Microsoft Office Tutorials and References
In Depth Information
Multi-Regression
FIGURE 14.1 The Data, Chart, Regression Line Equation, and R 2
the apartments: size in square feet and selling prices. Using the Statistical Regression
on the Excel chart (Chapter 12); we can see in Figure 14.1 the relationship between
size and price.
As you can see, the regression equation line is automatically calculated on the
chart:
Y
¼
30
:
141
þ
0
:
4525x
In other words, we can use this formula if we want to predict or estimate a price
in thousands of dollars, where:
Price
¼
30
:
141
þ
0
:
4525
S ize
ð
Þ
×
in square feet
Since R2 is relatively low, we cannot rely on this model to accurately predict the
price (check your statistics book or notes for Coefficient of Determination R2 or see
http://en.wikipedia.org/wiki/Coefficient_of_determination for further explanation).
MULTI-REGRESSION
The mathematical model of using more than one independent variable to forecast
results is called Multi-Regression (or multivariate regression). Our objective is to add
more independent variables to increase R 2 and, in doing so, increase the reliability or
accuracy of our model. On the worksheet, Apartments Sales w Baths in the work-
book of this chapter, we have an additional piece of information
also known as a
parameter
for every apartment. This information is the number of bathrooms for
these apartments. The data is shown in Figure 14.2.
The dependent variable Y is Price, while Apartment Size and Bathrooms will be
the independent variables. What we want to create is a model that calculates
Y
¼
a
þ
b 1 X 1
þ
b 2 X 2
 
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