least-squares-method[1].pdf
TRANSCRIPT
-
_______________________________________
3 4 5 6 7 8 9
1214
1618
20
x
y
-
2
2 (Independent variable) (Dependent variable)
1.
Y = a+bX Y X a Y b Y
2. (Scatter Diagram) 2
X Y X Y
X Y Y Y
X X
1 2 1 2 X Y
-
3
Y Y
X X 3 4
3 4 X Y
Y Y
X X
5 6
5 6 X Y
Y
X 7
7 X Y
-
4
3. (Least Squares Method) a b a b
Y = a+bX (Least squares method)
(Normal
equations) n n
i ii=1 i=1
n n n2
i i i ii=1 i=1 i=1
y = an+b x (1)
x y = a x +b x (2)
i i =
1,2,3,,n a, b i i(x ,y )
-
5
6
(X) 1 2 3 2 1 3 (Y) () 4 7 10 8 3 10
. . . 4
.
1.0 1.5 2.0 2.5 3.0
34
56
78
910
x
y
***************************
. Y = a+bX
n n
i ii=1 i=1
n n n2
i i i ii=1 i=1 i=1
y = an+b x (1)
x y = a x +b x (2)
(1) (2)
-
6
8
ii 1
x 12=
= 8
ii 1
y 42=
= 8
i ii 1
x y 97=
= 8
2i
i 1x 2
=8=
42 = 6a+12b (1)97 = 12a+28b (2)
a = 0.50 b = 3.25
Y=0.50+3.25X
*************************
. 4 (x=4)
Y=0 .50+3.25(4) = 13.5 () = 1,350
*************************
-
7
2541- 2551
1 1. x y
x -3 -1 0 1 3 y 0 a a+3 a+4 a+6
a x y 1.55 x = 4 y 1. 8.7 2. 10.8 3. 11.2 4. 12.8
2. y = mx + c (y) (x) 5
28 = 5c + 10m .......(1) 67 = 10c + 30m .......(2)
. x = 5 y = 8.9 . x = 5.6 1.
2. 3. 4.
3. ( x) GPA ( y) 0.02 Y 2.7
-
8
. 10 0.2
. 3 15
1. 2. 3. 4.
4. (y) () (x) () 130 2545
y = 8-0.5x 1-4 2545 4, 2, 8, 10
1. 2.5 2. 10 3. 17.5 4. 22.5 5. (y) ()
(x) () 8
8
ii 1
x 4=
= 8 1 8
ii 1
y 4=
= 8
i ii 1
x y 286=
=8
2i
i 1x 34
== 8
. 6 51,250
. 1 11,250
1. 2.
-
9
3. 4.
****************************************************************** 2 1. (x) (y)
y = 200 + 0.85x 1,000
2.
( y) ( x) y = a + 0.75x x = 40 y = 60 x = 60
3. () (y) ..2538-2545 x .. 2538 2539 2540 2541 2542 2543 2544 2545
x -7 -5 -3 -1 1 3 5 7 ( 2 ) y = 0.54x + 38.85 ..2547
4. ..2537 ..2546 (y) () (x) ..2541 2542 x = -1 1
y = 192 + cx
-
10
.. 2547 316.3 .. 2548
5. x y
8
ii 1
x 3=
= 2 8
ii 1
y 16=
=8
i ii 1
x y 65=
= 8
2i
i 1x 140
==
82i
i 1y 3
== 4
x = 8 y ()
. (2552). ADMISSIONS52 . : .
. (2551). .4-5-6. :
.
2 X Y X Y X Y Y Y Y