Microsoft Office Tutorials and References
In Depth Information
Chapter 14: Data Analysis—Multi-Regression
CHAPTER 14
Data Analysis—Multi-Regression
Chapter 12 discussed in detail simple linear regression using only one independent
variable where
Y
¼
a
þ
bX
With Multi-Regression we want to use more than one independent variable X.
To predict or estimate Y, the dependent variable, we use
¼
þ
þ
þþ
Y
a
b 1 X 1
b 2 X 2
b n X n
In Multi-Regression, multiple variables are used to predict the corresponding
value. For example, a real estate agent wanting to predict an apartment
s selling price
may use three variables based on historical data
size, location, and the number of
bathrooms
to predict that price. The prediction method will be developed based on
recently sold apartments. Predicted values from multiple regressions are linear
combinations of the input variables
that is, the independent variables (X).
Looking at the previous formula:
Y
¼
a
þ
b 1 X 1 þ
b 2 X 2 þ ::: þ
b n X n ,
Where:
Y is the predicted value
a is the Y intercept
X 1 is the score on the first input variable (historical data), X 2 the score on the
second, etc. . . .
The regression coefficients (b 1 ,b 2 , etc.) are equivalent to the slope in a simple
regression.
This chapter will describe how to use, read, and interpret the Data Analysis
ToolPak in Excel for Multi-Regressions. Unfortunately, Excel for Mac does not have
the Data Analysis ToolPak. For Mac Excel 2011 use the free download StatPlus:Mac
LE, the statistical tool for your Mac, at www.analystsoft.com/en/products/stat-
plusmacle/. This chapter does not cover the StatPlus product.
SIMPLE OR SINGLE VARIABLE REGRESSION
Consider the following example, found in the Chapter 14 web workbook in the sheet
Apartments Sales Data. In this initial example, we have two sets of information about
 
 
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