# Interactive least squares line

Begin the program, there are 6 points (A to F) and a line de ned from sliders a and b as y = ax + b. The square distances from the points to the line are shown as squares with the total area displayed below (observe that it is currently at 301.45). 1) Move the sliders a and b to limit this area to be as small as possible. Record the values of a, b, and the area. Note for teacher: a = 1:518049553  1:5, b = 2:782921207  2:8, Area  14:51 2) Open the table and change the values (note do not delete the values) to (1,1), (2,2.7), (3.2,8), (4.6,6), (5.1,7.2), and (5.9,8.1). Now nd the line of best t for this set of points and record a, b, and the area. Note for teacher: a = 1:344004441  1:3, b = 0:6167838638  0:6, Area  11:95 3) Add the point (6.1,0.9) into the table. Highlight those coordinates, right click and choose "create, list of points." This point should be labeled as point G. Now right click "pt" in the algebra view and choose "object properties" adding point G under the de nition of pt. Find the line of best t for this set of data and record a, b, and the area. What happened? Note for teacher: a = 0:6235547355  0:6, b = 2:35746125  2:3, Area  49:06 Note the rounding of b is o due to the rounding of a. 4) Change the values of points A, B, C, D, E, F, and G to any values you would like and again record a, b, and the area for the line of best t. Note for teacher: all answers should be di erent! 5) Play around!

Resource Type
Activity
Tags
square  statistics
Target Group (Age)
15 – 18
Language
English (United Kingdom)

GeoGebra version
4.0
Views
1372

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