Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Statistic Equations Cheat Sheet, Cheat Sheet of Statistics

James Madison University (JMU)Statistics

All formulas in statistics categorized by chapter

Typology: Cheat Sheet

2020/2021

Uploaded on 04/23/2021

damyen
damyen 🇺🇸

4.4

(27)

274 documents

1 / 5

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Formula Sheet
Chapter 2
Expected Value of a Discrete Random Variable (a.k.a. mean):
n
i
ii
xfxXE
1
)()(
The expected value of a function of a discrete random variable X:
n
i
ii
xfxgXgE
1
)()())((
The variance of a discrete random variable X:
n
i
iix
xfxXEXVar
1
2
22
)()()(
but also,
22
2
XEXE
Standard Deviation
2
xx
Rules of Expectation: where a and c are constants and X is a random variable
)()( XcEacXaE
Rules of Variance:
)()(
2
XVarccXaVar
Conditional Probability:
)(
),(
)|( Yf
YXf
YXf
where f(X,Y) is the joint probability
Covariance:
but also
yxyx
XYEYXE
)())((
where
),()(
iiii
yxfYXXYE
Correlation:
yx
xy
yxCov
),(
The sum of two random variables: Let X and Y be two random variables and a
and b are constants:
E(aX + bY) = aE(X) + bE(Y)
Var(aX + bY) = a2Var(X) + b2Var(Y) + 2abCov(X,Y)
pf3
pf4
pf5

Partial preview of the text

Download Statistic Equations Cheat Sheet and more Cheat Sheet Statistics in PDF only on Docsity!

Formula Sheet

Chapter 2

Expected Value of a Discrete Random Variable (a.k.a. mean):

n

i

i i

E X x f x

1

The expected value of a function of a discrete random variable X:

n

i

i i

E g X g x f x

1

The variance of a discrete random variable X:

n

i

x i i

Var X E X x f x

1

2 2 2

but also,     

2 2 2

E X    EX  

Standard Deviation

2

x x

Rules of Expectation: where a and c are constants and X is a random variable

E ( acX ) acE ( X )

Rules of Variance:

2

Var acXcVar X

Conditional Probability:

f Y

f X Y

f X Y

where f(X,Y) is the joint probability

Covariance:

x y i x i y i i

CovX YE XE X YEYE X   Y    X   Y   f x y

but also x y x y

E ( X   )( Y   ) E ( XY ) 

where

i i i i

E XY XY f x y

Correlation:

x y

xy

Covx y

The sum of two random variables: Let X and Y be two random variables and a

and b are constants:

E(aX + bY) = aE(X) + bE(Y)

Var(aX + bY) = a

2

Var(X) + b

2

Var(Y) + 2abCov(X,Y)

Sample Statistics: assume a sample of T observation on X

t

Sample Mean

Sample Variance

Sample Standard Deviation

Sample Covariance

Sample Correlation

Chapter 3 and 4 Formulas The Method of Least Squares

T

X

X

T

t

t

1

2

2

T

x x

s

i

x

2

x x

ss

x x y y

T

S

xy t t

 

2 2 2 2

x x y y

x x y y

s s

S

r

t t

t t

x y

xy

The estimated variance of the prediction error is:

R-squared is:

where

So that

Chapter 7 and 8

For the multiple regression model:

Adjusted R-squared:

F-statistic:

Let SSE

R

be the sum of squared residuals from the Restricted Model

Let SSE

U

be the sum of squared residuals from the Unrestricted Model.

Let J be the number of “restrictions” that are placed on the Unrestricted

model in constructing the Restricted model. Let T be the number of observations

in the data set. Let k be the number of RHS variables plus one for intercept in the

Unrestricted model.

Chapter 11

Goldfeld Quandt statistic:

o o

y b bx

1 2

2

2

2

ar( )

v

x x

x x

T

f

t

o

SST

SSE

SST

SSR

R   1 

2

 

2

2

ˆ

( )

t

t

SSE e

SST y y

2

2

2

y y

e

R

t

t

2

3 3

2

23

2

3

2

2 2

2

23

2

2

r x x

Var b

r x x

Var b

t

t

t t t t

y   x  x  e

1 2 2 3 3

T k

e

t

2

2

2

2

2

y y T

e T k

R

t

t

SSE T k

SSE SSE J

F

U

R U

2 2

1 1

2

2

2

1

SSE t k

SSE t k

GQ

This statistic has an F distribution with t

1

-k degrees of freedom in the numerator

and t

2

-k degrees of freedom in the denominator

The variance for b

2

when the error term is heteroskedastic is:

White standard errors use this Var(b

2

) formula, using

2

ˆ

t

e

as an estimate for

2

t

Chapter 12

Durbin-Watson test statistic is calculated as:

and

 

2 2

2 2

2 2 2

2 2

 

x x

x x

wVare w

Varb Var w e

t

t t

t t t t

t t

1

2

2

2

1

T

t

t

T

t

t t

e

e e

d

T

t

t

T

t

t t

e

e e

1

2

2

1

ˆ

ˆ ˆ

ˆ 