General Mathematics HSC Median Regression Line Stage 6

General Mathematics HSC Median Regression Line Stage 6 - Year 11 Press Ctrl-A ©G Dear 2009 – Not to be sold/Free to use 1

Median Regression Lines (1/6) 1. It is a line of best fit for a scatter plot. 2. The equation of best fit can be found by: a. Finding the gradient ‘m’; (it may be negative) b. Finding ‘b’, the y-intercept; c. Using the general equation y = mx + b. 3. The equation can be used to make predictions. 2

Median Regression Lines (2/6) 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 different. 3. Find the median/middle point in each of the sections. If there are 2 in the middle, average it. E. g. (2, 4) (4, 6) x= (2+4)/2, y= (4+6)/2 therefore median point is (3, 5). 4. Then link the 2 outer median points and draw in a light line with a pencil. 5. Shift the line up 1/3 of the way towards the middle median point. Linear Regression Web 3

Median Regression Lines (3/6) y 5 4 3 2 1. 2. 3. 4. 5. x 2. 5 8 9 9. 5 5 3 1 y 1. 5 4 3. 5 2 5 1 2 4 6 5. 5 4. 5 Median Regression Line Plot the points Divide into thirds Mark the medians Draw a line thru 1 st and 3 rd medians Move 1/3 towards centre median. 1 1 2 3 4 5 6 7 8 9 10 x 4

Equation of Line (4/6) y x 2. 5 8 9 9. 5 5 3 1 y 1. 5 4 3. 5 2 5 1 2 5 y = mx + b 4 y = 1 x + 1. 5 3 3 2 b 1 2 3 4 6 5. 5 4. 5 1. 5 = 1 m = +1. 5 3 4. 5 +4. 5 1 4 b = 1. 5 5 6 7 8 9 10 x 5

Median Regression Lines (5/6) x 2 1 3 7. 5 8. 5 4 y 4 5 3. 5 1. 5 0. 5 y 1 6 4. 5 1 0. 5 1. 5 5. 5 2 5 4 3 2 Median Regression Line 1 1 2 3 4 5 6 7 8 9 10 x 6

Equation of Line (6/6) x 2 1 3 7. 5 8. 5 4 y 4 5 3. 5 1. 5 0. 5 y 1 6 4. 5 1 0. 5 1. 5 5. 5 2 m = 1 , b = 4. 6 -2 b 5 y = mx + b 4 y = - 1 x + 4. 6 2 +1 3 -2 2 1 1 2 3 4 5 6 7 8 9 10 x 7