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hp calculators
HP 30S Statistics – Linear Regression
=
( ' x
) .
Answer:
10
5
Example 4: The previous examples are based on the regression of the final concentration (y) on the amount of
chemical added (x). Would the last result obtained be equal to
of x on y?
Solution:
The most likely answer is no. y is the dependent variable and x is the independent variable. Their roles
cannot be interchanged. If we interchange x and y, we change our experiment, the results of which may
well be meaningless. Let's see what happens, by swapping the given data, and then we'll find
Press aand reenter the data in the following order:
3?2???5?6?5?3???8?6?8.5?9?
( ' y
To find
10
b@@@@@@@@ (to select
Answer:
According to the new regression, the predicted value is 9.88 grams. The regression line is now
=
−
x
.
0
38
is not the same as before (
Example 5: By polling fifty people, a survey taker obtained the following data:
∑
=
x
3333
i
Judging by the correlation coefficient , is there a linear relation between x and y?
Solution:
r can be calculated using the formula given on page 2:
Let's enter it into the entry line by pressing:
r30549.75-333*459.9/50s
/pr231933-3333q/50sr43
08.57-459.9q/50and finally y.
Answer:
r = –0.12, so we can assume there's no linear relation at all.
hp calculators
= )
( x ˆ
.
10.89 grams.
10
5
) .
press:
5
+
.
y
(where x is still the amount of chemical added and y is the concentration), which
0
98
=
−
x
.
1
44
∑
∑
=
y
,
,
459.
9
i
30549
=
r
⎛
⎜
231933
⎜
⎝
' y
) y10.5y
+
.
y
)
1
18
∑
2
=
x
y
,
231933
i
⋅
.
3333
459
9
−
.
75
50
⎞
⎛
2
3333
⎟
⎜
−
−
.
4308
57
⎟
⎜
50
⎠
⎝
- 4 -
( ' y
) .
if we were studying the regression
10
5
∑
2
=
.
and
4308
57
i
⎞
.
2
459
9
⎟
⎟
50
⎠
HP 30S Statistics – Linear Regression - Version 1.0
( ' y
) .
.
10
5
=
x
y
30549.
75
i
i
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