Session on regression machine learning

1. Program Name : B.Tech CSE
Semester : 5th
Course Name: Machine Learning
Course Code:PEC-CS-D-501 (I)
Facilitator Name: Aastha

8. Introduction to Regression
Analysis
Slide-8
 Regression analysis is used to:
 Predict the value of a dependent variable based on the
value of at least one independent variable
 Explain the impact of changes in an independent
variable on the dependent variable
Dependent variable: the variable we wish to predict
or explain
Independent variable: the variable used to explain
the dependent variable

9. Simple Linear Regression Model
Slide-9
 Only one independent variable, X
 Relationship between X and Y is
described by a linear function
 Changes in Y are assumed to be caused
by changes in X

10. Types of Relationships
Slide-10
Y
Y
X
Y
Y
X
Linear relationships Curvilinear relationships
X X

11. Types of Relationships
Slide-11
Y
Y
X
Y
Y
X
Strong relationships Weak relationships
(continued)
X X

12. Types of Relationships
Slide-12
Y
X
Y
X
No relationship
(continued)

13. Yi  β0  β1Xi
Linear component
Simple Linear Regression Model
Slide-13
Population
Y intercept
Population
Slope
Coefficient
Random
Error
term
Dependent
Variable
Independent
Variable
 εi
Random Error
component

14. Random Error
ifor this X value
X
Y
Observed Value
of Y for Xi
Predicted Value
of Y for Xi
Yi  β0  β1Xi  εi
Xi
Slope = β1
Simple Linear Regression
Model
(continued)
Slide-14
Intercept = β0
εi

15. Yˆi  b0  b1Xi
The simple linear regression equation provides an
estimate of the population regression line
Simple Linear Regression
Equation (Prediction Line)
Slide-15
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

16. Sample Data for House Price
Model
Slide-16
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

17. Regression Using Excel
Slide-17
 Tools / Data Analysis / Regression

18. Assumptions of Regression
Department of Statistics, ITS Surabaya Slide-18
Use the acronym LINE:
 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

19. Pitfalls of Regression Analysis
Department of Statistics, ITS Surabaya Slide-19
 Lacking an awareness of the assumptions
underlying least-squares regression
 Not knowing how to evaluate the assumptions
 Not knowing the alternatives to least-squares
regression if a particular assumption is violated
 Using a regression model without knowledge of
the subject matter
 Extrapolating outside the relevant range

20. 9/10/2020 20
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