This is the comprehensive PPT on regression analysis. It covers the methods of identifying IV, DV, mediator, and moderators. How to interpreter using the parameters, R square, T-test. differentiation between linear and non-lienar regression

1. Regression Model: Types
and interpretation of
results
Part-II
Dr. Rajeev Kumar
M.S.W.,(TISS, Mumbai), M.Phil., (CIP, Ranchi) UGC-JRF.,
Ph.D. (IIT Kharagpur)
rajeev.iit.78@gmail.com
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2. So far as we discussed
What is regression?
Why we use ? And what is the utility of regression in our daily life?
The relation of regression with correlation and how it is different?
Understanding of bidirectional, unidirectional, and causation.
Understanding of independent and dependent variables and their
synonymous used in scientific literature.
Small example of graphic-scatter plot and equation of regression
The meaning of residuals in equation and its relevance in practical life
Now we will move on further discussion
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3. Broad types of regression
models
Regression
model
Linear mode
Non-linear
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4. Non-linear and linear
regression
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5. Difference between linear and
exponential curve
The major distinction between linear and exponential functions is the
rate of their growth. Its rate of change is much higher than that of a
linear function.
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7. How mediator works?
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8. Example-1: Mediator variable
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9. How does moderator works?
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10. Example of moderator variable
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12. Classification of Linear and non-linear regression
models
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Linear regression
model
(IV and DV both
are continuous
variable)
Complex linear
regression
Simple Linear
regression
(1 IV and 1 DV)
With mediator
or Moderator
variables
Multiple
regression
model
Multivariate
regression
model
DV =1
IV =more than
one
DV= more than
one
IV= one or more
than one
Non-Linear
Regression model
(Either IV or DV is
categorical
variable
Logistic
regression
DV or IV is
categorical
Binomial
IV= more than
one
DV=1
Multinomial
DV and IV=
more than one

13. What are statistical models?
A statistical model is a mathematical
model that embodies a set
of statistical assumptions concerning
the generation of sample data (and
similar data from a larger population).
A statistical model represents, often in
considerably idealized form, the data-
generating process.
A statistical model is usually specified
as a mathematical relationship
between one or more random
variables and other non-random
variables. As such, a statistical model
is "a formal representation of a theory
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14. Example-1: Simple linear
regression
Liver related diseases were found associated with high consumption of
alcohol.
Y (liver related disease) = β0 ( Liver disease without using alcohol)+ β1
(alcohol use) + C (residual: other factors)
XXxxxxxxxxxxxxxxxx X (IV) = Alcohol consumption
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Y (DV)= liver disease

15. .
Example-2: Multiple Linear Regression
In Kota several students preparing for IIT-JEE committed suicide. It was
further observed that parental pressure, previous unsuccessful attempts,
and mental stress were the major causes behind the suicides. Make
conceptual diagramand equation
Y= X0 β0 + X1 β1 + X2 β2+ X3 β3+ C
X0 β0 = Number of suicide already occurred,
when these three factors
are not there
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Y=Suicide
IV1=Parental
pressure
IV2=Unsuccessful
attempt
IV3=Mental
stress
Y (suicide)= Dependent variable
X1 (parental pressure) = IV1
(independent variable)
X2 (Unsuccessful attempt)= IV2
X3 (Mental stress) = IV3

16. Example-3:
1. Now identify DVs and IVs.
2. Present in equation and conceptual model.
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Example-3: Multivariate regression
Equation and conceptual diagram or conceptual model
DV1= Throat cancer (Y1)
DV2= Lung cancer (Y2)
DV3= Mouth cancer (Y3)
IV= Cigarate smoking (X1)
X0= When there is no Cigarate smoking
C= Residuals (other factors of cancer)
Y1+ Y2 +Y3 = X0β0+ X1 β1+C
Y1(throat cancer)+ Y2 (lung cancer)+Y3 (Mouth cancer)= X0β0+ X1
β1 (Cigarate smoking)+C
Throat cancer
Lung cancer
Mouth cancer
Cigarate
smoking

18. Example 4 : Complex Linear Regression with mediator
Prolonged cancer causes deaths and death of family member poses
financial burden on the family. (identify, dependent, independent and
mediator variable)
IV (Prolonged cancer), MeV (Mediator Variable: Death), DV (Financial Burden on
family)
H1: Y1 (Death) = X0β0+ X1 β1 (Prolonged cancer)+ C1
H2: Y2 (Financial Burden) = X0 β0+ X2 β2 (Death)+ C2
H3: Y3 (Financial Burden) =X0 β0+ X3 β3 (Prolonged cancer)+C3
Note (H1, H2, H3 are Hypotheses respectively)
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MeV= Death IV= Prolonged
cancer
DV= Financial burden on
family
Death
FB Cancer

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Example-5: Study hours, IQ level, quality of teaching, and
educational facilities determine the grades of students.
Further in their life, these grades determine job placement
and salary packages. Identify various variables and draw
conceptual diagram
Grades
Study
Hours
IQ
Placement
Educational
facilities
Teaching
Quality
Salary
Package
Professional
network
Place of stay

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Example-5: Identifications of variables
X1 (Study hours)= IV1 (IV= Independent variable)
X2 (IQ)= IV2
Grades = MeV (Mediator variable)
Placement= DV1
Salary package =DV2 (DV= Dependent variable)
Educational facilities = MoV1 (MoV= Moderator
variable)
Professional Network = MoV2
Place of stay= MoV3
Teaching Quality = MoV4

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Example-6:A complexconceptualdiagram
KumarR.(2020)DowrySystem:UnequalizingGenderEquality.In:LealFilhoW.,AzulA., BrandliL.,
ÖzuyarP.,WallT.(eds)GenderEquality.EncyclopediaoftheUNSustainableDevelopmentGoals.
Springer,Cham.https://doi.org/10.1007/978-3-319-70060-1_21-1

