This Presentation is tailor made for those who are willing to get an overview of Econometrics as to what it means, how it works and the methodology it follows.
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
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2006. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
This Presentation is tailor made for those who are willing to get an overview of Econometrics as to what it means, how it works and the methodology it follows.
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
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2006. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
1.Evaluate the function at the indicated value of x. Round your.docxpaynetawnya
1.
Evaluate the function at the indicated value of x. Round your result to three decimal places.
Function: f(x) = 0.5^x Value: x = 1.7
-0.308
1.7
0.308
0.5
2.
Solve for x. 3x = 81
7
3
4
-3
3.
Logarithms are the inverse of exponentials.
True
False
4.
The Logarithm Quotient Rule states:
logb(x / y) = logb(x) + logb(y)
logb(x / y) = logb(x) - logb(y)
logb(x y) = y ∙ logb(x)
logb(c) = 1 / logc(b)
5.
Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. Assume all variables are positive.
log3 9x
log3 9 * log3 x
log3 9 + log3 x
log3 9 - log3
none of these
6.
Select the graph of the function. Indicate which graph is correct: 1st, 2nd, 3rd, or 4th
f(x) = 5x-1
7.
Evaluate the function at the indicated value of x. Round your result to three decimal places.
Value: x=2
8.
The exponential equation y=bx is equivalent to the logarithmic equation x=logby
True
False
9.
Use the One-to-One property to solve the equation for x.
e(3x+5) = e6
x = -1/3
x2 = 6
x = 1/3
x = 3
10.
Write the logarithmic equation in exponential form.
log8 64 = 2
82 = 16
82 = 88
82 = 64
864 = 2
11.
Write the exponential equation in logarithmic form.
43 = 64
log64 4 = 3
log4 64 = 3
log4 64 = -3
log4 3 = 64
12.
The given x-value is a solution (or an approximate solution) of the equation.
42x-7 = 16
x = 5
True
False
13.
Find the magnitude R of each earthquake of intensity I (let I0=1). (Hint: R=log (I/I0)
I = 19000
3.28
5.28
4.28
2.38
14.
pH is a measure of the hydrogen ion concentration of a solution. It is defined as the negative logarithm of the hydrogen ion concentration. The equation is:
pH = - log [H+]
If an acid has an H+ concentration of 10-4, what's the pH?
15.
A general formula for exponential Growth can be given by:
A = P ekt
In your textbook, or using another reliable source, research what values, P, A, k and t represent and write your answer. (Hint: What do each of the variables stand for?)
16.
Continuously compounded interest means your principal is earning interest and you keep earning interest on the interest earned. Research the formula for Continuously Compounded Interest and write it below.
17.
$2500 is invested in an account at interest rate r, compounded continuously. Find the time required for the amount to double. (Approximate the result to two decimal places.)
r = 0.0570
13.16 years
10.16 years
11.16 years
12.16 years
18.
Write Eulers Number (e) to three decimal places.
19.
Exponential functions often involve the rate of increase or decrease of something such as a population, for example. If there is a population increase, it is a _______ function and when there is a decrease, it is a ________ function.
20.
Do some research on important numbers in mathematics. Choose one that is interesting to you (it can be on e or pi or a different number)
In your post, share with us what you ...
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2009. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2013. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
Micro review 1 for International Economics' students: the simple market model.
If you download this on a computer at the college (or open it on a computer that has PowerPoint), you'll be able to read detailed notes for each slide.
Discussion of elasticity (price-elasticity of demand and supply, income elasticity of demand, and cross-price elasticity of demand) for my Principles of Microeconomics students.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
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.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
3. Outline
Operators
Summation
Double summation
On math as a language
Math is, among other things, a language. We use language to
think ideas and share them with others.
In principle, the same ideas we express with math symbols we can
express with words (which are also symbols). Math symbols are
just abbreviations for words.
However, when we abbreviate and express our ideas in math
language, we economize resources. It is easier, for example, to
make the shared or communicable meaning of words clearer and
more precise when we use math symbols.
SFC - juliohuato@gmail.com Applied Statistics for Economics Summation Operator
4. Outline
Operators
Summation
Double summation
Operators
Operators are mathematical symbols that compress or abbreviate
further our math language. That is why they can be extremely
powerful tools in econometrics.
These are some familiar examples of operators:
Addition: +
Subtraction: −
Multiplication: ×
Division: ÷
In the context of a statement in math language, these operators
tell us to execute specific operations: (a + b) add b to a; (a − b)
subtract b from a; (a × b) multiply b times the number a; (a ÷ b)
divide a by b (or b into a).
