suppose we have independent random variables Y1,...,Yn withY; = 0x; + e;,i = 1, . .. , n,%3Diidwhere x1,.., Xn are fixed, known constants, 0 is a fixed but unknown parameter, and e;Normal(0, o?).a)What is the distribution of Y;? Are the Y;'s independent?b)Show that Yn/ã is an unbiased estimator of 0 and calculate its variance.c)Show that (1/) E1(Yi/x;) is an unbiased estimator of 0 and calculate its variance.This is called a linear regression model. It is very important in data analysis because it allows us toestimate the linear relationship between predictors (xi) and outcomes (yi).

Answered: suppose we have independent random…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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suppose we have independent random variables Y1,...,Yn with
Y; = 0x; + e;,
i = 1, . .. , n,
%3D
iid
where x1,
.., Xn are fixed, known constants, 0 is a fixed but unknown parameter, and e;
Normal(0, o?).
a)
What is the distribution of Y;? Are the Y;'s independent?
b)
Show that Yn/ã is an unbiased estimator of 0 and calculate its variance.
c)
Show that (1/) E1(Yi/x;) is an unbiased estimator of 0 and calculate its variance.
This is called a linear regression model. It is very important in data analysis because it allows us to
estimate the linear relationship between predictors (xi) and outcomes (yi).

Expert Solution

Step 1

Regression Analysis

Regression analysis helps to estimate the relationship between one independent variable and two or more dependent variable and also strength of the relationship. It has different types such as

Simple linear Regression
Multiple linear Regression and
Non linear regression.

The Linear model involves the values of the coefficient should be used in the representation of the data. It includes the statistical properties which are used to estimate those coefficients and it is an amalgamation of all the standard deviations, covariance and correlations.

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