ACEM_linearregression
                     Department of ComApravali Cuollege ofand Managet Engineering ment, r Science 
Faridabad 
& Engineering
(July – Dec 2020)
09/15/2020 1






Introduction to  Regression 
Analysis
 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
Slide-8
Simple Linear Regression  Model
 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
Slide-9
Types of Relationships
Linear relationships Curvilinear relationships
Y Y
X X
Y Y
X X
Slide-10
Types of Relationships
(continued)
Strong relationships Weak relationships
Y Y
X X
Y Y
X X
Slide-11
Types of Relationships
(continued)
No relationship
Y
X
Y
X
Slide-12
Simple Linear Regression  Model
Population Random 
Population  Independent 
 Slope   Error  
Y  Variable
Coefficient term
Dependent intercept
 Variable
Y i  β0 εi
β1Xi Random Error 
 component
Linear component
Slide-13
Simple Linear Regression  
Model
(continued)
Y Yi  β0 β1Xi  
Observed Value εi
 of Y for Xi
εi Slope = β1
Predicted Value Random Error
of Y for Xi   for this X i value
Intercept = β0
Xi X
Slide-14
Simple Linear Regression  
Equation (Prediction Line)
The simple linear regression equation provides an 
 estimate of the population regression line
Estimated
(or predicted) Estimate of  Estimate of the  
 Y value for the regression regression slope
observation i
intercept
Value of X for 
 observation i
Yˆi b0 
The indivibdual Xrandom error terms ei have a mean of zero1 i
Slide-15
Sample Data for House Price  
Model
House Price in $1000s Square Feet 
 (Y)  (X)
245 1400
312 1600
279 1700
308 1875
199 1100
219 1550
405 2350
324 2450
319 1425
255 1700
Slide-16
Regression Using Excel
 Tools / Data Analysis / Regression
Slide-17
Assumptions of Regression
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
Department of Statistics, ITS Surabaya Slide-18
Pitfalls of Regression Analysis
 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
Department of Statistics, ITS Surabaya Slide-19
    
Aravali College of Engineering And Management
Jasana, Tigoan Road, Neharpar, Faridabad, Delhi NCR
Toll Free Number : 91- 8527538785
Website : www.acem.edu.in
09/15/2020 20