Heteroscedasticity is the condition which refers to the violation of the Homoscedasticity condition of the linear regression model used in econometrics study. In simple words, it can be described as the situation which leads to increase in the variance of the residual terms with the increase in the fitted value of the variable. Copy the link given below and paste it in new browser window to get more information on Heteroscedasticity:- http://www.transtutors.com/homework-help/economics/heteroscedasticity.aspx
Brief notes on heteroscedasticity, very helpful for those who are bigners to econometrics. i thought this course to the students of BS economics, these notes include all the necessary proofs.
Brief notes on heteroscedasticity, very helpful for those who are bigners to econometrics. i thought this course to the students of BS economics, these notes include all the necessary proofs.
The presentation aims to explain the meaning of ECONOMETRICS and why this subject is studied as a separate discipline.
The reference is based on the book "BASIC ECONOMETRICS" by Damodar N. Gujarati.
For further explanation, check out the youtube link:
https://youtu.be/S3SUDiVpUGU
Econometrics notes (Introduction, Simple Linear regression, Multiple linear r...Muhammad Ali
Econometrics notes for BS economics students
Muhammad Ali
Assistant Professor of Statistics
Higher Education Department, KPK, Pakistan.
Email:Mohammadale1979@gmail.com
Cell#+923459990370
Skyp: mohammadali_1979
We can define heteroscedasticity as the condition in which the variance of the error term or the residual term in a regression model varies. As you can see in the above diagram, in the case of homoscedasticity, the data points are equally scattered while in the case of heteroscedasticity, the data points are not equally scattered.
Two Conditions:
1] Known Variance
2] Unknown Variance
We can define heteroscedasticity as the condition in which the variance of the error term or the residual term in a regression model varies. As you can see in the above diagram, in the case of homoscedasticity, the data points are equally scattered while in the case of heteroscedasticity, the data points are not equally scattered.
Two Conditions:
1] Known Variance
2] Unknown Variance
2. If you have a nonlinear relationship between an independent varia.pdfsuresh640714
2. If you have a nonlinear relationship between an independent variable x and a dependent
variable y, how can you apply the least -squares fit method? Does this work for all nonlinear
relationships? if not please give an example of a nonlinear equation where the fit method cannot
be used.(No need to use Matlab on this question).
Solution
A)The assumptions of linearity and additivity are both implicit in this specification. • Additivity
= assumption that for each IV X, the amount of change in E(Y) associated with a unit increase in
X (holding all other variables constant) is the same regardless of the values of the other IVs in
the model. That is, the effect of X1 does not depend on X2; increasing X1 from 10 to 11 will
have the same effect regardless of whether X2 = 0 or X2 = 1. • With non-additivity, the effect of
X on Y depends on the value of a third variable, e.g. gender. As we’ve just discussed, we use
models with multiplicative interaction effects when relationships are non-additive.
Linearity = assumption that for each IV, the amount of change in the mean value of Y associated
with a unit increase in the IV, holding all other variables constant, is the same regardless of the
level of X, e.g. increasing X from 10 to 11 will produce the same amount of increase in E(Y) as
increasing X from 20 to 21. Put another way, the effect of a 1 unit increase in X does not depend
on the value of X. • With nonlinearity, the effect of X on Y depends on the value of X; in effect,
X somehow interacts with itself. This is sometimes refered to as a self interaction. The
interaction may be multiplicative but it can take on other forms as well, e.g. you may need to
take logs of variables.
Dealing with Nonlinearity in variables. We will see that many nonlinear specifications can be
converted to linear form by performing transformations on the variables in the model. For
example, if Y is related to X by the equation E Yi Xi ( ) = + 2 and the relationship between the
variables is therefore nonlinear, we can define a new variable Z = X2 . The new variable Z is
then linearly related to Y, and OLS regression can be used to estimate the coefficients of the
model. There are numerous other cases where, given appropriate transformations of the
variables, nonlinear relationships can be converted into models for which coefficients can be
estimated using OLS. We’ll cover a few of the most important and common ones here, but there
are many others. Detecting nonlinearity and nonadditivity. The key question is whether the slope
of the relationship between an IV and a DV can be expected to vary depending on the context. •
The first step in detecting nonlinearity or nonadditivity is theoretical rather than technical. Once
the nature of the expected relationship is understood well enough to make a rough graph of it, the
technical work should begin. Hence, ask such questions as, can the slope of the relationship
between Xi and E(Y) be expected to have the same sign for all value.
