correlation and regression skill set

7/24/2019 Correlation and Regression Skill Set

1/8

020

40

6080

100

0 50 100

SKILLS SET

Chapter 9: Correlation & Regression

No. Skills Examples of questions involving the skills1 To obtain a

scatterdiagram for

bivariate data

(labeling max& min values

of each

variable)

Lecture example 1

, , C ( C ) , (

P

1P). E

. .

20 30 40 50 60 70 80 90

45 52 64 66 91 86 98 104

2

(

,

)

Lecture example 2

C .

() ()

0

50

100

0 20 40 60

45

104

20 90

020

40

6080

100

40 60 80200

0

5

10

15

20

25

30

0 10 20 30


2/8

3

84+

Lecture example 3 , () ()

.

===== 380,351,15298,13717,14257 22 yxyxxy F .

( ) ( )

( ) ( )2 2

351 38014257

10 0.839

351 38013717 15298

10 10

r

=

27 22 15 35 30 52 35 55 40 40

30 26 25 42 38 40 32 54 50 43

4

.

:

1=r

Lecture example 5 , (x ) (y)

.

1 2 3 4 5 6 7 8 9 10

(x ) 27 22 15 35 30 52 35 55 40 40

(y) 30 26 25 42 38 40 32 54 50 43

F

.

F 84+, y x 0.658 14.9y x= +

x y 1.07 5.60x y= .


3/8

5

;

:

() x

y x .

() F ,

y x y x.

x y,

x y.

E

:

() r 1 ( ).

() .

Using previous Lecture example 5

()

50 . G .

() G ()

60 .

() y

x y x .

50x = , = 0.658 (50) + 14.9 = 47.8 47.8 48 .

50 x

0.839r = 1 ,

x y. y

.

() 60

15, 55 (),

.

Lecture example 6A

5 .


4/8

, x (

)

0 5 10 15 20 25 30 35 40

, y

( C )0.4 1.5 3.4 5.5 7.7 9.7 11.7 13.5 15.4

E y x x

y

9P

PC.

F , x y

5 , y x. ,

y x .

6

Using previous Lecture example 5 .

: F 10 ,

6.6 . y ( )0,15 :

, 15 . , 0

x , .

7

,

Tutorial Example 4 10 () ()

:2 21782, 1483, 318086, 220257, 264582x y x y xy= = = = =

F .

178.2x = ; 148.3y =

( )2

2

311.40.58358

533.6

x yxy

nbx

xn

= = =

;

( ) 0.584 44.3y y b x x y x = = +

1

( )2

2

311.40.94910

328.1

x yxy

ndy

yn

= = =


5/8

( ) 0.949 37.4x x d y y x y = = +

22

2 20.7442310.94910

0.58358

r bd

rd

b

=

= = =

( ) 0.949 37.4x x d y y x y = = +

8

: x

y

Tutorial Example 8

A

.

7 151 7, 20

10 10 6y x x y= + = +

.

F .

7 151

10 10y x= + (1)

720

6x y= + (2)

(1) & (2) 13, 6x y= =

88

9413 10

8

x xx x

n

+= = = =

88

40 6 88

y yy yn

+= = = =

( )10,8 .

10 11 12 11 17 14 19

9 8 7 6 5 4 1

9

:

b

y ax=

( )

ln ln lny a b x= +

.., .

ebxy a=

(

)

ln lny a bx= +

..,

.


6/8

y ax b= +

2y ax b= +

..,2y

.

1y

ax b=

+

1

ax by = +

..,1

y

.

10

(A)

,

(

),

(B)

(

r

1).

(A)

Tutorial Example 7

, .

22.5 25.0 28.0 30.5 38.0 40.5 42.5 48.0 54.5 55.0 70.0

44.0 42.0 33.5 28.0 18.0 13.6 15.0 10.3 9.0 6.3 4.0

()

.

() , ,

:

()b

x at= > 0 < 0

()2

x a bt= + > 0 < 0.

() (: ,)

() () , 0, 0bx at a b= > < : G .

()2 , 0, 0x a bt a b= + > < : G .

F , ,

, 0, 0bx at a b= > <

.

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50

t

x


7/8

(B)

Lecture example 8

, , ,

.

4.5 5.2 6.1 6.5 7.0 7.3 8.5 9.5

1.14 1.20 1.26 1.29 1.33 1.35 1.42 1.48

, ,

:

()b

t ay= () t a by= +

ln ln lnb

t ay t a b y= = +

bt ay= , lny ln t .

t a by= + , y t .

84+, r lny ln t 0.99953

r y t 0.9976. r y t

1. b

t ay=

t a by= + .

11

Continue using Tutorial Example 7 from above.() F ,

. E .

ln ln lnb

x at x a b t= = +

G lnx ln t GC,

.

ln 4.9134 136.1 136a a= = ; 0.453b = 12

,

2ie ,


8/8

.

ie ( ) = y y

),( ii yx .

,

2

ie ,

ie ( ) = x x

),( ii yx .

correlation and regression skill set

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