Linear Transformations of the data, consider the least squares regression of y on K variables (with a
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 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?
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 68% (16 reviews)
Consider the least squares regression of y on K variables with a constant X Consider an alternati...View the full answer
Answered By
Vijesh J
My passion to become a tutor is a lifetime milestone. Being a finance and marketing professional with hands-on experience in wealth management, portfolio management, team handling and actively contributing in promoting the company. Highly talented in managing and educating students in most attractive ways were students get involved. I will always give perfection to my works. Time is the most important for the works and I provide every answer on time without a delay. I will proofread each and every work and will deliver a with more perfection.
4.70+
5+ Reviews
15+ Question Solved
Related Book For
Question Posted:
Students also viewed these 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....
-
Research serves as a guide by which to study, describe, and quantify an array of social and physical phenomenon. Theory, which is best described as a set of propositions or hypotheses that specify...
-
To find out what is happening in the venture capital industry in the United States, look at the National Venture Capital Association site (www.nvca.org). Now find the NVCA's Yearbook 2010 in the &...
-
Schmidt (1994) conducted a series of experiments examining the effects of humor on memory. In one study, participants were shown a list of sentences, of which half were humorous and half were...
-
Derive the first two equations of Equation 2.44. Q11=U+U cos 20+ U3 cos 40 Q12 U4-U3 cos 40 Q22 2=U-U cos 20+ U3 cos 40 U2 Q16 sin 20+ U3 sin 40 2 us Q26 sin 20-U3 sin 40 2 Q66 = (U-U4)-U3 cos 40...
-
Taylor Corporation has used a periodic inventory system and the LIFO cost method since its inception in 2004. The company began 2011 with the following inventory layers (listed in chronological order...
-
A machine is 77% efficient and loses 1.1 horsepower through its drivetrain. Determine the horsepower input of the machine. Round the answer to 1 decimal place.
-
Jims dog Sparky runs 50 m northeast to a tree, then 70 m west to a second tree, and finally 20 m south to a third tree. a. Draw a picture and establish a coordinate system. b. Calculate Sparkys net...
-
Change in the sum of squares. Suppose that b is the least squares coefficient vector in the regression of y on X and that c is any other K 1 vector. Prove that the difference in the two sums of...
-
Partial Frisch and Waugh 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,...
-
What do we call the quantity force distance, and what quantity does it change?
-
A mutation changes a codon that specifies tyrosine into a stop codon. This type of mutation is a a. missense mutation. b. nonsense mutation. c. frameshift mutation. d. neutral mutation.
-
A release factor is referred to as a molecular mimic because its structure is similar to that of a. a ribosome. b. an mRNA. c. a tRNA. d. an elongation factor.
-
Which of the following was not a goal of the Human Genome Project? a. To obtain the DNA sequence of the entire human genome b. To successfully clone a mammal c. To develop technology for the...
-
Explain how the use of the technique of replica plating supported the random mutation theory and not the physiological adaptation hypothesis.
-
A researcher identified a mutation in PR of phage that causes its transcription rate to be increased 10-fold. Do you think this mutation would favor the lytic or lysogenic cycle? Explain your answer.
-
When the hoof of a galloping horse hits the ground, the digital flexor tendon in its lower leg may stretch by 5% in length, a significant stretch for this 45 cm tendon. The tendon is elastic; mostbut...
-
You work as an operations consultant for a textile company. Your client has a well-established distribution system in the US market. The company has hundreds of stores and four distribution centers....
-
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...
-
On a particular day, there were 300 stocks that advanced on the NYSE and 800 that declined. The volume in advancing issues was 1000 and the volume in declining issues was 3000. What is the trin ratio?
-
A coupon bond that pays interest of $30 annually has a par value of $1000, matures in 6 years, and is selling today at $850. What is the yield to maturity on this bond?
-
A callable bond pays annual interest of $40, has a par value of $1000, matures in 4 years but is callable in 3 years at a price of $1100, and has a value today of $1020. What is the yield to call on...
Study smarter with the SolutionInn App