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