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I Points with second coordinate greater than the ﬁrst lie above the horizontal rising diagonal; points with second
coordinate less than the ﬁrst lie below the horizontal rising diagonal. If the horizontal and vertical axes have no units, or if they
have the same units, then the slope has no units. However,
if the axes have different units, the slope must have corresponding units. For example, if the vertical axis is
measured in feet and the horizontal in seconds, then the slope is measured in feet per second. Not surprisingly, the
units of slope are a rate. Why the Computation Makes Sense' If you picture the points of the scatter diagram plotted on a graph with standard unit scales, the point of averages lands at the origin. Points in the ﬁrst and third quadrant will have positive
products, providing a positive contribution to the average of
the products. If these points dominate, i" will be positive. Points in the second and fourth quadrant will have negative
products, providing a negative contribution to the average of
the products. If these points dominate, 7' will be negative. Pictures May be Deceiving' The appearance of the data in a scatter diagram depends
upon the size of the standard unit. The two scatter
diagrams belowr both have 1* = .70. The ﬁrst appears to be
more tightly clustered around the SD line because the
diagram is drawn with a smaller distance representing the
standard unit. If the graphs are scaled so that the standard
units coincide, it will become apparent that they have the
same correlation. Figure 3. The effem oi changing SDS. The two scatter diagrams have
the same correlation coefﬁcient 01' {lit}. The top diagram looks me tightly
rlustemd around the SI} line bonus: ils SDs In: smaller. «I a 1"
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I} II I 3 i I II T I Figure 4. Nonlinear association. Regression lines should not be used
when there is a noniinear association between the variables. ...
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 Fall '07
 Klimko
 Statistics, standard unit, ﬁrst lie

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