General Linear Model is an ANOVA procedure in which the calculations are performed using the least square regression approach to describe the statistical relationship between one or more prediction in continuous response variable. Predictors can be factors and covariates. Copy the link given below and paste it in new browser window to get more information on General Linear Model:- http://www.transtutors.com/homework-help/statistics/general-linear-model.aspx
It is essential for all regression models that the relationship between the independent and dependent variables are represented correctly. Functional form tries to do exactly this. A functional form will give an equation for the dependent and independent variables so that the hypothesis tests can be carried out properly. Copy the link given below and paste it in new browser window to get more information on Functional Forms of Regression Analysis:- http://www.transtutors.com/homework-help/economics/functional-forms-of-regression-models.aspx
Orthogonal Property of Standard Design/Orthogonality of Design and Factorial ...Hasnat Israq
This provides the basic description of Orthogonality of Design and Missing Values & Factorial Experiment under Design and Analysis of Experiment . This is one of the most important topic in Statistics and also for Mathematics and for Researchers-Scientists .
Contains
a.Statistics-1
b. SAS-1
c. Statistics-2
d. Market Research
e. MS Excel
f. SAS-2
g. Data Audit & Data Sanitization
h. SQL
i. Model Building
j. HR
General Linear Model is an ANOVA procedure in which the calculations are performed using the least square regression approach to describe the statistical relationship between one or more prediction in continuous response variable. Predictors can be factors and covariates. Copy the link given below and paste it in new browser window to get more information on General Linear Model:- http://www.transtutors.com/homework-help/statistics/general-linear-model.aspx
It is essential for all regression models that the relationship between the independent and dependent variables are represented correctly. Functional form tries to do exactly this. A functional form will give an equation for the dependent and independent variables so that the hypothesis tests can be carried out properly. Copy the link given below and paste it in new browser window to get more information on Functional Forms of Regression Analysis:- http://www.transtutors.com/homework-help/economics/functional-forms-of-regression-models.aspx
Orthogonal Property of Standard Design/Orthogonality of Design and Factorial ...Hasnat Israq
This provides the basic description of Orthogonality of Design and Missing Values & Factorial Experiment under Design and Analysis of Experiment . This is one of the most important topic in Statistics and also for Mathematics and for Researchers-Scientists .
Contains
a.Statistics-1
b. SAS-1
c. Statistics-2
d. Market Research
e. MS Excel
f. SAS-2
g. Data Audit & Data Sanitization
h. SQL
i. Model Building
j. HR
Background
Applications of Differential Equations
First order linear differential equations
Homogeneous ODE
Second Order Differential Equations
Laplace Transform Method
Dada la ecuacion de la conica -6x_1^2 + 20 x_1 x_2 + 8x_2^2 + 30 x_1.pdfnishadvtky
Dada la ecuacion de la conica -6x_1^2 + 20 x_1 x_2 + 8x_2^2 + 30 x_1 - 16 x_2 = 15
encontrar, por transformacion de efes, primero en traslacion y luego en rotacion Centro de la
coniea Orintacion de sus ejes principales Identifiear el tipo de conica: elipse, parabola o
hyoerbola
Solution
Ans-
the problem of a vibrating string such as that of a musical instrument was studied by Jean le
Rond d\'Alembert, Leonhard Euler, Daniel Bernoulli, and Joseph-Louis Lagrange.[4][5][6][7] In
1746, d’Alembert discovered the one-dimensional wave equation, and within ten years Euler
discovered the three-dimensional wave equation.[8]
The Euler–Lagrange equation was developed in the 1750s by Euler and Lagrange in connection
with their studies of the tautochrone problem. This is the problem of determining a curve on
which a weighted particle will fall to a fixed point in a fixed amount of time, independent of the
starting point.
Lagrange solved this problem in 1755 and sent the solution to Euler. Both further developed
Lagrange\'s method and applied it to mechanics, which led to the formulation ofLagrangian
mechanics.
Fourier published his work on heat flow in Théorie analytique de la chaleur (The Analytic
Theory of Heat),[9] in which he based his reasoning on Newton\'s law of cooling, namely, that
the flow of heat between two adjacent molecules is proportional to the extremely small
difference of their temperatures. Contained in this book was Fourier\'s proposal of hisheat
equation for conductive diffusion of heat. This partial differential equation is now taught to every
student of mathematical physics.
