Introduction to regression

EXCEL Spreadsheet
3-median
regression
SkillSHEET 3.1
SkillSHEET 3.2
SkillSHEET 3.3
112 Further Mathematics
WORKED
Example
3
remember
remember
1. Assuming data points are in order of increasing x-values:
Step 1: Divide the data points into 3 groups
Step 2: Adjust for ‘unequal’ groups; if there is 1 extra point, put it in the
middle; if there are 2 extra points, put them in the outer groups.
Step 3: Calculate the medians for the 3 groups , , , , ( , ) .
2. For a graphical approach:
Step 4: Place a ruler through the two ‘outer’ medians and move the ruler onethird
of the way towards the middle median.
Step 5: Calculate the y-intercept and the gradient and use these to find the
equation of the regression line.
3. For an arithmetic approach:
Step 4: Calculate the gradient using the formula:
Step 5: Calculate the y-intercept using the formula:
3B
b
=
m
yU – yL ----------------xU
– xL ( xL yL) ( xM yM) xU yU Fitting a straight line —
the 3-median method
1 Find the regression line for the data in the table below using the 3-median
method.
x 2 3 3 4 4 5 5 7
y 1 3 5 3 6 6 7 8
2 a Using the data in the table below, find the regression line using the 3-median
method.
b Using this regression line determine:
i the value of y when x = 25
ii the value of x when y = 65
iii the x-intercept of the regression line.
=
1
-- ( y 3 L + yM + yU) – mxL+ xM + xU [ ( ) ]
x 5 10 20 20 30 40 50 55 60 65 75
y 80 60 50 70 40 55 40 30 10 25 15