Introduction to regression 3D. Interpretation, interpolation, and extrapolation

Interpreting slope and intercept The slope (m) of a regression line indicates the rate at which data is increasing or decreasing. The y-intercept indicates the approximate value of the data when x=0 Example, Ex 3D, Q.1

Interpolation and extrapolation Remember that a regression line is an estimate of the true relationship between two variables. But, the regression line is used to make predictions about the data set. The two types of prediction are called interpolation and extrapolation.

Interpolation Interpolation predicts values between two values already in the data set. If the data is very linear (r near +1 or -1) then we know the interpolated point is quite accurate.

Extrapolation Extrapolation predicts values smaller than the smallest value already in the data set or larger than the largest value. Two problems 1.It may not be reasonable to extrapolate too far away from the given data values. 2.The data may be linear in a narrow band of the given data set.

Generally, interpolations are more reliable than extrapolations. But remember, our confidence depends on the correlation coefficient (r).

Example: Ex 3D: 4 You do: 2, 5, 7, 8, 9