# how to do a median regression line (1 Viewer)

#### kieransgirl

##### Member
1. plot all the points on a number plane
2. divide the points into 3 even sections. If there is an odd number of points then make sure that the two outer ones are the same and the middle one is the odd one
3. find the median/ middle point in each of the sections. if there are two in the middle, average it. eg (2,4) (4,6)
x= (2+4)/2 y= (4+6)/2 therefoe the media point is (3,5)
4. then link the 2 outer median points and draw in a light line iwht pencil
5. shift the line up 1/3 of the way towards the middle median point

presto ur finished. nemore help then ask for me specifically in a thread

M

#### mushi

##### Guest
if they asks us to label the regression line

step 5 is the median regression line yeh?

not step 4 right?

#### kieransgirl

##### Member
nu huh

no step 5 is the median regression line. if u want to check though i just got it off the csu hsc site cause so many ppl were asking

#### craz

##### Member
there's a great exam in the maths section at http://hsc.csu.edu.au. it does it step by step - if u find the data analysis section.

#### Pogaz

##### New Member
Just wondered if anyone could explain why you can obtain several varied equations of the line when you determine the equation of the line using the median regression line on a scatter plot but only obtain one equation of the line when you use a graphics calculator.

Thanks

#### PC

##### Member
If you do a median regression line yourself by plotting points on a graph, then you should get the same slope, but the y-intercept comes by observation usually. That's where different people doing the same question might get different answers. A calculator will run complicated algorithms to get the y-intercept as accurately as possible, so they'll all end up with the same number.

#### berra

##### Member
uhm... at skl (n i go 2 a private skl) we were never taught this way, coz my teacher sed it wasnt in the syllabus 4 gen. maths.. and im trying to learn it now, coz i dnt wanna lose marks coz of sum stupid thing thats not in d syllabus....

i went on the link sum1 posted, and on the final step, it sed 2 do this;

The final step is to place your ruler on the line just drawn and slide it one third of the way vertically towards the median point of the central section.

??? wat dus this mean? do we draw another line??

sum1 plz help me <?xml:namespace prefix = o ns = "urn:schemas-microsoft-comfficeffice" /><o></o>

#### PC

##### Member
Yes. You kind of draw two lines.

1. First you have to find the three median points and plot them. Get that out of the way first.
2. Then you draw a line through the first and third median points. This is not the median regression line.
3. Now you draw a new line one third of the way between your first line and the second median point. This line is the median regression line.

The two lines will be parallel, so that's why we're told to use a ruler for the first line, and then to "move the ruler" a third of the way up or down.

Here's a good top: because the two lines are parallel and parallel lines have the same slope or gradient, you can work out the gradient of the final line of regression before you even draw it by using the first and third median points. Then you just use the last line to get the y-intercept.

#### helper10

##### New Member
A nice method of finding the Median of each 'cluster' of points is to draw a rectangle so that all points of the cluster are either ON or INSIDE the rectangle. Now construct the diagonals of the rectangle. The point of intersection of the diagonals is the centre of the rectangle, and also the MEDIAN of the 'cluster'.
Repeat for the other two 'clusters' of points. Construct line M1 M3. Construct line parallel to M1 M3 and passing through M2. Read off the distance between these two Y-intercepts. Divide by 3, use this number to adjust the Y-intercept of M1 M3.
The Median Regression Line will have same gradient and Y-intercept such that it will be 'one-third' of the way towards M2.

cheers