22. PART-III
How to interpret the results of
regression model?
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The values and indicators requires
for interpretation of regression
results
Model
fitness
value
Standardized
β
SE
(Standard
error of β
T value P value R²
IV→DV

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Standardized Beta (β)
Therefore, Unstandardized (β1) is the value of 1 unit increase or
decrease in X (Independent variable) and subsequently expected to
increase 1 unit in dependent variable (Y). We can calculate the
standardized beta according to given formula
Standardized beta also measure the effect size. (below .30= low
effect size) ( between .30-.50= moderate effect size) and above .50
will be high effect size. It means higher the value of standardized
beta gives the stronger result.
Sx= Standard deviation of X (IV)
Sy= Standard deviation of Y (DV)
βz = Standardized beta
βi = Unstandardized beta

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SE= Standardized Error of beta
SE is also one of the measurement of dispersion.
The formula of SE is given below.
It means, lower the SD (standard deviation) less
the SE. If sample size increase SE will also
decrease. It means, there will be less error in data
and less variability in the data.
The less value of SE is considered good.

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T test in regression analysis
As we know T test measures the differences of two means. In regression
analysis T test measures the difference between Beta (observed) – Beta
(expected). Higher the T test, stronger the result of regression.
We learnt that the Value of T is significant, if ≥ 1.96.

29. All about R² in Regression
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30. How does R² reflects in graph?
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31. What does R² tells?
The value of R² tells how much independent variable
explains the dependent variable.
If the value of R² = .36, it means (.36x100= 36), the X is
explains the Y only 36%, rest 64% are other factors.
Suppose.
Liver related diseases were found associated with high
consumption of alcohol.
Y (liver related disease) = β0 ( Liver disease without using
alcohol)+ β1 (alcohol use) + C (residual: other factors)
Suppose, here R²=.68 , it means (.68x100=68) alcohol
consumption cause liver disease in 68% cases. Rest 32% (
100-68=32) are other factors causing liver diseases.

32. R² : Fitness of Model
R² indicates the fitness of overall model. How the variables and data
are fitted into the proposed model.
Higher the R² better fitness of the model. Low R² indicates the
weakness of model. In given example R² is 0.06, it means, it explains
the outcome variable only 6%
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33. Example-7: A relation between HIV/AIDS and
percapita incomes of states
Kumar, R., Suar, D., & Singh, S. K. (2017). Regional differences, socio-
demographics, and hidden population of HIV/AIDS in India. AIDS
care, 29(2), 204-208. Available at:
https://www.tandfonline.com/doi/abs/10.1080/09540121.2016.121160
5
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Methodology and result of study
A panel data regression was run using LIMDEP software to examine
the relationship of new infection of HIV/AIDS for the period 2002–
2012 with per capita income of 32 Indian states and union territories
of the same period. The data for the period 2002–2012 were obtained
from the Reserve Bank of India (2012) and all the per capita income
was with reference to the base year 2004.
IV= Per-capita income of states
DV= New rate of HIV infections in the states
Hausman
value for
the
model
P
value
of the
model
Standardized
Beta (β)
SE
(Standardized
Error) of beta
T value P
value
R²
(χ2 (1) =
6.76
p <
.009)
−.369 .059 6.49 0.001 .93

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Kumar,R., Suar, D., & Singh, S. K. (2017).Regional differences, socio-demographics, and
hidden populationof HIV/AIDSin India.AIDScare, 29(2), 204-208. Availableat:
https://www.tandfonline.com/doi/abs/10.1080/09540121.2016.1211605
IV (Per-capita income of states), DV(New rate of HIV infections in the states)
Y (New rate of HIV infections)= X0β0+ X1 β1 (Per-capita income of states) + C
The negative value of beta indicated that there is negative or reverse relation
between percapita income and new rate of HIV infection. Means, if percapita
income will increase, there will be reduction in new HIV cases. The value of
standardized beta (-.369) is above .300, so it give the moderate effect size, there
is moderate impact. R² indicates that percapita income predict new HIV
infection 93%, rest 7% are other causes of HIV infections in group C states
(Jharkhand, West Bengal, Odisha etc.,)
Hausman
value for
the
model
P
value
of the
model
Standardized
Beta (β)
SE
(Standardized
Error) of beta
T value P
value
R²
(χ2 (1) =
6.76
p <
.009)
−.369 .059 6.49 0.001 .93

36. Kumar,R., Suar,D.,& Singh,S. K. (2017).Regional differences,socio-
demographics, and hiddenpopulation of HIV/AIDSin India. AIDScare,29(2),
204-208. Availableat:
https://www.tandfonline.com/doi/abs/10.1080/09540121.2016.1211605
The inverse relationship between per capita income
and HIV/AIDS incidence reaffirms that AIDS is a disease
of poverty (Guillies, Tolley, & Wolstenholme, 1996).
The states and union territories of category A and B with
higher per capita income spend more money on the
prevention and treatment of HIV/AIDS compared to states
of category C with lower per capita income (Ministry of
Statistics and Programme Implementation, 2011).
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37. Summary of the session
We learnt the difference between linear and non-linear regression.
There was in-depth description on independent, dependent, mediator,
and moderator variables. Those were explained using examples.
The model fitness, T value, R square, standardized beta all were
explained.
At the last, we applied all the learning in understanding through a
regression result published in an international journal.
However, the logistic and other non-linear regressions were skipped
for time being.
With this session, Quantitative statistics is over. From the next session,
we will learn Qualitative research methods.
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38. Thanks for showing your
interest in learning
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