文档介绍：Simple Linear Regression
Lecture 8
Like correlation, there are two major
Simple Linear assumptions:
Regression • The relationship should be linear; and
• The level of data must be continuous
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Simple Linear Regression The regression equation
(Bivariate Regression)
The purpose of simple linear regression is
We already looked at measuring relationships to fit a line to the two variables. This line is
between two interval variables using correlation. called the line of best fit, or the
Now we continue to look at the bivariate analysis regression line. When we do a scatterplot
of the two variables using regression analysis.
However, the purpose of doing regression rather of two variables, it is possible to fit a line
than correlation is that we can predict results in which best represents the data.
one variable, based on another variable. So,
rather than simply see if the variables are
related, we can interpret their effect.
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The regression equation The regression equation
A regression equation is used to define
the relationship between two variables. It
takes the form:
or
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The regression equation Scatterplot and regression line
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They are essentially the same, except that 60
the second includes an error term at the
50
end. This error term indicates that what we Change in Y is 10
40
Change in X is 1
have is in fact a model, and hence won't fit Y
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the data perfectly.
20 Intercept is 20
10
0
012345
X
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How do we fit a line to data?
In order to fit a line of best fit we use a
method called the Method of Least
Squares. This method allows us to
determine which line, out of all the lines
that could be drawn, best represents the
least amount of difference between the
actual values (the data points) and the
predicted line.
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In the Figure above, three data points fall on the Example 1
line, while the remaining 6 are slightly above or
be