Random Numbers and Linear Regression
Irregular Numbers and Linear Regression
The Test Case y = rand + x
The objective is to perceive how great we can fit a line to the focuses produced by the condition:
y = rand + x
where rand is an irregular created number between 0 + 1. Plotting such condition will show that y = rand + x will be limited in the middle of y = x and y = x + 1 (see screen shot underneath):
In every one of the three tests cases introduced, let x be a scope of numbers somewhere in the range of 0 and 14.
X = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}
In the cases introduced today, all arbitrary sums are adjusted to three decimal spots.
Case 1
Y = {0.735, 1.931, 2.007, 3.029, 4.499, 5.578, 6.794, 7.235, 8.847, 9.485, 10.326, 11.873, 12.287, 13.795, 14.101}
Block ≈ 0.530
Incline ≈ 0.996
Relationship ≈ 0.997
Case 2
Y = {0.900, 1.792, 2.462, 3.639, 4.083, 5.869, 6.088, 7.225, 8.458, 9.394, 10.401, 11.329, 12.283, 13.441, 14.478}
Block ≈ 0.627
Incline ≈ 0.976
Relationship ≈ 0.999
Case 3
Y = {0.066, 1.687, 2.654, 3.166, 4.879, 5.098, 6.891, 7.235, 8.504, 9.615, 10.217, 11.040, 12.823, 13.725, 14.397}
Block ≈ 0.428
Incline ≈ 1.006
Relationship ≈ 0.998
Testing 100 Curve Fits
The program RANDLR will test 100 experiments of 50 information points, X is a rundown created of the whole numbers from – 24 to 25, while Y is determined by X + rand, adjusted to three decimal places. The catch, incline, and connection indicated are the math normal of 100 test runs. I utilized different irregular seeds to here are the outcomes I utilized from five trials:
Test 1:
Block ≈ 0.4977
Incline ≈ 1.0007
Relationship ≈ 0.9998
Test 2:
Block ≈ 0.4976
Incline ≈ 1.0007
Relationship ≈ 0.9998
Test 3:
Block ≈ 0.5012
Incline ≈ 1.0002
Relationship ≈ 0.9998
Test 4:
Block ≈ 0.5046
Incline ≈ 0.9997
Relationship ≈ 0.9998
Test 5:
Block ≈ 0.5012
Incline ≈ 1.0002
Relationship ≈ 0.9998
I can generally evaluate that a line to assess y = x + rand is y = x + 0.5.
TI-84 Plus CE Program: RANDLR
Size: 322 bytes
“2020-07-26 EWS”
ClrHome
Disp “TEST: Y=AX+B”,”AGAINST Y=X+rand”,”PLEASE WAIT.”
Fix 4
seq(X,X,- 24,25,1) → L1
0 → A
0 → B
0 → R
For(I,1,100)
Output(5,10,” “) \ six spaces
Output(5,1,”PROGRESS:”)
Output(5,12,I)
seq(round(X+rand,3),X,- 24,25,1) → L2
LinReg(ax+b) L1, L2
A+a → A
B+b → B
R+r → R
End
.01 A → A
.01 B → B
.01 R → R
ClrHome
Output(3,1,”AVERAGE”)
Output(4,1,”ITC:”)
Output(4,6,B)
Output(5,1,”SLP:”)
Output(5,6,A)
Output(6,1,”COR:”)
Output(6,6,R)
Note:
The lines
Output(5,10,” “) \ six spaces
Output(5,1,”PROGRESS:”)
Output(5,12,I)
create an “in progress” counter with the goal that the client how much longer the program will take.
L1 speaks to list 1 by squeezing [ second ] [ 1 ]. In like manner, L2 represents list 2 and you can get the L2 character by squeezing [ second ] [ 2 ].
The insights factors a, b, r are found in the VARS, Statistics, EQ menu.
The code above should take a shot at any of the TI-83 Plus/TI-84 Plus family, however I just utilized it on the current TI-84 Plus CE.
