y = mx + b is the equation for a line. It is called a linear equation.
LINEar
----
Notice how choosing the right slope m and intercept b
reduces the sum of squares of deviations and
try to see how the LINE better FITS the points.
Getting a good estimate for the SLOPE of the best fitting line -- what does the line have to FIT?
Fit the 4 points a, b, c and d where a = (1, 1) and b = (1, 7) for the two points at x = 1.
... and where c = (5, 2) and d = (5, 4) for the two points at x = 5.
End of REVIEW of y = mx + b and Data Flyer portion of Tuesday, March 10th class.
Find the best fitting (smallest "Sum of squares of deviations:")
line
f(x) = mx + b
for the following two points using Data Flyer:
-5 -1 <------ point a
0 3 <------ point b
Now, REFRESH the Data Flyer application and try these three points:
-5 -1 point a (same as before)
0 3 point b (same as before)
-2.5 2 point c <----- ths new 3rd point
Can you get the Sum of squares of deviations: 0.67 or less????
Note: It is helpful to click on "Light Grid Lines"
When you get the 0.67 or less
for the Sum of the squares of the deviations,
after doing enough Change Function and Slider adjusting,
you have discovered your
best fitting function
f(x) = mx + b, or
y = mx + b What is m? What is b?
Know the idea
of the RISE
(the y2 - y1 or y difference
or distance or change)
and
the RUN
(the x difference, x2 - x1,
the x distance or change)
E E R
S S I
I I S
R or R E
R U N R U N R U N
Run across (the x-axis) Rise UP (on the y-axis)
Rise
------ = slope of the line connecting the two points = m
Run
y = mx + b m is the SLOPE b is the INTERCEPT