Lecture Managerial economics (Ninth edition): Chapter 4 – Thomas, Maurice

Chapter 4 - Basic estimation techniques. After completing this unit, you should be able to: Set up a regression equation that can be estimated using a computerized regression routine, interpret and understand how to use the computer output to investigate problems that are of interest to managers of a firm, specify a relation or model between a dependent variable and the appropriate independent variable(s) that can be estimated using regression techniques,...

Trang 1

McGrawHill/Irwin

Managerial Economics, 9e

Maurice

ninth edition

McGrawHill/Irwin

Managerial Economics, 9e

Maurice

ninth edition

Chapter 4

Basic Estimation

Techniques

Trang 2

Managerial Economics Managerial Economics

42

Simple Linear Regression

• Simple linear regression model relates

Y a bX

Y

I nt e r c e pt par am e t e r ( ) g ive s value o f

wh e r e r e g r e s s io n line c r o s s e s ax is (value

o f wh e n is ze r o )

• Slope parameter ( b ) gives the change in Y associated with a oneunit change in X,

Trang 3

43

Method of Least Squares

• The sample regression line is an

estimate of the true regression line

•

a b

Parameter estimates are obtained by choosing values of & that minimize the sum of squared residuals

•

Y Y Y

T h e r e s id ual is t h e d if f e r e nc e b e t we e n t h e

ac t ual & f it t e d value s o f ,

ˆ

Y a bX

Trang 4

44

i

ˆS , A

Sample regression line

11573 4 9719

Sample Regression Line

(Figure 4.2)

A

0 2,000 4,000 6,000 8,000 10,000 10,000

20,000 30,000 40,000 50,000 60,000 70,000

Advertising expenditures (dollars)

S

•

i

ˆS 46,376

e i

i

S 60,000

Trang 5

45

• The distribution of values the estimates might take is centered around the true value of the parameter

• An estimator is unbiased if its average

value (or expected value) is equal to the true value of the parameter

Unbiased Estimators

a b

The estimates of & do not generally equal the true values of &

• ˆa b & ar e r and o m var iab le s c o m put e d us ing ˆ

d at a f r o m a r and o m s am ple

Trang 6

46

Relative Frequency Distribution*

(Figure 4.3)

0 2 4 6 8 10

1

Relative frequency of ˆb

*Also called a probability density function (pdf)

Relative Frequency Distribution* ˆ

for when b b = 5

Trang 7

47

• Must determine if there is sufficient statistical evidence to indicate that

Y is truly related to X (i.e., b 0)

Statistical Significance

ˆb

Even if = 0 it is possible that the sample will produce an estimate that is different from zero

• Test for statistical significance using t-tests or p-values

Trang 8

48

• First determine the level of

significance

• Probability of finding a parameter estimate to be statistically different from zero when, in fact, it is zero

• Probability of a Type I Error

• 1 – level of significance = level of

confidence

Performing a t-Test

Trang 9

49

Performing a t -Test

• Use t-table to choose critical t-value

with n – k degrees of freedom for the

chosen level of significance

• n = number of observations

• k = number of parameters estimated

•

ˆb

S

-ratio is computed as

where is the standard error of the estimate

Trang 10

4

10

Performing a t -Test

estimate is statistically significant

Trang 11

4

11

Using p -Values

• Treat as statistically significant

only those parameter estimates

maximum acceptable significance level

• p-value gives exact level of

significance

• Also the probability of finding significance when none exists

Trang 12

4

12

Coefficient of Determination

variation in the dependent variable that is explained by the regression equation

• Ranges from 0 to 1

• High R2 indicates Y and X are highly correlated

Trang 13

4

13

F -Test

• Used to test for significance of

overall regression equation

• Two degrees of freedom, n – k & k – 1

• Level of significance

the regression equation overall is statistically significant

Trang 14

4

14

Multiple Regression

• Uses more than one explanatory

variable

• Coefficient for each explanatory

variable measures the change in the dependent variable associated with a one-unit change in that

explanatory variable

Trang 15

4

15

• Use when curve fitting scatter plot

Quadratic Regression Models

•

2

Z X

Fo r line ar t r ans f o r m at io n c o m put e

ne w var iab le

Trang 16

4

16

Log-Linear Regression Models

X

Pe r c e nt ag e c h ang e in

Z

Pe r c e nt ag e c h ange in

•

lnY lna bln X c ln Z

T r ans f o r m b y t aking nat ur al lo g ar it h m s :

Định dạng
Số trang	16
Dung lượng	818,42 KB