4.19. Consider a regression through the origin,Yi = Bx; +€;, with E(e;)=0,V(€) =o²x}, i=1,2,., 12a. Derive the generalized least squaresestmate of ß in Eq. (4.58) and obtain itsvariance. Note that the covariance matrixV and its inverse V' are diagonalmatrices. The generalized least squaresestimate minimizes a weighted sum ofsquares with weights given by the diagonalelements in V-. Hence, one refers to it asthe weighted least squares estimate.b. Suppose that z, = y;/x; and ", Z = 30.Find the numerical value for the weightedleast squares estimate in (a) and express itsvariance as a function of o².%3D

Answered: Image /qna-images/answer/b712c074-2799-4e37-b4cd-a2f717713497.jpg

Answered: Consider a regression through the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Find the least-squares regression line y^=b0+b1x through the points (−1,2),(1,8),(6,13),(7,19),(10,23), and then use it to find point estimates y^ corresponding to x=1 and x=8 For x=1, y^ = For x=8, y^ =
The null hypothesis being tested in the least-squares regression output for B is B1 = B1,0=1. True False
find the least squares regression line equation from the given data.
Consider the following population model for household consumption: cons = a + b1 * inc+ b2 * educ+ b3 * hhsize + u where cons is consumption, inc is income, educ is the education level of household head, hhsize is the size of a household. Suppose a researcher estimates the model and gets the predicted value, cons_hat, and then runs a regression of cons_hat on educ, inc, and hhsize. Which of the following choice is correct and please explain why. A) be certain that R^2 = 1 B) be certain that R^2 = 0 C) be certain that R^2 is less than 1 but greater than 0. D) not be certain
Find the least-squares regression line y^=b0+b1x through the points (−2,2),(3,6),(4,15),(8,20),(12,26) and then use it to find point estimates y^ corresponding to x=4 and x=8. For x=4, y^ = For x=8, y^ =
A financial analyst is examinıng the Pela each the company's current stock price and the company's earnings per share reported for the past 12 months. Her data are given below, with x denoting the earnings per share from the previous year, and y denoting the current stock price (both in dollars). Based on these data, she computes the least-squares regression line to be y = -0.147+0.043x. This line, along with a scatter plot of her data, is shown below. Earnings per Current stock price, y (in dollars) share, x (in dollars) 36.55 1.64 14.18 0.57 41.79 1.37 39.16 1.10 2.5+ 57.70 2.71 26.95 0.90 32.65 1.70 41.94 1.17 52.79 2.56 42.72 2.01 16.89 0.76 22.46 0.58 Earnings per share, x (in dollars) 58.88 2.19 30.13 1.48 50.08 1.73 28.92 0.81 Submit Assi Continue D 2021 McGraw-H Education. All Rights Reserved. Terms of Use Privacy e to search 近 Current stock price, y (in dollars)
If beta1_hat = 0.4571 use the data below to find beta0_hat for the simple linear model using the method of Least Squares. Y 17 2 3 11 4 20 15 18 13 13.07 50.88 24.57 32.11
Suppose Derrick is an insect enthusiast who measured the body length and weight of three insects in his backyard. His data are shown in the table. Length (mm) Weight (mg) Variable ?x ?y Insect 1 7 28 Insect 2 21 42 Insect 3 35 70 Derrick used the data to compute the least squares regression line. ?̂ =1.5?+15.167y^=1.5x+15.167 Calculate the residual value for each of Derrick's data points and the sum of the residual values. Report your answers precise to three decimal places. Residual 1: Residual 2: Residual 3: Sum of the residuals:
Find the coefficients for the least-squares regression line y^=b0+b1x through the points (−2,0),(2,6),(4,14),(9,20),(9,25) b0 =. b1 =
An engineer is testing a new car model to determine how its fuel efficiency, measured in L/(100 km), is related to its speed, which is measured in km/hour. The engineer calculates the average speed for 30 trials. The average speed is an example of a (statistic or parameter) The engineer would like to find the least squares regression line predicting fuel used (y) from speed (x) for the 30 cars he observed. He collected the data below. Speed 62 65 80 82 85 87 90 96 98 100 Fuel 12 13 14 13 14 14 15 15 16 15 Speed 100 102 104 107 112 114 114 117 121 122 Fuel 16 17 16 17 18 17 18 17 18 19 Speed 124 127 127 130 132 137 138 142 144 150 Fuel 18 19 20 19 21 23 22 23 24 26 The regression line equation is Round each number to four decimal places.

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