2. Adapted from Walch Education

3. 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

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

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

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

7. Ms. Dambreville