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SUMMARY OF FORMULAS FOR CHAPTER 9 457
of variance, which tests the significance of the regression mean square. The
strength of the relationship between two variables under the correlation model is
assessed by testing the null hypothesis that there is no correlation in the population.
If this hypothesis can be rejected we may conclude, at the chosen level of
significance, that the two variables are correlated.
5. Use the equation. Once it has been determined that it is likely that the regression
equation provides a good description of the relationship between two variables, X
and Y, it may be used for one of two purposes:
a. To predict what value Y is likely to assume, given a particular value of X, or
b. To estimate the mean of the subpopulation of Y values for a particular value
of X.
This necessarily abridged treatment of simple linear regression and correlation may
have raised more questions than it has answered. It may have occurred to the reader, for
example, that a dependent variable can be more precisely predicted using two or more independent
variables rather than one. Or, perhaps, he or she may feel that knowledge of the
strength of the relationship among several variables might be of more interest than knowledge
of the relationship between only two variables. The exploration of these possibilities
is the subject of the next chapter, and the reader’s curiosity along these lines should be at
least partially relieved.
For those who would like to pursue further the topic of regression analysis a number
of excellent references are available, including those by Dielman (7), Hocking (8),
Mendenhall and Sincich (9), and Neter et al. (10).
SUMMARY OF FORMULAS FOR CHAPTER 9
Formula Name Formula
Number
9.2.1 Assumption of
linearity
9.2.2 Simple linear
regression model
9.2.3 Error (residual) term
9.3.1 Algebraic
representation
of a straight line
m y ƒ x = b 0 + b 1 x
y = b 0 + b 1 x +P
P=y - 1b 0 + b 1 x2 = y - m y ƒ x
y = a + bx
9.3.2 Least square
estimate of the
slope of a
regression line
Nb 1 =
n
a 1x i - x21y i - y2
i = 1
n
a 1x i - x2 2
i = 1
(Continued)