Page 18-54
Example 1 -- For the following (x,y) data, determine the 95% confidence
interval for the slope B and the intercept A
x
2.0 2.5 3.0 3.5 4.0
y
5.5 7.2 9.4 10.0
12.2
Enter the (x,y) data in columns 1 and 2 of
Σ
DAT, respectively. A scatterplot of
the data shows a good linear trend:
Use the
Fit Data..
option in the
‚Ù
menu, to get:
3: '-.86 + 3.24*X'
2: Correlation: 0.989720229749
1: Covariance: 2.025
These results are interpreted as a = -0.86, b = 3.24, r
xy
= 0.989720229749,
and s
xy
= 2.025. The correlation coefficient is close enough to 1.0 to confirm
the linear trend observed in the graph.
From the
Single-var…
option of the
‚Ù
menu we find:
x = 3, s
x
=
0.790569415042,
y = 8.86, s
y
= 2.58804945857.
Next, with n = 5, calculate
5
.
2
42
7905694150
.
0
)
1
5
(
)
1
(
2
2
=
⋅
−
=
⋅
−
=
x
xx
s
n
S
=
−
⋅
⋅
−
−
=
)
1
(
2
1
2
2
2
xy
y
e
r
s
n
n
s
...
1826
.
0
)
...
9897
.
0
1
(
...
5880
.
2
2
5
1
5
2
2
=
−
⋅
⋅
−
−