Example[edit]
For example, in classical mechanics, the motion of a body is described by its position and
velocity as the time value varies. Newton\'s laws allow (given the position, velocity, acceleration
and various forces acting on the body) one to express these variables dynamically as a
differential equation for the unknown position of the body as a function of time.
In some cases, this differential equation (called an equation of motion) may be solved explicitly.
An example of modelling a real world problem using differential equations is the determination
of the velocity of a ball falling through the air, considering only gravity and air resistance. The
ball\'s acceleration towards the ground is the acceleration due to gravity minus the acceleration
due to air resistance.
Gravity is considered constant, and air resistance may be modeled as proportional to the ball\'s
velocity. This means that the ball\'s acceleration, which is a derivative of its velocity, depends on
the velocity (and the velocity depends on time). Finding the velocity as a function of time
involves solving a differential equation and verifying its validity.
Types[edit]
Differential equations can be divided into several types. Apart from describing the properties of
the equation itself, these classes of differential equations can help inform the choice of approach
to a solution. Commonly us.
Find the explicit solution of the linear DE dyxdx=-6x^3-6x^2 y+1 u.pdfsales89
Find the explicit solution of the linear DE dy/xdx=-6/x^3-6x^2 y+1 using the appropriate
integrating factor and with the initial value of y(10)=-15. (b)Find the largest interval of definition
I for x. (c)Which of the terms in the solution are transient(show limits)?
Solution
A differential equation is a mathematicalequation for an unknown function of one
or several variables that relates the values of the function itself and its derivatives of various
orders. Differential equations play a prominent role in engineering, physics, economics, and
other disciplines. Differential equations arise in many areas of science and technology,
specifically whenever a deterministic relation involving some continuously varying quantities
(modeled by functions) and their rates of change in space and/or time (expressed as derivatives)
is known or postulated. This is illustrated in classical mechanics, where the motion of a body is
described by its position and velocity as the time varies. Newton\'s laws allow one to relate the
position, velocity, acceleration and various forces acting on the body and state this relation as a
differential equation for the unknown position of the body as a function of time. In some cases,
this differential equation (called an equation of motion) may be solved explicitly. An example of
modelling a real world problem using differential equations is determination of the velocity of a
ball falling through the air, considering only gravity and air resistance. The ball\'s acceleration
towards the ground is the acceleration due to gravity minus the deceleration due to air resistance.
Gravity is constant but air resistance may be modelled as proportional to the ball\'s velocity. This
means the ball\'s acceleration, which is the derivative of its velocity, depends on the velocity.
Finding the velocity as a function of time involves solving a differential equation. Differential
equations are mathematically studied from several different perspectives, mostly concerned with
their solutions—the set of functions that satisfy the equation. Only the simplest differential
equations admit solutions given by explicit formulas; however, some properties of solutions of a
given differential equation may be determined without finding their exact form. If a self-
contained formula for the solution is not available, the solution may be numerically
approximated using computers. The theory of dynamical systems puts emphasis on qualitative
analysis of systems described by differential equations, while many numerical methods have
been developed to determine solutions with a given degree of accuracy. The term homogeneous
differential equation has several distinct meanings. One meaning is that a first-order ordinary
differential equation is homogeneous (of degree 0) if it has the form \\frac{dy}{dx} = F(x,y)
where F(x,y) is a homogeneous function of degree zero; that is to say, such that F(tx,ty) = F(x,y).
In a related, but distinct, usage, the term linear .
A researcher in attempting to run a regression model noticed a neg.docxevonnehoggarth79783
A researcher in attempting to run a regression model noticed a negative beta sign for an explanatory variable when s/he was expecting a positive sign based on theoretical considerations. What advice would you give to the researcher as to what is going on and what specific diagnostics would you look at? Explain conceptually and statisticallythe different ways you cancorrect for this problem.
Reason
One of the most common and important reasons for such situations is the existence of multicollinearity. Multicollinearity can happen if some of the independent variables are highly correlated to each other or to another variable that is not in the model.
