A linear equation describes a situation where there is a near-
constant 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. 2 5.9.1: Solving Problems Given Functions Fitted to
Data
Slide 4
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. 3 5.9.1: Solving Problems Given Functions
Fitted to Data
Slide 5
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. 4 5.9.1: Solving Problems Given Functions
Fitted to Data
Slide 6
To interpolate, substitute the x- value into the given
regression equation and solve for the y- value. 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 x- value
into the regression equation and solve for the y- value. 5 5.9.1:
Solving Problems Given Functions Fitted to Data