Casio fx 991MS User Guide - Page 33

Logarithmic, Exponential, Power, and Inverse, Regression, Quadratic Regression

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Temperature at 1000 hPa = 4.642857143 1000 A X r r r 1 = Coefficient of Determination = 0.965517241 A X r r 3 K = Sample Covariance = 35 E A U r 3 , A U 3 - A X 1 - A X r 1 F \ E A U 3 , 1 F = u Logarithmic, Exponential, Power, and Inverse Regression • Use the same key operations as linear regression to recall results for these types of regression. • The following shows the regression formulas for each type of regression. Logarithmic Regression y ҃ A ѿ B ؒ In x Exponential Regression y ҃ A ؒ eB·x (In y ҃ In A + Bx) Power Regression y ҃ A ؒ xB (In y ҃ In A + B In x) Inverse Regression y ҃ A ѿ B ؒ 1/x u Quadratic Regression • The regression formula for quadratic regression is: y = A + Bx + Cx2. • Example: xi yi Perform quadratic regression to de- 29 1.6 termine the regression formula terms for the data nearby. Next, use the 50 23.5 regression formula to estimate the 74 38.0 values for n (estimated value of y) for 103 46.4 xi = 16 and m (estimated value of x) 118 48.0 for yi = 20. In the REG Mode: r 3(Quad) A B 1 (Scl) = (Stat clear) 29 P 1.6 S 50 P 23.5 S 74 P 38.0 S 103 P 46.4 S 118 P 48.0 S 31

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31
Temperature at 1000 hPa =
4.642857143
1000
A
X
r
r
r
1
=
Coefficient of Determination =
0.965517241
A
X
r
r
3
K
=
Sample Covariance =
35
E
A
U
r
3
,
A
U
3
-
A
X
1
-
A
X
r
1
F
\
E
A
U
3
,
1
F
=
u
Logarithmic, Exponential, Power, and Inverse
Regression
Use the same key operations as linear regression to re-
call results for these types of regression.
• The following shows the regression formulas for each
type of regression.
Logarithmic Regression
y
²
A
³
B
±
In
x
Exponential Regression
y
²
A
±
e
B
·
x
(In
y
²
In A + B
x
)
Power Regression
y
²
A
±
x
B
(In
y
²
In A + BIn
x
)
Inverse Regression
y
²
A
³
B
±
1
/
x
u
Quadratic Regression
The regression formula for quadratic regression is:
y
= A + B
x
+ C
x
2
.
In the REG Mode:
r
3
(Quad)
A
B
1
(Scl)
=
(Stat clear)
29
P
1.6
S
50
P
23.5
S
74
P
38.0
S
103
P
46.4
S
118
P
48.0
S
Example:
Perform quadratic regression to de-
termine the regression formula terms
for the data nearby. Next, use the
regression formula to estimate the
values for
n
(estimated value of
y
) for
x
i
= 16 and
m
(estimated value of
x
)
for
y
i
= 20.
x
i
y
i
29
1.6
50
23.5
74
38.0
103
46.4
118
48.0