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The regression line through a set of points
is placed at the position that minimizes
the sum of the squares of the deviations
of the points from the line:
Linear regression uses a linear
regression model:
The parameters can be found
from:
Where:
Logistics Regression is used to create
the relationship between a probability and
a quantity. The mathematics are too complex
to describe, use Minitab or other statistical
package.
The type of question that it answers is:
At a call center that provides insurance
quotations callers are put on hold if an
operator is not available. Some callers
hang up. Data on calls showing where the
calls are abandoned:
| |
Wait |
Abandon |
|
Wait |
Abandon |
Wait |
Abandon |
|
| 1 |
10 |
N |
11 |
28 |
N |
21 |
60 |
N |
| 2 |
12 |
N |
12 |
29 |
N |
22 |
64 |
Y |
| 3 |
15 |
N |
13 |
35 |
Y |
23 |
68 |
Y |
| 4 |
18 |
N |
14 |
38 |
Y |
24 |
75 |
N |
| 5 |
18 |
N |
15 |
42 |
N |
25 |
80 |
N |
| 6 |
20 |
N |
16 |
43 |
N |
26 |
86 |
N |
| 7 |
22 |
N |
17 |
44 |
N |
27 |
89 |
Y |
| 8 |
26 |
N |
18 |
49 |
Y |
28 |
92 |
N |
| 9 |
27 |
Y |
19 |
50 |
N |
29 |
97 |
Y |
| 10 |
27 |
N |
20 |
52 |
Y |
30 |
100 |
Y |
(a real dataset would include many more
results).
Linear regression will give a regression
equation for the probability of a caller
abandoning the calls against wait time.
Logistics regression works by transforming
the binary data so that it becomes a linear
function.
In the example of the abandoned calls (see
the 'logistics' definition we need to find
a function where the probability of abandoning
the call 'P(x)' is a function of the wait
time 'x'. The logit function is:
| Multiple
Linear Regression |
|
A linear regression model that relates the
response to several inputs:
Logistics regression works
by transforming the binary data so that
it becomes a linear function.
In the example of the abandoned calls (see
the 'logistics' definition we need to find
a function where the probability of abandoning
the call 'P(x)' is a function of the wait
time 'x'. The probit function is the inverse
of the normal distribution:
Regression analysis involves finding the
line of best fit through a series of points.
The most common type is Simple Linear regression
that assumes a linear relationship between
a single input variable 'X' and the output
'Y'. Multiple Linear Regression gives a
linear equation that includes several input
variables.
Regression analysis should always be carried
out in conjunction with correlation.
The equation that shows the relation between
'X' and 'Y' and that is created by regression
analysis.
The difference between the
value obtained from the process and the
value predicted by the regression model.
Residual analysis is an important part of
the analysis in experimental design because,
for the results to be valid, the residuals
should conform to a normal distribution
(note that experimental design is a specialized
form of regression analysis)..
A scatter plot is a plot of
one variable against another. The 'y' (vertical)
axis is the dependent variable and the 'x'
axis is the independent variable:
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