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HP 30S Statistics – Linear Regression
Example 6: An experimenter obtained the following data:
x
y
Determine whether there is a linear relation between x and y.
Solution:
First of all, let's clear any previous data: –1, select CLR-DATA and press y. This is not required
in this example: since the number of data items did not change, new data would overwrite the old ones.
But, it's a good habit to clear previous data before starting a new regression calculation. 2-VAR mode was
already set, so we can now enter the data as follows:
a300?11.1?420?12.2?450?12
.5?500?13?610?15.6?780?15.
8?800?16.1?
Let's now find the linear correlation coefficient: b<<<<<<.
Rounded to four decimal places, r = 0.9624. Even though it is quite close
to one, the experimenter expected a more conclusive result. By plotting a
scatter graph (figure 1), she notices that point (610, 15.6) is anomalous,
and is consequently removed from the data set. To do so, press:
a& seven times, and e(NB: not o).
The new correlation coefficient is displayed as above. i.e. by pressing b and then the left arrow key six
times.
Answer:
r = 0.9997, so there's strong evidence that the relation is linear. The regression line is
Example 7: Find the power curve
Solution:
This problem can be solved on your HP 30S by making the substitutions y' = ln y, and x' = ln x. The model
becomes:
and press y) and enter the new data as follows:
ah.5?h.47?h.75?h1.43?h1?
h3.15?h1.25?h5.75?h1.5?h
9.45?h2?h20.68?
In the STATVAR menu ( b), we find that a = 1.140696782 and b = 2.728608754. Since b = n and
a =
ln
m
, then n = 2.728608754, and
o—Hb<(eight times) yy
Answer:
Rounding to two decimal digits,
hp calculators
300
420
11.1
12.2
n
=
⋅
y
m
x
that best fits the following data:
x
0.50
0.75
y
0.47
1.43
=
+
⋅
' y
ln
m
n
' x
, which is a linear form. Clear the statistical data ( –1, select CLR-DATA
=
y
450
500
610
12.5
13
15.6
=
+
y
.
.
x
8
03
0
01
1.00
1.25
3.15
5.75
a
m =
e
, which can be calculated as follows:
.
⋅
2
73
.
x
3
13
- 5 -
780
800
15.8
16.1
1.50
2.00
9.45
20.68
HP 30S Statistics – Linear Regression - Version 1.0
Figure 1
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