SFC - juliohuato@gmail.com Applied Statistics for Economics Summation Operator
5. Outline
Operators
Summation
Double summation
Summation Operator ( )
The summation operator is heavily used in econometrics.
We now let a, b, k, and n be constant numbers, and x, y , and i be
variables. The following are some properties of the summation
operator.
SFC - juliohuato@gmail.com Applied Statistics for Economics Summation Operator
6. Outline
Operators
Summation
Double summation
Summation ( xi )
Suppose we have a list of numbers (the ages of 6 students):
20, 19, 22, 19, 21, 18. Let x be the age of a student and use the
natural numbers (1, 2, 3, . . .) to index these ages. Thus, xi means
the age of student i, where i = 1, 2, . . . , 6). Then:
6
x1 + x2 + x3 + x4 + x5 + x6 = x1 + x2 + . . . + x6 = xi
i=1
The last expression is the most compact. It reads: “The sum of xi ,
where i goes from 1 to 6.” The summation operator tells us to
add up the values of the variable x from the first to the sixth value:
6
xi = 20 + 19 + 22 + 19 + 21 + 18 = 119.
i=1
SFC - juliohuato@gmail.com Applied Statistics for Economics Summation Operator
7. Outline
Operators
Summation
Double summation
Summation ( xi )
Note the following:
n m n
xi = xi + xi
i=1 i=1 i=m+1
Example:
6 3 6
xi = xi + xi = (20+19+22)+(19+21+18) = 61+58 = 119.
i=1 i=1 i=4
We can always split the sum into various sub-sums.
SFC - juliohuato@gmail.com Applied Statistics for Economics Summation Operator
8. Outline
Operators
Summation
Double summation
Summing n times the constant number (k)
This property also holds for the summation operator:
n
k = nk
i=1
Example:
4
3 = 3 + 3 + 3 + 3 = 4 × 3 = 12.
i=1
SFC - juliohuato@gmail.com Applied Statistics for Economics Summation Operator
9. Outline
Operators
Summation
Double summation
Summing n times the product of a constant k and a
variable x
n n
kxi = k xi
i=1 i=1
Example:
3 3
5xi = 5x1 + 5x2 + 5x3 = 5(x1 + x2 + x3 ) = 5 xi .
i=1 i=1
SFC - juliohuato@gmail.com Applied Statistics for Economics Summation Operator
10. Outline
Operators
Summation
Double summation
Summing the sum of two variables (x and y )
n n n
(xi + yi ) = xi + yi
i=1 i=1 i=1
Example:
2
(xi + yi ) = (x1 + y1 ) + (x2 + y2 ) = x1 + y1 + x2 + y2
i=1
2 2
= x1 + x2 + y1 + y2 = (x1 + x2 ) + (y1 + y2 ) = xi + yi .
i=1 i=1
SFC - juliohuato@gmail.com Applied Statistics for Economics Summation Operator
11. Outline
Operators
Summation
Double summation
Summing the linear rule of a variable (x)
The linear rule of a variable x is: a + bx. E.g.: 4 + 5x.
If the n values of the variables are indexed (i = 1, 2, . . . , n), then
we can express the sum of this linear rule of x over its n values as
follows:
n n
(a + bxi ) = na + b xi
i=1 i=1
Example:
3 3 3 3 3
(4 + 5xi ) = 4+ 5xi = (3 × 4) + 5 xi = 12 + 5 xi .
i=1 i=1 i=1 i=1 i=1
SFC - juliohuato@gmail.com Applied Statistics for Economics Summation Operator
12. Outline
Operators
Summation
Double summation
Double summation
The double summation operator is used to sum up twice for the
same variable:
n m n
xij = (xi1 + xi2 + . . . + xim )
i=1 j=1 i=1
= (x11 +x21 +. . .+xn1 )+(x12 +x22 +. . .+xn2 )+. . .+(x1m +x2m +. . .+xnm )
SFC - juliohuato@gmail.com Applied Statistics for Economics Summation Operator
13. Outline
Operators
Summation
Double summation
Double summation
A property of the double summation operator is that the
summations are interchangeable:
n m m n
xij = xij .
i=1 j=1 i=1 j=1
SFC - juliohuato@gmail.com Applied Statistics for Economics Summation Operator
14. Outline
Operators
Summation
Double summation
The product operator
The product operator ( ) is defined as:
n
xi = x1 · x2 · · · xn .
i=1
Example: Let x be a list of numbers: 20, 19, 22. Then,
3
xi = 20 × 19 × 22 = 8, 360.
i=1
n
Note that i=1 k = k n . The n-product of a constant is the
constant raised to the n-th power.
SFC - juliohuato@gmail.com Applied Statistics for Economics Summation Operator