Download Solving Problems Given Functions Fitted to Data - 3

Adapted from Walch Education
• A linear equation
describes a situation
where there is a nearconstant rate of change.
• An exponential equation
describes a situation
where the data changes
by a constant multiple.
• A quadratic equation
describes data that
increases then
decreases, or vice versa.
5.9.1: Solving Problems Given Functions Fitted
to Data
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• In a linear model, the y-value
changes by a constant when
the x-value increases by 1.
The change in y when x
increases by 1 is called a first
difference. If your first
differences are all about the
same, then a linear model is
appropriate.
• In a quadratic model, the first
differences are not the same,
but the change in the first
differences is constant. The
change in successive first
differences is called a second
difference.
• A quadratic regression
equation fits a parabola to the
data.
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to Data
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• The regression equation
closely models the data but is
not necessarily an exact fit.
Actual data values and
regression values might differ.
• Regression equations can be
used to make predictions
about the dependent variable
for given values of the
independent variable.
• Interpolation is when a
regression equation is used to
make predictions about a
dependent variable that is
within the range of the given
data.
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to Data
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To interpolate, substitute the xvalue into the given regression
equation and solve for the yvalue.
Extrapolation is when a
regression equation is used to
make predictions about a
dependent variable that is
outside the range of the given
data.
Think of extrapolation as
predicting data values based on
the model outside of the given
data.
To extrapolate, substitute the xvalue into the regression
equation and solve for the yvalue.
5.9.1: Solving Problems Given Functions Fitted
to Data
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Dr. Dambreville