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Examining Relationships
Least-Squares Regression &
Cautions about Correlation and
Regression
Sections 2.3 and 2.4
r ranges
from -1 to +1
Strength: how closely the points
follow a straight line. !
Direction: is positive when
individuals with higher X values
tend to have higher values of Y.!
Correlation tells us about
strength (scatter) and direction
of the linear relationship
between two quantitative
variables.
In addition, we would like to have a numerical description of how both
variables vary together. For instance, is one variable increasing faster
than the other one? And we would like to make predictions based on that
numerical description.
The regression line
!!A regression line is a straight line that describes how a
response variable y changes as an explanatory variable
x changes.
"! We often use a regression line to predict the value of y
for a given value of x.
"! In regression, the distinction between explanatory and
response variables is impo...

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