2000 words economic assignment due 13 hours

EQAWeek14.pptx

Home >Business & Finance homework help >Economics homework help >2000 words economic assignment due 13 hours

8220 Economics and Quantitative Analysis

Week 14

Learning Outcome 4:

Analyze business and economic data and interpret quantitative analysis to inform business decisions using quantitative analytic techniques.

Lecturer: Dr. Dayal Talukder

ICL Business School, Auckland

‹#›

Slide

or duplicated, or posted to a publicly accessible website, in whole or in part.

Key elements:

Introductions to simple linear regression

Linear correlations

Simple linear regression

Introduction to multiple linear regression

Multiple regression

LO 4 :

Analyze business and economic data and interpret quantitative analysis to inform business decisions using quantitative analytic techniques.

‹#›

Slide

or duplicated, or posted to a publicly accessible website, in whole or in part.

Regression analysis

Objectives

On completion of this topic students should be able to:

apply and interpret linear correlations

apply and interpret simple linear regression

interpret output that relates to simple linear regression

apply and interpret multiple regression

• interpret the output that relates to multiple linear regression.

‹#›

Slide

or duplicated, or posted to a publicly accessible website, in whole or in part.

Simple Linear Regression

Regression analysis can be used to develop an

equation showing how the variables are related.

Managerial decisions often are based on the

relationship between two or more variables.

The variables being used to predict the value of the

dependent variable are called the independent

variables and are denoted by x.

The variable being predicted is called the dependent

variable and is denoted by y.

‹#›

Slide

or duplicated, or posted to a publicly accessible website, in whole or in part.

‹#›

Simple Linear Regression

The relationship between the two variables is

approximated by a straight line.

Simple linear regression involves one independent

variable and one dependent variable.

Regression analysis involving two or more

independent variables is called multiple regression.

‹#›

Slide

or duplicated, or posted to a publicly accessible website, in whole or in part.

‹#›

Simple Linear Regression Model

y = b0 + b1x +e

where:

b0 and b1 are called parameters of the model,

e is a random variable called the error term.

The simple linear regression model is:

The equation that describes how y is related to x and

an error term is called the regression model.

‹#›

Slide

or duplicated, or posted to a publicly accessible website, in whole or in part.

‹#›

Simple Linear Regression Equation

The simple linear regression equation is:

E(y) is the expected value of y for a given x value.

b1 is the slope of the regression line.

b0 is the y intercept of the regression line.

Graph of the regression equation is a straight line.

E(y) = 0 + 1x

‹#›

Slide

or duplicated, or posted to a publicly accessible website, in whole or in part.

‹#›

Simple Linear Regression Equation

Positive Linear Relationship

E(y)

Slope b1

is positive

Regression line

Intercept

‹#›

Slide

or duplicated, or posted to a publicly accessible website, in whole or in part.

‹#›

Simple Linear Regression Equation

Negative Linear Relationship

E(y)

Slope b1

is negative

Regression line

Intercept

‹#›

Slide

or duplicated, or posted to a publicly accessible website, in whole or in part.

‹#›

Simple Linear Regression Equation

No Relationship

E(y)

Slope b1

is 0

Regression line

Intercept

‹#›

Slide

or duplicated, or posted to a publicly accessible website, in whole or in part.

‹#›

Estimated Simple Linear Regression Equation

The estimated simple linear regression equation

is the estimated value of y for a given x value.

b1 is the slope of the line.

b0 is the y intercept of the line.

The graph is called the estimated regression line.

‹#›

Slide

or duplicated, or posted to a publicly accessible website, in whole or in part.

‹#›

Estimation Process

Regression Model

y = b0 + b1x +e

Regression Equation

E(y) = b0 + b1x

Unknown Parameters

b0, b1

Sample Data:

x y

x1 y1

. .

xn yn

b0 and b1

provide estimates of

b0 and b1

Estimated

Regression Equation

Sample Statistics

b0, b1

‹#›

Slide

or duplicated, or posted to a publicly accessible website, in whole or in part.

