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calculating pearson factor, Lecture notes of Statistics

Arab Academy for Science & Technology Statistics

calculating pearson factor as part of stat course

Typology: Lecture notes

2018/2019

Uploaded on 11/27/2019

emad.hassan 🇪🇬

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Simple linear correlation analysis

Coefficient of correlation “ Pearson ”

∑( X – X ) ( Y – Y )

r =

ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ

∑( X – X )2 * ∑( Y – Y )2

Discover Lecture notes of Statistics Arab Academy for Science & Technology

Partial preview of the text

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Simple linear correlation analysis

Coefficient of correlation “ Pearson ”

∑( X – X ) ( Y – Y )

r =

∑( X – X )

* ∑( Y – Y )

Where :

X Value of the first 1 st variable Y Value of the second 2 nd variable X Mean of the first 1 st variable ∑X = ــــــــــ n Y Mean of the second 2 nd variable ∑Y = ــــــــــ n n Number of observations

N.B

1 < r < 1

N.B

Coefficient of determination = R 2 o < R 2 < 1

N.B

Scatter diagram y y X X Direct Inverse (Indirect)

Testing the significance of the

correlation coefficient:

(1) Null hypothesis H

: ρ = o

Alternative hypothesis H

Where ρ : correlation in population.

(2) “ t ” calculated ( t

r n – 2

t

1 – r

Ex.

In a study of the relationship between two variables X

and Y, the following information was given :

X 10 9 8 7 6

Y 8 5 4 2 1

(a) Draw a scatter diagram.

(b) Find coefficient of correlation

and calculate coefficient of determination.

(c) Test the significance of the correlation coefficient at

α = 0.05, given that : t ( 3 ) = 3.182, t(4) = 2.776,

t (5) = 2.

(a) Scatter diagram

6 7 8 9 10 (Direct)

Sol

Coefficient of determination R

(c) Test the significance of the correlation

coefficient :

(1) H o : ρ = 0 H 1 : ρ ≠ 0 r n – 2 0.98 5 – 2 0.98 x 1. (2) t c = = ــــــــــــــــــــــــــــــــ = ـــــــــــــــــــــــــ 8.529= ـــــــــــــــــــــــــــــ 1 – r 2 1 – (0.98) 2

(3) t t : column (0.05), Row (n-2 = 3), two tailed test, t t = 3. (4) t c ( 8.529 ) > t t ( 3.182 )

calculating pearson factor, Lecture notes of Statistics

Related documents

Partial preview of the text

Download calculating pearson factor and more Lecture notes Statistics in PDF only on Docsity!

Simple linear correlation analysis

Coefficient of correlation “ Pearson ”

∑( X – X ) ( Y – Y )

r =

∑( X – X )

* ∑( Y – Y )

Where :

N.B

N.B

N.B

Testing the significance of the

correlation coefficient:

(1) Null hypothesis H

: ρ = o

Alternative hypothesis H

Where ρ : correlation in population.

(2) “ t ” calculated ( t

r n – 2

t

1 – r

Ex.

In a study of the relationship between two variables X

and Y, the following information was given :

X 10 9 8 7 6

Y 8 5 4 2 1

(a) Draw a scatter diagram.

(b) Find coefficient of correlation

and calculate coefficient of determination.

(c) Test the significance of the correlation coefficient at

α = 0.05, given that : t ( 3 ) = 3.182, t(4) = 2.776,

t (5) = 2.

(a) Scatter diagram

Sol

Coefficient of determination R

(c) Test the significance of the correlation

coefficient :