Multicollinearity also has other symptoms such as
· Large variance for regression coefficients
· Non-significant individual coefficients while the general model is significant
· Change of marginal contributions depending on the variables in the model
· Large correlation coefficients in the correlation matrix of variables
It should however be noted that the general model can preserve its predictive ability and it is only the explanatory power that is lost
Before going to the solutions and measures the researcher can take it is wise to take a step back and see the underlying reason for the multicollinearity. An extreme case where two variables are identical gives the best understanding of problem
In this case we are trying to define y as a function of and while in reality . Therefore any linear combination of and is replaceable by infinite other linear combinations (ie )
It is simply understandable that while the y is predicted correctly in all the instances individual coefficients for and are meaningless.
Diagnosis
One of the most common diagnoses for multicollinearity is the variance inflation factor (VIF)
Where
And is the coefficient of multiple determination of regression of on other variables
The variance inflation factor therefore determines how much the variance of each coefficient inflates. when equals zero VIF equals 1 which suggests zero multicollinearity heuristic is that any value of VIF larger than 10 is alerting and a case of strong multicollinearity exists.
Solution
s
There are a few solutions for the multi Collinearity problem:
1- Ignoring the problem completely is possible for cases where we only care about the final model fit and prediction capability rather than individual coefficients and explanation power
2- Removing some of the correlated variables from the model, this can be justified since we can argue the effect of variable is however seen by similar highly correlated variables that are kept in the model
3- Principle component analysis (or any orthogonal transformation) can reduce the number of factors to a few orthogonal factors with no collinearity; however we should note that the interpretation of variables after a PC transformation is hard.
4- For cases where we intend to keep all the variables in the model without any major transformation, the Ridge regr.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
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.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
2. A differential equation is an equation which contains one or more terms and the derivatives of one variable (i.e.,
dependent variable) with respect to the other variable (i.e., independent variable)
dy/dx = f(x)
Here “x” is an independent variable and “y” is a dependent variable
For example, dy/dx = 5x
A differential equation contains derivatives which are either partial derivatives or ordinary derivatives. The
derivative represents a rate of change, and the differential equation describes a relationship between the
quantity that is continuously varying with respect to the change in another quantity. There are a lot
of differential equations formulas to find the solution of the derivatives.
Differential Equation Definition
3. 2
Order of Differential Equation
The order of the differential equation is the order of the highest order derivative present in the equation. Here
some examples for different orders of the differential equation are given.
dy/dx = 3x + 2 , The order of the equation is 1
(d2y/dx2)+ 2 (dy/dx)+y = 0. The order is 2
(dy/dt)+y = kt. The order is 1
First Order Differential Equation
You can see in the first example, it is a first-order differential equation which has degree equal to 1. All the linear
equations in the form of derivatives are in the first order. It has only the first derivative such as dy/dx, where x
and y are the two variables and is represented as:
dy/dx = f(x, y) = y’
Second-Order Differential Equation
The equation which includes the second-order derivative is the second-order differential equation. It is
represented as;
d/dx(dy/dx) = d2y/dx2 = f”(x) = y”
4. Types of Differential Equations and their Solutions
Differential equations can be divided into several types namely :
Ordinary Differential Equations
Partial Differential Equations
Linear Differential Equations
Nonlinear differential equations
Homogeneous Differential Equations
Nonhomogeneous Differential Equations
Ordinary Differential Equation
A function that satisfies the given differential equation is called its solution. The solution that contains as many arbitrary
constants as the order of the differential equation is called a general solution. The solution free from arbitrary constants is
called a particular solution. There exist two methods to find the solution of the differential equation.
1) Separation of variables
2) Integrating factor
5. Applications
Differential equations have several applications in different fields such as applied mathematics, science, and
engineering. Apart from the technical applications, they are also used in solving many real life problems. Let us
see some differential equation applications in real-time.
1) Differential equations describe various exponential growths and decays.
2) They are also used to describe the change in return on investment over time.
3) They are used in the field of medical science for modelling cancer growth or the spread of disease in the body.
4) Movement of electricity can also be described with the help of it.
5) They help economists in finding optimum investment strategies.
6) The motion of waves or a pendulum can also be described using these equations.
The various other applications in engineering are: heat conduction analysis, in physics it can be used to
understand the motion of waves. The ordinary differential equation can be utilized as an application in the
engineering field for finding the relationship between various parts of the bridge.
Now, go through the differential equations examples in real-life applications .