Question: Consider a multiple linear regression model. Let X be the n (k + 1) design matrix. Use linear algebra to answer the questions below. (a)

Consider a multiple linear regression model. Let X be the n (k + 1) design matrix. Use linear algebra to answer the questions below.

(a) Show that the vector of residuals e is orthogonal to each column of the design matrix X.

(b) Use the result in (a) to show that the residuals sum to 0 and thus the sum of the residuals has expectation 0 if the model contains an intercept term.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Consider the (multiple) linear regression model y = X +5, 5 ~ N03, 021...), X = [1\" | $1 | | mp] 6 BMW\"). (1) As usual (3" = (3;) is the LSE of , = (g) = XE the vector of tted values and e = (as) =...

Consider the (multiple) linear regression model 3; = X+5, 5 ~ N(0, U21\"), X = [1,. |m1 | | gap] 6 BMW\"). (1) As usual 3 = (1'31) is the LSE of 13, E = (Iii) = X3 the vector of tted values and e =...

= = = - (XTX) Tiyi - Y), Q3. Consider the multiple linear regression model given by Y = X8+ where Y nx 1 vector of the dependent variables, X nx (p+1) design matrix of full rank, B (p+1) x1 vector of...

1. The data considered is part of a larger study conducted by Dr. Rick Linthurst (1979) at North Carolina State University as his Ph.D. thesis research. Fourty ve samples of the soil substrate were...

Please answer the following! Quite urgent !! Please dont copy from another websites (the answer is incorrect) 1. [Derivation / Conceptual] Consider the multiple linear regression model i7 : XE + s...

please help 2. [Derivation/Conceptual] Consider the multiple linear regression model Y = XB + E where Y is the n x 1 column vector of responses, X is the n x (p + 1) matrix for the predictors (with...

each part plz Consider the multiple linear regression model Y = XB + E where Y is the n x 1 column vector of responses, X is the n x (p + 1) matrix for the predictors (with intercept), and E ~ MVN(0,...

2. [Derivation/Conceptual] Consider the multiple linear regression model Y = XBFE where Y is the n x 1 column vector of responses, X is the n x (p + 1) matrix for the predictors (with intercept),...

1. [Derivation/ Conceptual] Consider the multiple linear regression model \" = X E + E' with the usual setup, where Y is the n x 1 column vector of responses, X is the n x (p + 1) matrix for the...

4. Consider the general linear regression model Y = X+ where Y is n x 1, X is n x p and of rank P, 3 is p x 1, e is n x 1, and e is N(0, 21). (a) The hat matrix H is given by H = X(X'X) X'. Show that...

Prepare Journal Entry On October 15, company car was destroyed in an accident. The vehicle had a cost of $23,000, and an accumulated depreciation of $17,000. Grow-a-Lot received a check for $5,500...

At the time of his marriage to Ann, Robert owned several parcels of real estate in joint tenancy with his brother, Sam. During his marriage, Robert purchased a house and put the title in his name and...

16. What is unearned income? Give two examples of items that would be classified as unearned income.

Expenses that are incurred directly or entirely in connection with the selling of merchandise are classified as

4. Using the same examples you gave in question 3, try to identify circular sequences, i.e. A affects B, but B also affects A.

6. Give three examples that nothing (doing nothing) can function as a cause.

2. To store it and