# Additional Equations For Linear Regression; Prediction Error - HP F2226A - 48GII Graphic Calculator User Manual

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## Additional equations for linear regression

The summary statistics such as Σx, Σx
following quantities:
n
S
(
x
xx
i
=
1
n
S
(
y
y
i
i
=
1
n
S
(
x
x
)(
y
xy
i
i
i
=
1
From which it follows that the standard deviations of x and y, and the
covariance of x,y are given, respectively, by
s
=
x
n
Also, the sample correlation coefficient is
In terms of x, y, S
, S
xx

### Prediction error

The regression curve of Y on x is defined as Y = Α + Β⋅x + ε. If we have a set
of n data points (x
, y
), then we can write Y
i
i
where Y
= independent, normally distributed random variables with mean
i
(Α + Β⋅x
) and the common variance σ
i
random variables with mean zero and the common variance σ
2
, etc., can be used to define the
2
2
x
)
(
n
) 1
s
i
x
2
2
y
)
(
n
) 1
s
y
i
2
y
)
(
n
) 1
s
xy
S
S
yy
s
=
xx
,
, and
y
1
n
1
r
xy
, and S
, the solution to the normal equations is:
yy
xy
S
xy
a
=
y
x b
b
=
,
S
xx
i
2
; ε
= independent, normally distributed
i
n
1
n
2
x
x
i
i
n
i
=
1
i
=
1
2
n
1
n
2
y
y
i
i
n
=
1
i
=
1
n
1
n
x
y
x
i
i
i
n
i
=
1
i
=
1
i
S
yx
s
=
xy
n
1
S
xy
.
S
S
xx
yy
s
xy
=
2
s
x
= Α + Β⋅x
+ ε
, (i = 1,2,...,n),
i
I
2
.
Page 18-51
n
y
i
=
1

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