‹#›

Least Squares Method

Least Squares Criterion

where:

yi = observed value of the dependent variable

for the ith observation

yi = estimated value of the dependent variable

for the ith observation

‹#›

Slide

or duplicated, or posted to a publicly accessible website, in whole or in part.

‹#›

Slope for the Estimated Regression Equation

Least Squares Method

where:

xi = value of independent variable for ith

observation

y = mean value for dependent variable

x = mean value for independent variable

yi = value of dependent variable for ith

observation

‹#›

Slide

or duplicated, or posted to a publicly accessible website, in whole or in part.

‹#›

y-Intercept for the Estimated Regression Equation

Least Squares Method

‹#›

Slide

or duplicated, or posted to a publicly accessible website, in whole or in part.

‹#›

Reed Auto periodically has a special week-long sale.

As part of the advertising campaign Reed runs one or

more television commercials during the weekend

preceding the sale. Data from a sample of 5 previous

sales are shown on the next slide.

Simple Linear Regression

Example: Reed Auto Sales

‹#›

Slide

or duplicated, or posted to a publicly accessible website, in whole or in part.

‹#›

Simple Linear Regression

Example: Reed Auto Sales

Number of

TV Ads (x)

Number of

Cars Sold (y)

Sx = 10

Sy = 100

‹#›

Slide

or duplicated, or posted to a publicly accessible website, in whole or in part.

‹#›

Estimated Regression Equation

Slope for the Estimated Regression Equation

y-Intercept for the Estimated Regression Equation

Estimated Regression Equation

‹#›

Slide

or duplicated, or posted to a publicly accessible website, in whole or in part.

‹#›

Coefficient of Determination

Relationship Among SST, SSR, SSE

where:

SST = total sum of squares

SSR = sum of squares due to regression

SSE = sum of squares due to error

SST = SSR + SSE

‹#›

Slide

or duplicated, or posted to a publicly accessible website, in whole or in part.

‹#›

The coefficient of determination is:

Coefficient of Determination

where:

SSR = sum of squares due to regression

SST = total sum of squares

r2 = SSR/SST

‹#›

Slide

or duplicated, or posted to a publicly accessible website, in whole or in part.

‹#›

Coefficient of Determination

r2 = SSR/SST = 100/114 = .8772

The regression relationship is very strong; 87.72%

of the variability in the number of cars sold can be

explained by the linear relationship between the

number of TV ads and the number of cars sold.

‹#›

Slide

or duplicated, or posted to a publicly accessible website, in whole or in part.

‹#›

Sample Correlation Coefficient

where:

b1 = the slope of the estimated regression

equation

‹#›

Slide

or duplicated, or posted to a publicly accessible website, in whole or in part.

The sign of b1 in the equation is “+”.

Sample Correlation Coefficient

rxy = +.9366

‹#›

Slide

or duplicated, or posted to a publicly accessible website, in whole or in part.

‹#›

Assumptions About the Error Term e

1. The error  is a random variable with mean of zero.

2. The variance of  , denoted by  2, is the same for

all values of the independent variable.

3. The values of  are independent.

4. The error  is a normally distributed random

variable.

‹#›

Slide

or duplicated, or posted to a publicly accessible website, in whole or in part.

‹#›

Testing for Significance

To test for a significant regression relationship, we

must conduct a hypothesis test to determine whether

the value of b1 is zero.

Two tests are commonly used:

t Test

and

F Test

Both the t test and F test require an estimate of s 2,

the variance of e in the regression model.

‹#›

Slide

or duplicated, or posted to a publicly accessible website, in whole or in part.

‹#›

01ˆybbx

ˆy

01ˆybbx

min (y y

i i







)

12()()()iiixxyybxx

01bybx

2x

20y

ˆ105yx

12()()205()4iiixxyybxx

01205(2)10bybx

2()iyy

2ˆ()iyy

2ˆ()iiyy

) of(sign rbr



ionDeterminat oft Coefficien ) of(sign



xbby



) of(sign rbr



ˆ105yx

=+.8772xyr