The presentation aims to explain the meaning of ECONOMETRICS and why this subject is studied as a separate discipline.
The reference is based on the book "BASIC ECONOMETRICS" by Damodar N. Gujarati.
For further explanation, check out the youtube link:
https://youtu.be/S3SUDiVpUGU
Econometrics notes (Introduction, Simple Linear regression, Multiple linear r...Muhammad Ali
Econometrics notes for BS economics students
Muhammad Ali
Assistant Professor of Statistics
Higher Education Department, KPK, Pakistan.
Email:Mohammadale1979@gmail.com
Cell#+923459990370
Skyp: mohammadali_1979
We can define heteroscedasticity as the condition in which the variance of the error term or the residual term in a regression model varies. As you can see in the above diagram, in the case of homoscedasticity, the data points are equally scattered while in the case of heteroscedasticity, the data points are not equally scattered.
Two Conditions:
1] Known Variance
2] Unknown Variance
We can define heteroscedasticity as the condition in which the variance of the error term or the residual term in a regression model varies. As you can see in the above diagram, in the case of homoscedasticity, the data points are equally scattered while in the case of heteroscedasticity, the data points are not equally scattered.
Two Conditions:
1] Known Variance
2] Unknown Variance
2. If you have a nonlinear relationship between an independent varia.pdfsuresh640714
2. If you have a nonlinear relationship between an independent variable x and a dependent
variable y, how can you apply the least -squares fit method? Does this work for all nonlinear
relationships? if not please give an example of a nonlinear equation where the fit method cannot
be used.(No need to use Matlab on this question).
Solution
A)The assumptions of linearity and additivity are both implicit in this specification. • Additivity
= assumption that for each IV X, the amount of change in E(Y) associated with a unit increase in
X (holding all other variables constant) is the same regardless of the values of the other IVs in
the model. That is, the effect of X1 does not depend on X2; increasing X1 from 10 to 11 will
have the same effect regardless of whether X2 = 0 or X2 = 1. • With non-additivity, the effect of
X on Y depends on the value of a third variable, e.g. gender. As we’ve just discussed, we use
models with multiplicative interaction effects when relationships are non-additive.
Linearity = assumption that for each IV, the amount of change in the mean value of Y associated
with a unit increase in the IV, holding all other variables constant, is the same regardless of the
level of X, e.g. increasing X from 10 to 11 will produce the same amount of increase in E(Y) as
increasing X from 20 to 21. Put another way, the effect of a 1 unit increase in X does not depend
on the value of X. • With nonlinearity, the effect of X on Y depends on the value of X; in effect,
X somehow interacts with itself. This is sometimes refered to as a self interaction. The
interaction may be multiplicative but it can take on other forms as well, e.g. you may need to
take logs of variables.
Dealing with Nonlinearity in variables. We will see that many nonlinear specifications can be
converted to linear form by performing transformations on the variables in the model. For
example, if Y is related to X by the equation E Yi Xi ( ) = + 2 and the relationship between the
variables is therefore nonlinear, we can define a new variable Z = X2 . The new variable Z is
then linearly related to Y, and OLS regression can be used to estimate the coefficients of the
model. There are numerous other cases where, given appropriate transformations of the
variables, nonlinear relationships can be converted into models for which coefficients can be
estimated using OLS. We’ll cover a few of the most important and common ones here, but there
are many others. Detecting nonlinearity and nonadditivity. The key question is whether the slope
of the relationship between an IV and a DV can be expected to vary depending on the context. •
The first step in detecting nonlinearity or nonadditivity is theoretical rather than technical. Once
the nature of the expected relationship is understood well enough to make a rough graph of it, the
technical work should begin. Hence, ask such questions as, can the slope of the relationship
between Xi and E(Y) be expected to have the same sign for all value.
