Tor ,18-54 – HP 50g Graphing Calculator User Manual
Page 621
Page 18-54
a+b
⋅x+(t
n-2,
α /2
)
⋅s
e
⋅[1+(1/n)+(x
0
-
⎯x)
2
/S
xx
]
1/2
.
Procedure for inference statistics for linear regression using the
calculator
1) Enter (x,y) as columns of data in the statistical matrix
ΣDAT.
2) Produce a scatterplot for the appropriate columns of
ΣDAT, and use
appropriate H- and V-VIEWS to check linear trend.
3) Use ‚Ù˜˜
@@@OK@@@, to fit straight line, and get a, b, s
xy
(Covariance), and r
xy
(Correlation).
4) Use ‚Ù˜
@@@OK@@@, to obtain ⎯x, ⎯y, s
x
, s
y
. Column 1 will show the
statistics for x while column 2 will show the statistics for y.
5) Calculate
,
6) For either confidence intervals or two-tailed tests, obtain t
α/2
, with (1-
α)100% confidence, from t-distribution with ν = n -2.
7) For one- or two-tailed tests, find the value of t using the appropriate
equation for either
Α or Β. Reject the null hypothesis if
P-value
<
α.
8) For confidence intervals use the appropriate formulas as shown above.
Example 1 -- For the following (x,y) data, determine the 95% confidence
interval for the slope B and the intercept A
Enter the (x,y) data in columns 1 and 2 of
ΣDAT, 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
x
2.0
2.5
3.0
3.5
4.0
y
5.5
7.2
9.4
10.0
12.2
2
)
1
(
x
xx
s
n
S
⋅
−
=
)
1
(
2
1
2
2
2
xy
y
e
r
s
n
n
s
−
⋅
⋅
−
−
=