# 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.