Chapter 14 Simple Linear Regression
Hypotheses tests and Confidence Intervals
In simple linear regression we assume there is a
linear relationship between the explanatory
variable (x) and the response variable (y). For
example, assume the growth rate (y) of microscopic
marine plants is linearly related to the nitrogen
concentration in water (x) according to the
following equation.
∧
y
=
β
0
+ β
1
x
(the “hat”
above the y indicates
the y is a
predicted
value)
However, if we were to actually measure growth
rates at specific concentrations we would find that
the y values do not all occur on the line. The
reason for this is that even though the
relationship between nitrogen concentration and
growth rate is linear there are other confounding
variables (light, temperature, etc.) which we don’t
completely control and which add scatter or “noise”
to the data.
The actual observed y values are therefore
described by the following equation:
y = β
0
+ β
1
x
+
ε
Notice that since we are now dealing with observed
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 Fall '10
 RaySievers
 Statistics, Linear Regression, Normal Distribution, Regression Analysis, linear relationship

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