TI84 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.
TI84 Plus CE
Program PARAM
Notes:
L1: list 1, [ 2nd ] [ 1 ]; L2: list 2, [ 2nd ] [ 2 ],
etc. X1T, Y1T are from the [ vars ],
YVARS, 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
TI83/TI84, 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.