Resultant of Coplanar Parallel Forces | Mechanical EngineeringTransweb Global Inc
If two or more than two forces are acting on a single plane then the forces are known as System of Coplanar Forces and if they are acting on different planes then the forces are called as Non-Coplanar Forces. Copy the link given below and paste it in new browser window to get more information on Resultant of Coplanar Parallel Forces:-
http://www.transtutors.com/homework-help/mechanical-engineering/force-systems-and-analysis/resultant-of-coplanar-parallel-forces.aspx
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A force is a physical quantity that tends to change the behavior of a solid body when applied upon. This change in behavior may be change in shape of the body or motion of the body in the direction of its action. The force is a vector quantity since it has magnitude and direction. Copy the link given below and paste it in new browser window to get more information on System Of Coplanar Forces:-
http://www.transtutors.com/homework-help/mechanical-engineering/force-systems-and-analysis/system-of-coplanar-forces.aspx
Resultant of Two Unlike and Unequal Parallel Forces | Mechanical EngineeringTransweb Global Inc
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http://www.transtutors.com/homework-help/mechanical-engineering/force-systems-and-analysis/resultant-of-two-unlike-and-unequal-parallel-forces.aspx
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http://www.transtutors.com/homework-help/mechanical-engineering/bending-moment-and-shear-force/sfd-load-diagram-examples.aspx
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http://www.transtutors.com/homework-help/mechanical-engineering/force-systems-and-analysis/principle-of-transmissibility.aspx
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http://www.transtutors.com/homework-help/mechanical-engineering/force-systems-and-analysis/law-of-polygon.aspx
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In many aspects, leadership and management are almost known as Synonymous but both the words mean different. Similarities between Leadership and ManagementLeadership is an important and essential part of management. Without leadership, the meaning of management won’t be completed. Copy the link given below and paste it in new browser window to get more information on Similarities between Leadership and Management:-
http://www.transtutors.com/homework-help/industrial-management/leadership/similarities-between-leadership-and-management.aspx
The Rank Positional Weight Method can be used to develop and balance an assembly line. In this method, work elements are divided among workstations depending on the duration of work elements and their precedence position. Copy the link given below and paste it in new browser window to get more information on Ranked Positional Weight Method:-
http://www.transtutors.com/homework-help/industrial-management/line-balancing/ranked-positional-weight-method.aspx
Business Intelligence And Business Analytics | ManagementTransweb Global Inc
Business Intelligence is the initial basic step of Business Analytics. It refers to gathering raw and complex data, and converting it into systematic and logical information in a format that is usable by the end user. Copy the link given below and paste it in new browser window to get more information on Business Intelligence And Business Analytics:-
http://www.transtutors.com/homework-help/management/managing-information-technology/business-intelligence-analytics/
The ABC (Activity Based Costing) System is a system whereby the categorization of the cost is done one the basis of the various cost drivers. A cost driver is an activity that generates the cost. Copy the link given below and paste it in new browser window to get more information on ABC Cost Hierarchy:-
http://www.transtutors.com/homework-help/cost-management/activity-based-costing/abc-cost-hierarchy/
In today’s competitive world the term Speed to Market plays an important role for everyone. So, Speed to Market means the pace of introducing any change, innovation, creativity, any market practice for the purpose of increasing the Promotion of the product as quickly as possible in the market. Copy the link given below and paste it in new browser window to get more information on Speed To Market:-
http://www.transtutors.com/homework-help/industrial-management/product-development/speed-to-market.aspx
Hubris prevalent in an organizational context is referred as ‘managerial hubris’, which means the cognitive bias in the decision making process by one of the senior officials in an organization. Copy the link given below and paste it in new browser window to get more information on Managerial Hubris:-
http://www.transtutors.com/homework-help/finance/theories-of-merger-and-acquisition/managerial-hubris/
Conductance is an ability of a material to allow the passage of current or fluid or temperature through different materials. It is opposite of resistance through a path, higher the conductivity of material lower is its resistance. It is most commonly used with electrical circuits, though it is also used in fluid and thermals. Copy the link given below and paste it in new browser window to get more information on Conductance:-
