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Lecture

# Chapter 14

6 Pages
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Department
Quantitative Methods
Course Code
QMS 202
Professor
Jason Chin- Tiong Chan

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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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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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Description
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 ( x 1) , per-capita income ( x 2) and regional unemployment rate ( x3 ). The regression equation was computed to be (in dollars): y = 64100 + 0.394 x + 9.6 x âˆ’ 11600 x 1 2 3 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 www.notesolution.com 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 y = Î² 0 Î² x 1 1 x + 2..2+ Î² x + Îµk k y where is the dependent variable x1, x 2..., x k are independent variables E (y) = Î² 0 Î² x +1 1x + .2.2+ Î² x k k is the deterministic portion of the model Î² i determines the contribution of the independent variable x i Note: The symbols x 1 x ,2.., xk may represent higher-order terms. For example, x 1 might represent the current interest rate, x 2 might 2 represent x1 , and so forth. Fall2010 Page#2 www.notesolution.com CQMS202-Business Statistics II
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