Question: Linear Transformations of the data, consider the least squares regression of y on K variables (with a constant) X. Consider an alternative set of regressors

Linear Transformations of the data, consider the least squares regression of y on K variables (with a constant) X. Consider an alternative set of regressors Z = XP, where P is a nonsingular matrix. Thus, each column of Z is a mixture of some of the columns of X. Prove that the residual vectors in the regressions of y on X and y on Z are identical. What relevance does this have to the question of changing the fit of a regression by changing the units of measurement of the independent variables?

Step by Step Solution

★★★★★

3.48 Rating (171 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Consider the least squares regression of y on K variables with a constant X Consider an alternati... View full answer

Question Has Been Solved by an Expert!

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

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

3-M-E-E-A (3).docx

120 KBs Word File

Students Have Also Explored These Related Econometric Questions!

Consider the multiple regression of y on K variables X and an additional variable z. Prove that under the assumptions A1 through A6 of the classical regression model, the true variance of the least...

In the least squares regression of y on a constant and X, to compute the regression coefficients on X, we can first transform y to deviations from the mean y and, likewise, transform each column of X...

Suppose we developed the following least squares regression equation: Y = 3.5 + 2.1X. Which of the following statements are correct? A. The dependent variable increases 2.1 for an increase of 1 in X....

Logarithms and polynomials Interaction effects Dummy variables ECMT1020: Introduction to Econometrics Lecture 10: Multivar. regr. & transformations Peter Exterkate peter.exterkate@sydney.edu.au...

An Investigation into obesity rates Researchers have been interested in studying the obesity trends worldwide over the past 25 years. In 2014 the World Health Organization (WHO) declared there were....

Math\t107-6381\t-\tQuiz\t#4\t-\tSchultz\t-\tDue\tFebruary\t21,\t2016\t-\tpage\t1\tof 3 Follow\tthese\tdirections\tcarefully. This\tquiz\tis\tdue\tby\t11:59\tEastern\ttime\ton\tFebruary\t21,\t2016. o...

Final Exam MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) The average age of the students in a statistics class is 22...

APStatistics 3.02 Looking at the Data Directions: Complete the assignment. Clearly label each answer. Your answers for this assignment must include reasons; simply stating the answer without...

What is a learning organization?

The following transitions occurred for London Engineering: Journalize the transactions of London Engineering. Include an explanation with each journal entry. Use the following accounts: Cash;...

Explain how Garth and Lynn could use first the nominal group method, and then brainstorming, to come up with ideas for marketing the widgets. Which would work better in this case? Why?

For the following statement determine whether each of them is "True" or "False". "True" means "always true" and "False" means "not necessarily true". A subdivision of a connected graph is connected....

What are the different material handling system? Describe any two equipment's used for material handling with their appropriate sketches.

Polyoxymethylene burns in a mixture of 12 % oxygen by mass and nitrogen is present. Assume it burns purely convectively with a heat transfer coefficient of 8 W/mK. Find in m^n? Given:...

A current distribution produces a magnetic flux density, B = (-6xz + 4xy + 3xz)a, + (y + 6yz - 4xy2)ay + (y - z - 2x-z)az Wb/m. Calculate magnetic flux through the surface defined by y = 1,0 x, z ...

Briefly describe the Robinson Crusoe metaphor underpinning the traditional economics perspective.

Using the matrices of sums of squares and cross products immediately preceding Section 3.2.3, compute the coefficients in the multiple regression of real investment on a constant, real GNP and the...

Suppose that you have two independent unbiased estimators of the same parameter , say 1 and 2, with different variances v1 and v2. What linear combination = c11 + c22 is the minimum variance...

Consider the simple regression yt = xt + 1 where E p[ | x] = 0 and E [2 | x ] = 2 (a) What is the minimum mean squared error linear estimator of ? Choose e to minimize Var [] + [E( ?? )]2. The answer...

Suppose that the regression model is yi = + xi + i, where the disturbances i have f (i) = (1/) exp (i), i 0. This model is rather peculiar in that all the disturbances are assumed to be positive....

The following sample moments for x = [1, x1, x2, x3] were computed from 100 observations produced using a random number generator:? The true model underlying these data is y = x1 + x2 + x3 + . a....

Your task is to analyze options on a fund. The time horizon for the analysis is T = 1 ar. The fund has time 0 price S0 = 80 and continuous dividend rate = 0, 02 (pro anno). Use a 4-period binomial...