Warda Iftikhar 13041519-014Department of Computer Science

RegressionPresented to: Miss Madiha

Investopedia defines Regression as ‘A statistical measure that attempts to determine the strength of the relationship between one dependent variable

(usually denoted by Y) and a series of other changing

variables (known as independent variables).’

Concept of Regression

It investigates the dependence of one variable, conventionally called the dependent variable, on one or more other variables, called independent variables.

It then provides an equation to be used for estimating or predicting the average value of the dependent variable from the unknown values of the independent variable.

The relation between the expected value of the dependent variable and the independent variable, is called a regression relation.

Concept of Regression(Contd.)

The dependence of a variable on a single independent variable, is called a single or two-variable regression.

The dependence of a variable on two or more independent variable, is called multiple regression.

Regression is represented by a straight line equation, and said to be linear regression.

Least SquaresRegression Line

Least SquaresRegression Line

Dependent Variable

Least SquaresRegression Line

Dependent Variable

Independent Variable

Least SquaresRegression Line

Dependent Variable

Independent Variable

Intercept

Least SquaresRegression Line

Dependent Variable

Independent Variable

Intercept

slope

Least SquaresRegression Line (Where a & b are Regression Coefficients)

Dependent Variable

Independent Variable

Intercept

slope

b = 𝑎=𝑌 −𝑏 𝑋

ExampleX 5 6 8 10 12 13 15 16 17

Y 16 19 23 28 36 41 44 45 50

Compute the least squares regression equation of Y on X for the following data. What is regression coefficient and what does it mean?

We Know, the estimated regression line of Y on X is

𝑌=𝑎+𝑏𝑋

Example (Contd.,)

b = 𝑎=𝑌 −𝑏 𝑋X Y

5 16

6 19

8 23

10 28

12 36

13 41

15 44

16 45

17 50

Example (Contd.,)

b = 𝑎=𝑌 −𝑏 𝑋X Y XY

5 16 80

6 19 114

8 23 184

10 28 280

12 36 432

13 41 533

15 44 660

16 45 720

17 50 850

Example (Contd.,)

b = 𝑎=𝑌 −𝑏 𝑋X Y XY X2

5 16 80 25

6 19 114 36

8 23 184 64

10 28 280 100

12 36 432 144

13 41 533 169

15 44 660 225

16 45 720 256

17 50 850 289

Example (Contd.,)

b = 𝑎=𝑌 −𝑏 𝑋X Y XY X2

5 16 80 25

6 19 114 36

8 23 184 64

10 28 280 100

12 36 432 144

13 41 533 169

15 44 660 225

16 45 720 256

17 50 850 289

Total

Example (Contd.,)

b=9 (3853 )− (102 )(302)9 (1308 )− (102 )2

Example (Contd.,)

Example (Contd.,)

Example (Contd.,)

and

Example (Contd.,)

and

and

Example (Contd.,)

and

and

and

Example (Contd.,)

and

and

and

Example (Contd.,)

and

and

and

Example (Contd.,)

and

and

and

Hence the desired estimated regression line of Y on X is

𝑌=1 .47+2 .831𝑋

The estimated regression co-efficient, which indicates that the values of Y increase by units for a unit increase in X.

THAT’S ALL…QUESTIONS??