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

Graphing calculator.

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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