Introduction to regression

126 Further Mathematics
THINK WRITE/DISPLAY
3
Using the regression equation, find the
height when the age is 8. Take into
account that in y = 9.23x + 55.63, x is
age in years and y is height in
centimetres.
Alternatively, get the graphics
calculator to do the work by calculating
Y1(8).
Notes:
1. Y1 is under VARS, Y-VARS,
1:Function, 1:Y1
2. Since there was a good fit (r = 0.97),
then one can be confident of an
accurate prediction.
Height = 9.23 × age + 55.63
= 9.23 × 8 + 55.63
= 129.5 cm
Extrapolation
Use the data from worked example 6 to predict the height of the girl when she turns 15.
Discuss the reliability of this prediction.
THINK WRITE
1
2
WORKED Example
Use the regression equation to calculate
the girl’s height at age 15.
Alternatively, use the graphics
calculator to find Y1(15).
7
Height = 9.23 × age + 55.63
= 9.23 × 15 + 55.63
= 194.08 cm
Analyse the result. Since we have extrapolated the result (that is,
since the greatest age in our data set is 11 and
we are predicting outside the data set) we
cannot claim that the prediction is reliable.
remember
remember
1. The slope (m) indicates the rate at which the data are increasing or decreasing.
2. The y-intercept indicates the approximate value of the data when x = 0.
3. Interpolation is the use of the regression line to predict values ‘in between’ two
values already in the data set.
4. Extrapolation is the use of the regression line to predict values smaller than the
smallest value already in the data set or larger than the largest value.
5. The reliability of these predictions depends on the value of r 2 and the limits of
the data set.