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Regression Analysis

Regression analysis is covered in the MiC Quality course in Advanced Statistics.

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Least Squares

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

Linear regression uses a linear regression model:

The parameters can be found from:

Where:



Logistics Regression

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.

Logit Regression

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:

Probit Regression

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

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.

Regression Equation

The equation that shows the relation between 'X' and 'Y' and that is created by regression analysis.

Residual 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)..

Scatter Plot

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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