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