Question

4. (20 points. You are given the following pairs of observations on (C1, yi), i = 1, 2, 3, 4: 0 Yi 1 1 2 4 3 3 4 5 Consider t

0 0
Add a comment Improve this question Transcribed image text
Answer #1

Yi = utui E = { uteui => 1+4+3+ 5 = 4x u to = 13 = 4x u => û = 13 = 3:25 (RE(ui) =ū =o) 1.5 Eni=0 xiyi x? - w 14 sl 2016 દર ક- 38 Amd xiyp = dxi +Bet tu xí ..Exeigi = <xi łax + ß £x* to => 38 = 1 x 10 + 2 x 30 => lo + 30 f - 38 >> 2 + 38 = 3.8 - © NoSlope of the timeo linear regression model ů = 1) rie, positive. So, the correlation between xi and y. is also position posit

Add a comment
Know the answer?
Add Answer to:
4. (20 points. You are given the following pairs of observations on (C1, yi), i =...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
  • 1. Given data on (yi, xi) for i = 1, , n, consider the following least...

    1. Given data on (yi, xi) for i = 1, , n, consider the following least square problem for a imple linear regression bo,b We assume the four linear regression model assumptions dicussed in class hold (i) Compute the partial derivatives of the objective function. (ii) Put the derived partial derivatives in (i) equal to zeros. Explain why the resulting equa tions are called normal equation'. (Hin wo n-dimesional vectors (viand (wi)- are normal-orthogonal ) if Σ-1 ui wi-0. )...

  • 2. Suppose we are given data on n observations (zi, y), î i, . . ....

    2. Suppose we are given data on n observations (zi, y), î i, . . . , n, and we have a linear model, so that E (Y,) = Ao +Ari. Let A = SXY/Sxx and A,-F-Ax be the least-square estimates given in lecture. (a) Show that E(SXY)-ASxx and E(y)-Ao +AT. (b) Use (a) to show that E (A)-A and E(A)-A- In other words, these are unbiased estimators (c) The fitted values Yī = β0+812 i are used as estimates...

  • Consider a simple linear regression model with nonstochastic regressor: Yi = β1 + β2Xi + ui....

    Consider a simple linear regression model with nonstochastic regressor: Yi = β1 + β2Xi + ui. 1. [3 points] What are the assumptions of this model so that the OLS estimators are BLUE (best linear unbiased estimates)? 2. [4 points] Let βˆ and βˆ be the OLS estimators of β and β . Derive βˆ and βˆ. 12 1212 3. [2 points] Show that βˆ is an unbiased estimator of β .22

  • We have a dataset with n = 10 pairs of observations (xi; yi), and Xn i=1...

    We have a dataset with n = 10 pairs of observations (xi; yi), and Xn i=1 xi = 683; Xn i=1 yi = 813; Xn i=1 x2i = 47; 405; Xn i=1 xiyi = 56; 089; Xn i=1 y2 i = 66; 731: What is an approximate 95% prediction interval for the response y0 at x0 = 60? We have a dataset with n= 10 pairs of observations (li, Yi), and n n Ii 683, Yi = 813, i=1 п...

  • 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...

  • linear stat modeling & regression 1) Consider n data points with 3 covariates and observations {xn, ^i2, xi3,yid; i,,n, and you fit the following model, y Bi+Br2+Br+e that is yi A) +Ari,1 +Ari...

    linear stat modeling & regression 1) Consider n data points with 3 covariates and observations {xn, ^i2, xi3,yid; i,,n, and you fit the following model, y Bi+Br2+Br+e that is yi A) +Ari,1 +Ari,2 +Buri,3 + єї where є,'s are independent normal distribution with mean zero and variance ơ2 . H the vectors of (Y1, . . . ,Yn). Assume the covariates are centered: Σίχί,,-0, k = 1,2,3. ere, n = 50, Let L are Assume, X'X is a diagonal matrix...

  • 4. (60%) Consider the following linear regression model s XIXJ YB1+B2X u, i 1,2.. .n Suppose...

    4. (60%) Consider the following linear regression model s XIXJ YB1+B2X u, i 1,2.. .n Suppose the following sample is observed. 6 X 2 10 8 4 Y 3 4 5 6 2 4.8 3.Y 4c (1) Find the OLS estimates for B, and B2. (2) Compute the estimate of Var(u). (3) What are the variances of the OLS estimates? (4) Compute the coefficient of determination. (5) Show the relationship between r2 and Dxy (6) Compute the correlation coefficient pxy...

  • Given are five observations for two variables, x and y. 4 8 12 16 18 yi...

    Given are five observations for two variables, x and y. 4 8 12 16 18 yi 58 51 48 14 15 The estimated regression equation for these data is y= 76.77 - 3.41x a. Compute SSE, SST, and SSR (to 2 SSE decimals) (to 2 SST decimals) (to 2 SSR decimals) b. Compute the coefficient of determination r. Comment on the goodness of fit (to 3 decimals) % of the variability in y has been explained by the estimated regression...

  • Given are five observations for two variables, x and y. xi Yi 1 4 2 7...

    Given are five observations for two variables, x and y. xi Yi 1 4 2 7 3 8 4 5 11 15 The estimated regression equation for these data is y = 1.2 + 2.6x. a. Compute SSE, SST, and SSR using the following equations (to 1 decimal). SSD = 2(y - ý) SST = 2(y; - 5)2 SSR = 2() - 12 SSE SST SSR b. Compute the coefficient of determination 2 (to 3 decimals). Does this least squares...

  • A simple linear regression model is given as follows Yi = Bo + B1Xi+ €i, for...

    A simple linear regression model is given as follows Yi = Bo + B1Xi+ €i, for i = 1, ...,n, where are i.i.d. following N (0, o2) distribution. It is known that x4 n, and x = 0, otherwise. Denote by n2 = n - ni, Ji = 1 yi, and j2 = 1 1. for i = 1, ... ,n1 < n2 Lizn1+1 Yi. n1 Zi=1 1. Find the least squares estimators of Bo and 31, in terms of...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT