TI-84 Plus CE: Fitting a Parametric Line
The program PARLIN attempts to fit a parametric line for a
collection of points (x(t), y(t)) using the following equations:
x = a * t + b
y = c * t + d
where the independent variable is t. The program also plots
the estimated line and the scatter plot.
I decided to keep the correlation (r^2) separate, so we can tell how
well the line fits both the x and y data.
TI-84 Plus CE
Program PARAM
Notes:
L1: list 1, [ 2nd ] [ 1 ]; L2: list 2, [ 2nd ] [ 2 ],
etc. X1T, Y1T are from the [ vars ],
Y-VARS, Parametric submenu
[square] is from [2nd] [ y= ] (stat plot) , MARK submenu,
option 1
Program:
Param
Input "T LIST:
",L1
Input "X LIST:
",L2
Input "Y LIST:
",L3
FnOff
PlotsOff
LinReg(ax+b) L1,L2
a→A:b→B:r²→E
"AT+B"→X1T
ClrHome
Disp "X = A*T +
B"
Disp A
Disp B
Disp "CORR:
"
Pause E
LinReg(ax+b) L1,L3
a→C:b→D:r²→F
"CT+D"→Y1T
ClrHome
Disp "Y = C*T +
D"
Disp C
Disp D
Disp "CORR:
"
Pause F
min(L1)-5→Tmin
max(L1)+5→Tmax
FnOn 1
PlotsOn 1
GraphColor(1,BLUE)
Plot1(Scatter,L2,L3,
[square] ,ORANGE)
ZoomStat
(Obviously use the colors and makers you like. If you are working with a monochrome
TI-83/TI-84, ignore the color commands.)
You can also download the program here:
Example 1
Fit the data to a parametric line:
|
T
|
X
|
Y
|
|
1
|
2.3
|
-3.0
|
|
2
|
2.8
|
-2.6
|
|
3
|
3.2
|
-2.3
|
|
4
|
3.7
|
-1.9
|
|
5
|
4.2
|
-1.6
|
Results:
x = 0.47*t + 1.83 (r^2 ≈ 0.998)
y = 0.35*t – 3.33 (r^2 ≈ 0.997)
Example 2
Fit the data to a parametric line:
|
T
|
X
|
Y
|
|
1
|
-1.0
|
1.000
|
|
2
|
1.0
|
1.250
|
|
4
|
5.3
|
1.746
|
|
8
|
13.6
|
2.825
|
|
16
|
30.1
|
4.275
|
Results:
x = 2.075268817 * t – 3.066666667 (r^2 ≈ 0.99997)
y = 0.2196827957* t + 0.857166667 (r^2 ≈ 0.99145)
Eddie
This blog is property of Edward Shore, 2017.
