Prediction Error; Confidence Intervals And Hypothesis Testing In Linear Regression - HP 50g User Manual

From which it follows that the standard deviations of x and y, and the
covariance of x,y are given, respectively, by
Also, the sample correlation coefficient is
In terms of x, y, S

Prediction error

The regression curve of Y on x is defined as Y =
of n data points (x
where Y = independent, normally distributed random variables with mean (
i
x ) and the common variance
i
random variables with mean zero and the common variance
Let y = actual data value,
i
Then, the prediction error is: e
An estimate of
1 n
∑
2
s [
e
n 2
i 1

Confidence intervals and hypothesis testing in linear regression

Here are some concepts and equations related to statistical inference for linear
regression:
S
s
xx
x
n 1
,
, S , and S
xx yy
a y
, y ), then we can write Y
i i
^
y = a + b x
i
i
2
is the, so-called, standard error of the estimate,
y ( a bx )]
i i
S
yy
s
y
n 1
, and
r
xy
, the solution to the normal equations is:
xy
S
xy
b
S
x b
xx
,
=
i
2
; = independent, normally distributed
i
= least-square prediction of the data.
i
^
= y - y = y - (a + b x
i i i
S ( S )
yy xy
2
n 2
S
yx
s
xy
n 1
S
xy
.
S S
xx yy
s
xy
2
s
x
+ x + . If we have a set
+ x + , (i = 1,2,...,n),
i I
2
.
).
i
2
/ S
n 1
xx
n 2
2 2
s 1 ( r )
y xy
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