Introduction to regression

EXCEL Spreadsheet
GC program
Transforming
data
Logfit
138 Further Mathematics
WORKED
Example
10
WORKED
Example
11
WORKED
Example
12
3F
Transforming to linearity
1 Apply a parabolic (x2 ) transformation to the following data set.
The regression line has been determined as y = −27.7x + 186 with r = −0.91.
x 2 3 4 5 7 9
y 96 95 92 90 14 −100
2 The average heights of 50 girls of various ages were measured as follows.
Age group (years) Average height (cm)
9 128
10 144
11 148
12 154
13 158
14 161
15 165
16 164
17 166
18 167
The original linear regression yielded height = 3.76 × (age) + 104.7, with r = 0.92
a Plot the original data and regression line.
b Transform using the log 10x transformation.
c Perform regression analysis on the transformed data and comment on your results.
3 a Use the transformed data from question 2 to predict the heights of girls of the
following ages.
i 7 years old ii 10.5 years old iii 20 years old.
b Identify the interpolations from these predictions.
4 Comment on the suitability of transforming the data of question 2 in order to improve
predictions for girls under 8 or over 18.
5 a Apply a reciprocal transformation to the following data obtained by a Physics
student studying light intensity.
Distance from light source (metres) 1 2 3 4 5 10
Intensity (candlepower) 90 60 28 22 20 12
b Use the transformed regression equation to predict the intensity at a distance of
20 metres.