This document provides an overview of regression and correlation analysis. It discusses simple linear regression, including defining the dependent and independent variables, the linear regression model and equation, and assumptions of regression like linearity and equal variance. Graphs are presented showing different types of relationships between variables. The document concludes with examples of using Excel to analyze a simple linear regression problem to predict house prices based on square footage.

1. Data Analytics for Beginners
Predictive Analytics
September 5-9, 2022
Dr. Roma Mitra Debnath
Associate Professor (Applied Statistics)
Indian Instituteof Public Administration
Email: roma.mitra@gmail.com
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2. Regression and Correlation
• Regression analysis is the process of
constructing a mathematical model that can
be used to predict or determine one variable
by another variable.
• Correlation is a measure of the degree of
relatedness of two variables.
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3. Roma Mitra IIPA Chap 12-3
• Only one independentvariable, X
• Relationship between X and Y is described
by a linear function
• Changes in Y are assumed to be caused by
changes in X
Regression Analysis
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4. Regression Analysis
• ForecastingTool
• Assumes Causal Relation between dependent(DV) and
independentvariable (IV)
• Linear/non-linearRelation
• Select a model based on relation
 Causal::
 Education (IV) reduces Poverty (DV)
• Government expenditureon health Infant mortality
rate
• Efficiency of Government depends on Governance
• Corporate social responsibilityand financial
performance of the organization
• …
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5. Simple Regression Analysis
• bivariate (two variables) linear regression --
the most elementary regression model
–dependent variable, the variable to be
predicted, usually called Y
–independent variable, the predictor or
explanatory variable, usually called X
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6. i
i
1
0
i ε
X
β
β
Y 


Linear component
Simple Linear Regression Model
Population
Y intercept
Population
Slope
Coefficient
Random
Error
term
Dependent
Variable
Independent
Variable
Random Error
component
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7. i
1
0
i X
b
b
Ŷ 

The simple linear regressionequation provides an estimateof the
population regression line
Simple Linear Regression Equation (Prediction Line)
Estimate of the
regression
intercept
Estimate of the
regression slope
Estimated (or
predicted) Y
value for
observation i
Value of X for
observation i
The individual random error terms ei have a mean of zero
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8. Types of Relationships
Y
X
Y
X
Y
Y
X
X
Linear relationships Curvilinear relationships
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9. Types of Relationships
Y
X
Y
X
Y
Y
X
X
Strong relationships Weak relationships
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10. Types of Relationships
Y
X
Y
X
No relationship
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11. Assumptions of Regression
• Linearity
– The underlying relationship between X and Y is linear
• Independence of Errors
– Error values are statistically independent
• Normality of Error
– Error values (ε) are normally distributed for any given value of X
• Equal Variance (Homoscedasticity)
– The probability distribution of the errors has constant variance
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12. Scatter Diagram
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0
200
400
600
800
1000
1200
0 10 20 30 40 50 60 70
Sales
Sales

13. Excel Output
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SUMMARY OUTPUT
Regression Statistics
Multiple R 0.947662558
R Square 0.898064324
Adjusted R Square 0.881075045
Standard Error 108.7575267
Observations 8
ANOVA
df SS MS F Significance F
Regression 1 625246.3024 625246.3 52.86065 0.000344486
Residual 6 70969.19765 11828.2
Total 7 696215.5
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept -46.29180548 64.89096049 -0.71338 0.502402 -205.0742654 112.4906545
Advertising 15.23977165 2.096101053 7.270533 0.000344 10.11079715 20.36874615

14. Sample Data for House Price
Model : Quiz
House Price in $1000s
(Y)
Square Feet
(X)
245 1400
312 1600
279 1700
308 1875
199 1100
219 1550
405 2350
324 2450
319 1425
255 1700
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15. • The duration of QUIZ is 20 minutes. There are 20
questions.
• Filling up the Feedback form is mandatory.
• Please use the link ( shared on Email, Whatsapp
and Chat box) and fill it only once.
• Certificates will be uploaded on IIPA Portal on
Tuesday (September 13, 2022) . Please check in
the evening (Indian Standard Time).
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