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Probability and Statistics > Correlation and Regression > Flashcards

Correlation and Regression Flashcards

1
Q

Correlation

A

Correlation is the statistical relationship between variables such that change in one variable affects change in another variable

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2
Q

Analysis of _______________ of two or more variables refer to __________________

A

Analysis of covariance of two or more variables refer to correlation

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3
Q

Types of correlation

A

1.) Positive correlation
2.) Negative correlation
3.) Linear and non-linear
4.)Partial and total

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4
Q

What does positive correlation indicate?

A

A positive correlation means that as one variable increases, the other also increases and as ne decreases, the other decreases

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5
Q

What does negative correlation indicate?

A

A negative correlation means that one variable increases, the other variable decreases and vice versa

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6
Q

How to denote correlation coefficient

A

γ (gamma)

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7
Q

What is correlation coefficient

A

It is a numerical measure that quantifies the strength and direction of linear relationship between two variables

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8
Q

Range of correlation coefficient

A

[-1,1]

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9
Q

What does γ=0

A

At γ=0 indicates no linear relationship between two variables
or
covariance(x,y) = 0

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10
Q

Example of real world positive correlation

A

Height and Weight

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11
Q

Example of real world negative correlation

A

Supply and demand

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12
Q

Value of γ for perfect positive correlation

A

1

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13
Q

Value of γ for perfect negative correlation

A

-1

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14
Q

Value of γ for partial positive correlation

A

0 < γ < 1

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15
Q

Value of γ for partial negative correlation

A

-1 < γ < 0

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16
Q

Value of γ for no correlation

A

0

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17
Q

What is scatter plot used for

A

To visualize linear correlation between two variables

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18
Q

Scatter diagram of perfect positive correlation

A
19
Q

Scatter diagram of perfect negative correlation

A
20
Q

Scatter diagram of partial positive correlation

A
21
Q

Scatter diagram of perfect negative correlation

A
22
Q

Scatter diagram of no correlation

A
23
Q

Linear correlation

A

Changes in one variable are associated with proportional changes in the other, either positively or negatively.

24
Q

Non-linear correlation

A

Changes in one variable are not associated with proportional changes in the other

25
Q

Methods of studying correlation

A

1.) Graphic methods
* a.)Scatter diagram
* b.)Simple graphs

2.)Mathematical Methods
* a.)Pearson’s coefficient of correlation (γ)
* b.)Spearman’s rank coefficient of correlation (ρ)

26
Q

Coefficient of correlation

A

Pearson Coefficient of correlation

27
Q

Property second of coefficient of correlation

A
28
Q

Third property of coefficient of correlation

A
29
Q

Fourth property of coefficient of correlation

A
30
Q
A
31
Q
A
32
Q
A
33
Q
A
34
Q

If X, Y are orthogonal in nature, what about its correlation

A

γ = 0 since orthogonal vectors are independent vectors

35
Q

Cov(X,Y)

A

E(XY) - E(X).E(Y)

36
Q

Definition of rank correlation coefficient

A

This method based on rank is useful in dealing with quantitave characteristics such as morality, character, beauty. It is based on the ranks given to observations .

37
Q

Full name of rank correlation coeffiecient

A

Seaman’s rank correlation coefficient

38
Q

How to denote rank correlation coefficient

A

ρ

39
Q

Formula of rank correlation coefficient

A
40
Q

Range of rank correlation coefficient

A

ρ ∈ [-1,1]

41
Q

Property second of rank correlation coefficient

A

If ρ =1, there is complete agreement in the order if the ranks and direction of ranks is same

42
Q

Property third of rank correlation coefficient

A

If ρ =-1, there is complete disagreement in the order of ranks and they are in opposite directions

43
Q

if ρ=1, then

A

If ρ =1, there is complete agreement in the order if the ranks and direction of ranks is same

44
Q

If ρ =-1, then

A

If ρ =-1, there is complete disagreement in the order of ranks and they are in opposite directions

Probability and Statistics (4 decks)

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