Consider a multiple linear regression modely=XB +(nx p) (p x 1)€(n x 1)(n x 1)where n is the sample size, p=k+1 with k is the number of regressors andE(e)=0, V(e)=o² In.1[Note]3(6)3- (X'X)-¹h₁ = x(X'X)-¹₁,SVThe Cook's distance FOR I-th observation is defined byD₁(3B))'(X'X) (3 – ß())ps²Show that2²2haDip 1-ha

Given information: β^(i)=β^-X'X-1xi·ei1-hii .............. (1)hii=xi'X'X-1xi…

Answered: Consider a multiple linear regression…

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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The peanut crop was harvested from five fields of various area. The following data are the mass of the crop from each field y (in kilograms) and the field area x (in hectares). X 6² Round your intermediate answers to four decimal places (e.g. 98.7654). (a) Fit the simple linear regression model using the method of least squares. Find the estimate of ². Round your answer to the nearest integer (e.g. 9876). i B₁ = (b) What change in the mean mass is expected when the field area changes by 1 hectare? Round your answer to the nearest integer (e.g. 9876). ŷ: 7280 15730 13590 19820 12860 = 2.01 3.93 3.68 4.33 2.33 (c) Calculate the fitted value of y corresponding to x = 2.01. Find the corresponding residual. Round your answer to the nearest integer (e.g. 9876). =
How do I prove the left equals the right? Using a one-way ANOVA model
Let s be the sample variance of a random sample of size n1 fron a Normal(41,o²) population and s, be the sample variance of a random sample of size 12 from a Nornal(µ2,0²) population and the two samples are independent. Note that the two samples have the same population variance o² but µi # j12 and n1 # 12. Define the pooled variance estimator as (n1 – 1)sỉ + (n12 – 1)s3 T1 + n2 - 2 -- Is s? unbiased for o2 ? Explain with precisc computation. Find the distribution of ºP. Give the reasoning of your answer. Find the variance of s.
Show that the maximum likelihood estimation for the error variance oin linear regression is given by: (see attached)
4. Suppose that n=100 i.i.d observations for (Y₁, X₁) yield the following results Ỹ = 32.1 +66.8X, SER=15.1, R² = 0.81 (15.1) (12.2) Another researcher is interested in the same regression, but he makes an error when he enters the data in his regression program: He enters each observation twice, so he has 200 observations. Using these 200 observations, what results will be produced by his program? Write it in the following format: Ỹ +---X, SER= (---) (---) R² =
2.2 (31) Virulence and pathogen transmission The number of new infections produced by an individual infected with a pathogen such as influenza depends on the mortality rate that the pathogen causes. This pathogen-induced mortality rate is referred to as the pathogen's virulence. (The photo shows victims at Camp Funston of the influenza epidemic of 1918.] Extremely high levels of virulence result in very little transmission because the infected individual dies before infecting other individuals. Under certain assumptions, the number of new infections N is related to virulence v by the function
question 2
Suppose that n= 195 I.I.d. observations for (Y, X;) yleld the following regression results: v= 32.68 + 67.55Xx, SER= 18.63, R = 0.84 (15.7) (12.5) Another researcher is interested in the same regression, but he makes an error when he enters the data into the regression: He enters each observation twice, so he has 390 observations (with observation 1 entered twice, observation 2 entered twice, and so forth). Which of the following eatimated parameters change result? (Check all that apply) O A. The estimated intercept and slope. O B. The R of the regression. Yc. The standard error of the regrussion (SER). YD. The standard errors of the estimated coefficients. Using the 390 observations, what results will be produced by his regression program? Ý= 32.68 + 67.55X, SER =.R = 0.84 (Round your responses to two decimal places)

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