6. Suppose we estimate a linear regression equation Y; = Bo + B1X; + u; byOLS.(a) Show thatE ûi0, where the û;'s are the regression residuals.i3D1(b) Suppose we regress X; on û; by OLS, including a constant term inthe regression. Show that the estimated coefficient on û; is equal to zero.(c)Suppose we regress Y; on the predicted value Y; by OLS, includinga constant term in the regression. Show that the estimated coefficienton Y; is equal to one.(Hint: the regression residual is defined by û; = Y; – Y; where the predictedvalue Y; = Bo + B,X;. Here, Bo and B1 are the OLS estimators.)

Given regression model, Yi = 0 + 1Xi + ui

Answered: OLS. (a) Show that û; = 0,_where the…

Math

Advanced Math

OLS. (a) Show that û; = 0,_where the û;'s are the regression residuals. n Li: 1

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

6. Suppose we estimate a linear regression equation Y; = Bo + B1X; + u; by
OLS.
(a) Show thatE ûi
0, where the û;'s are the regression residuals.
i3D1
(b) Suppose we regress X; on û; by OLS, including a constant term in
the regression. Show that the estimated coefficient on û; is equal to zero.
(c)
Suppose we regress Y; on the predicted value Y; by OLS, including
a constant term in the regression. Show that the estimated coefficient
on Y; is equal to one.
(Hint: the regression residual is defined by û; = Y; – Y; where the predicted
value Y; = Bo + B,X;. Here, Bo and B1 are the OLS estimators.)

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