School

Ryerson University
Department

Quantitative Methods

Course Code

QMS 202

Professor

Jason Chin- Tiong Chan

CQMS202-Business Statistics II Chapter14

Chapter14 Multiple Regression

Outcomes:

1. Describe the relationship between several independent variables

and a dependent variable using a multiple regression

2. Compute and interpret the multiple standard error and the

coefficient of determination

3. Conduct a Global test (F test) to determine the usefulness of the

model

4. Conduct a test of hypothesis on each of the regression coefficient.

5. Use the multiple regression model for estimation and prediction

Multiple Regression Models

1. The simple linear regression model was used to analyze how one

quantitative variable (the dependent variable y) is related to one

other quantitative variable (the independent variable x).

2.

Multiple regression allows for any number of independent variables.

Example 1

The director of marketing at Ryerson Wholesale Products is studying

the monthly sales. Three independent variables were selected as

estimators of sales: regional population (

1

x

) , per-capita income (

2

x

)

and regional unemployment rate (

3

x

). The regression equation was

computed to be (in dollars):

321

116006.9394.064100

Ë†xxxy

âˆ’++=

a. What is the full name of the equation?

b. Interpret the number 64100

c. What are the estimated monthly sales for a particular region with a

population of 796000 per-capita income of $6940, and an

Fall2010 Page#1

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CQMS202-Business Statistics II Chapter14

unemployment rate of 6.0 percent?(Use 6.0 in your calculation)

3.

We expect to develop models that fit the data better than would a

simple linear regression model.

4. General form of the Multiple Regression Model

ÎµÎ²Î²Î²Î²

+++++=

kk

xxxy ...

22110

where

y

is the dependent variable

k

xxx ,...,,

21

are independent variables

kk

xxxyE

Î²Î²Î²Î²

++++=

...)(

22110

is the deterministic portion of

the

model

i

Î²

determines the contribution of the independent variable

i

x

Note: The symbols

k

xxx ,...,,

21

may represent higher-order terms.

For example,

1

x

might represent the current interest rate,

2

x

might

represent

2

1

x

, and so forth.

Fall2010 Page#2

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