Aravali College of Engineering and Management,

Faridabad

Department of Computer Science & Engineering

(July – Dec 2020)

05/22/2023 1

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 explainthe dependent variable

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

Types of Relationships

Slide-10

Y

Y

X

Y

Y

X

Linear relationships Curvilinear relationships

X X

Types of Relationships

Slide-11

Y

Y

X

Y

Y

X

Strong relationships Weak relationships

(continued)

X X

Types of Relationships

Slide-12

Y

X

Y

X

No relationship(continued)

Yi β0 β1Xi

Linear component

Simple Linear Regression Model

Slide-13

Population Yintercept

Population Slope Coefficient

Random Error term

Dependent Variable

Independent Variable

εi

Random Error component

Random Errorifor this X value

X

YObserved Value

of Y for Xi

Predicted Valueof Y for Xi

Yi β0 β1Xi εi

Xi

Slope = β1

Simple Linear Regression Model

(continued)

Slide-14

Intercept = β0

εi

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 forobservation i

Value of X for observation i

The individual random error terms ei have a mean of zero

Sample Data for House Price Model

Slide-16

House Price in $1000s (Y)

Square Feet (X)

245 1400312 1600279 1700308 1875199 1100219 1550405 2350324 2450319 1425255 1700

Regression Using Excel

Slide-17

Tools / Data Analysis / Regression

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

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

05/22/2023 20

Aravali College of Engineering And ManagementJasana, Tigoan Road, Neharpar, Faridabad, Delhi NCR

Toll Free Number : 91- 8527538785Website : www.acem.edu.in