residuals is the square of the length of the vector ü (c) The residual vector is orthogonal to each of the columns of X (d) The square of the length of y is equal to the square of the length of y plus the square of the length of û by the Pythagoras theorem In all...
a. (5) From the multiple regression model we want to test the following hypothesis: Ho: β1-0 and β2-β3 and β5-1 Rewrite the null hypothesis Ho in the form of RB-r using the matrix R and two vectors B and r b. (5) Consider the following wage regression result: log(wage) 3.240.06educ 0.51Female 0.01educ Female, where educ denotes years of education and Female is a dummy variable for females. What is the return to schooling for male workers? What is the return...
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