http://www.transtutors.com/homework-help/electrical-engineering/conductance.aspx
Advantages and Disadvantages of Digital Electronics | Electrical EngineeringTransweb Global Inc
Digital Electronics circuits are those which operate with digital signals. These are discrete signals which are sampled from analog signal. Digital circuits use binary notation for transmission of signal. Copy the link given below and paste it in new browser window to get more information on Advantages and Disadvantages of Digital Electronics:-
http://www.transtutors.com/homework-help/electrical-engineering/digital-electronics/advantages-disadvantages/
Stabilization Of Operating Point | Electrical EngineeringTransweb Global Inc
Biasing of BJT amplifiers plays an important role in operation of these amplifiers. Broadly biasing means application of DC voltage for amplification of AC signal. For individual devices biasing circuit mainly includes resistance. Copy the link given below and paste it in new browser window to get more information on Stabilization Of Operating Point:-
http://www.transtutors.com/homework-help/electrical-engineering/transistors/stabilization-of-operating-point.aspx
Curves are of different types and for different purposes. Some of the curves are utility curve, margin curves, demand and supply curve, offer curves, etc. International trade is based on international specialization. Copy the link given below and paste it in new browser window to get more information on Offer Curves:-
http://www.transtutors.com/homework-help/international-economics/analytical-tools/offer-curves.aspx
Currency is any form of money in general circulation in a country. Foreign exchange is money denominated in the currency of another country or a group of countries. Simply, an exchange rate is defined as the rate at which the market converts one currency into another. Copy the link given below and paste it in new browser window to get more information on Fixed Exchange Rate:-
http://www.transtutors.com/homework-help/international-economics/economic-policy-in-open-economy/fixed-exchange-rate/
Computer Architecture is the set of pre-defined rules and methods that describes the functionality of computer system. In other words, a computer consists of both hardware and software and using some rules and methods for the interaction of both hardware and software of a computer is known as computer architecture. Copy the link given below and paste it in new browser window to get more information on Computer Architecture:-
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One of the great advantages of high-level programming languages such as c, c++, and java is that they are machine independent. Programs written in the high-level languages can run on any machine. This is possible because of the compiler. Copy the link given below and paste it in new browser window to get more information on Compilers computer program:-
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Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
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The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
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2. One of the important assumption of the regression
model is that all the disturbances have same variance,
2 . This condition is known as homoscedastic,
which implies that the errors scatter in similar fashion
regardless of the value of X. But there are instances
where the error scatter is different, depending on the
value of the independent variables. When this condition
prevails ,the error terms are said to
be heteroscedastic.
Introduction
3. Yi = 1 + 2Xi + Ui
Regression Model
Var(Ui) = 2Homoscedasticity:
Heteroscedasticity:
Var(Ui) = i
2
Or E(Ui
2) = 2
Or E(Ui
2) = i
2
i =1,2,… N
4. Reasons for violation of Homoscedasticity
condition are many, such as:
Data with outliners
Functional form is incorrect
Transformation is incorrect of the data
observations being mixed with different measures of
scale.
If any one of these present in the data, there is
Heteroscedasticity.
HETEROSCEDASTICITY
5. Heteroscedasticity, thus can be defined as
a condition where errors have different
variance.
When the variance of the error term differ
across the observation, it makes the reliability
of observation unequal, that gives a wrong or
inaccurate inference about the data.
HETEROSCEDASTICITY
9. In case of Heteroscedasticity Ordinary least
squares estimators are
• linear and unbiased.
• not efficient.
Also, the data shows
• incorrect standard variation
• wrong confidence of interval and hypothesis test
CONSEQUENCES OF HETEROSCEDASTICITY
10. Hey Friends,
This was just a summary on Heteroscedasticity. For more
detailed information on this topic, please type the link
given below or copy it from the description of this PPT and
open it in a new browser window.
http://www.transtutors.com/homework-
help/economics/heteroscedasticity.aspx