statistics for engineers

1. Regression

2. Introduction of Regression;
Cause and effect relationships,
Simple linear regression,
Logistic regression, and
Multiple regression

3. Regression analysis is a set of statistical
methods used for the estimation of
relationships between a dependent variable and
one or more independent variables. It can be
utilized to assess the strength of the
relationship between variables and for modeling
the future relationship between them
Regression

5.  Regression analysis includes several variations,
such as linear, multiple linear, and nonlinear.
The most common models are simple linear
and multiple linear. Nonlinear regression
analysis is commonly used for more
complicated data sets in which the dependent
and independent variables show a nonlinear
relationship.
 Regression analysis offers numerous
applications in various disciplines,
including finance.

6. Cause and effect is
the relationship between two
things or events where one event
caused another event, or several
events, to happen.
Cause and Effect Relationship

7. For example: Smoking causes lung
cancer, is not about an particular smoker
but states a special relationship exists
between the property of smoking and the
property of getting lung cancer.

8. Simple linear regression is a model that
assesses the relationship between a
dependent variable and an independent
variable. The simple linear model is
expressed using the following equation:
Y = a + bX + ϵ
Simple linear regression

9. Where:
 Y – Dependent variable
 X – Independent (explanatory) variable
 a – Intercept
 b – Slope
 ϵ – Residual (error)

11. Find the correlation between age and blood
pressure using simple and Spearman's correlation
coefficients, and comment.
Find the regression analysis?
Solve through SPSS

12. Logistic regression is the
appropriate regression analysis to conduct
when the dependent variable is dichotomous
(binary). Logistic regression is used to describe
data and to explain the relationship between
one dependent binary variable and one or more
nominal, ordinal, interval or ratio-level
independent variables.
Logistic regression

13.  The dependent variable should be dichotomous in nature
(e.g., presence vs. absent).
 There should be no outliers in the data, which can be
assessed by converting the continuous predictors to
standardized scores, and removing values below -3.29 or
greater than 3.29.
 There should be no high correlations (multicollinearity)
among the predictors. This can be assessed by a
correlation matrix among the predictors. Tabachnick and
Fidell (2013) suggest that as long correlation coefficients
among independent variables are less than 0.90 the
assumption is met.
Binary Logistic Regression Major
Assumptions

14. Logistic regression (1)
Age CD Age CD Age CD
22 0 40 0 54 0
23 0 41 1 55 1
24 0 46 0 58 1
27 0 47 0 60 1
28 0 48 0 60 0
30 0 49 1 62 1
30 0 49 0 65 1
32 0 50 1 67 1
33 0 51 0 71 1
35 1 51 1 77 1
38 0 52 0 81 1
Table 2 Age and signs of coronary heart disease (CD)

15. Multiple regression is an extension of
simple linear regression. It is used when
we want to predict the value of a variable
based on the value of two or more other
variables. The variable we want to predict
is called the dependent variable (or
sometimes, the outcome, target or
criterion variable).
Multiple Regression

17. Simple linear regression is a function that
allows an analyst or statistician to make
predictions about one variable based on the
information that is known about another
variable. Linear regression can only be used
when one has two continuous variables—an
independent variable and a dependent
variable. The independent variable is the
parameter that is used to calculate the
dependent variable or outcome. A multiple
regression model extends to several
explanatory variables.