Consider the following models Model I Y i 1 2 X i u i Model II Y i 1 2 X i u i where Y and X are standardized variables Show that 2 2 (S x S y ) and hence establish that although the regression slope coefficients are independent of the change of origin they are not independent of the change of scale

Question: Consider the following models: Model I: Y i = 1 + 2 X i + u i Model II: Y * i

Consider the following models:

Model I: Y_i = β₁ + β₂X_i + u_i

Model II: Y^*_i α₁ + α₂X^∗_i+ u_i

where Y^* and X^* are standardized variables. Show that α̂₂ = β̂₂(S_x/S_y ) and hence establish that although the regression slope coefficients are independent of the change of origin they are not independent of the change of scale.

Step by Step Solution

★★★★★

3.37 Rating (172 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

For Model I we know that 2 x i y i x i 2 ... 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 (2 attachments)

1529_605d88e1cd46a_656218.pdf

180 KBs PDF File

1529_605d88e1cd46a_656218.docx

120 KBs Word File

Students Have Also Explored These Related Econometrics Questions!

Consider the following models: ln Y i = 1 + 2 ln X i + u i ln Y i = 1 + 2 ln X i + u i where Y i = w 1 Y i and X i = w 2 X i , the ws being constants. a. Establish the relationships between...

Consider the following models. a. Will OLS estimates of Î± 1 and Î² 1 be the same? Why? b. Will OLS estimates of Î± 3 and Î² 3 be the same? Why? c....

Consider the following model: Y i = e 1+2Xi / (1 + e 1+2Xi ) As it stands, is this a linear regression model? If not, what trick, if any, can you use to make it a linear regression model? How would...

Consider the following linear programming model: Max X 1 2 + X 2 + 3X 3 Subject to: X 1 + X2 3 X 1 + X2 1 X 1, X 2 0 This problem violates which of the following assumptions? a. certainty b....

Consider the following polynomial functions . g(x) = - 3 * (x + 1) ^ 2 * (x + 3) ^ 2; h(x) = x ^ 3 - x ^ 2 - 6x Choose the graph of each function from the choices below . 2 2 Graph D Graph E Graph F...

I am having trouble with the following problem, any assistance with it would be much appreciated. Let x and n be integers greater than 1. Consider the following algorithm. t + 0, 5+0 for / {1, 2,...

Please include all math steps. Will leave good reviews if helped. No reposts pls. 1. Consider the following system of equations : 1 3 - 1 2 X L - 2 0 O O 2 O X3 O X y a ) solve the above system (or...

Consider the following LP problem max 3 x 1 + 2 x 2

True, False or Uncertain: Justify your answer.(6 Marks)14*5-20 Marks(a) Suppose the estimate of A, in the regression model Y -A+BX +Ax, +,X +e, is notsignificantly different from zero at the 5% level...

Name the three common causes of flocculation. Also name four types of mud additives used to control flocculation.

The circuit above has Vs 80L60, R1 = 100 Q, R2 330 Q, R3 = 820 2, R4 = 680 Q. jXc = -j470 Q and jXL = j 220 Q. Use any method of circuit analysis to find the voltage across the capacitor in polar...

Suppose that the index model for stocks A and B is estimated from excess returns with the following results: RA = 2 . 0 0 % + 0 . 4 0 RM + eARA = 2 . 0 0 % + 0 . 4 0 RM + eA RB = 1 . 8 0 % + 0 . 9 0...

Economic growth is the sustained expansion of production possibilities. The annual percentage change in real GDP measures the economic growth rate.

If a company sells its products only from a website, which is accessible over the Internet to customers from all over the world, does it still need to worry about having a specific ta r get market?...

Explain, in your own words, what each of the four Ps involves.

Evaluate the texts statement, A marketing strategy sets the details of implement a tion.

Eco Plastics Company: The target capital structure for ECO is given by the weights in the following table: Source of Capital Weight Long-term debt 30 % Preferred stock 20 Common stock equity 50 Total...

Cochrane, Inc., is considering a new three-year expansion project that requires an initial fixed asset investment of $2,580,000. The fixed asset will be depreciated straight-line to zero over its...

Question: A researcher wishes to determine whether people with high blood pressure can reduce the blood pressure by following diet. Use a significance level of 0.01 to test the claim that the...