4 SLE: APPLICATIONS The normal system: 70 1 1 21 A = and b = -7 1 110 5 -35 ATA = [ ] 84 -4 4 门 1134] and ATб= 166 [ATA\ATU] [AT A|ATƖ] = 84 1134] -12.1 - 4 166 29.4 The least squares solution is y = -12.1x + 29.4. A Rem: Visually: 110f A 62 " ATA 84-4 31-75 い AT (2x4) -7 ↑ (482) 31-75 い = 707=-1134 166 21 110 (2x4) -35_ (4x1) -44 Do it!! Do it!! ☺ ? m 4 4 -1134 ∙12.1 (૪૫(૧)-૯-૫)l) (84(4)-(-4)(-41) 4 84 40 (ATA)- 166 29.4 ↑ b
question1 (2)
Bob the Businessman has decided to take his company, LAspaceX, public. Bob is eager to make quick money and plans to sell his stocks as soon as they reach a high value. On the day LAspaceX goes public, Bob keeps track of the stock value by the minute. The recorded values are as follows:
Initially (at t=0 minutes), the stock is worth $2.
After 10 minutes, the stock is worth $3.
After 20 minutes, the stock is worth $5.
After 30 minutes, the stock is worth $6.
After 40 minutes, the stock is worth $8.
a) Finding the Value of the Stock Using the Least Squares Method
Using the data provided, determine the best-fit line V(t) = mt + b that represents the value V of the stock in dollars after t minutes using the least squares method.
You must submit your solution here using a
Identify the variables.
Construct the system of linear equation in matrix form : Ax = b. Label A and b. This system has no solution (you don't need to verify this.).
Compute ATA and ATb and verify that det(ATA) is not equal to zero.
Solve the normal system [ATA | ATb ]. Show all your steps (using the inverse is probably the safest way).
Give the equation V(t) = mt + b.
b) Predicting the time when the Stock Value will reach $45.
Using the best-fit line from Part 1, determine the time t at which the stock will reach $45. You must submit the answer here below by rounding to one decimal place.
follow the method present in the image
![4 SLE: APPLICATIONS
The normal system:
70
1
1
21
A =
and b =
-7 1
110
5
-35
ATA =
[ ]
84
-4
4
门
1134]
and ATб=
166
[ATA\ATU]
[AT A|ATƖ] =
84
1134]
-12.1
-
4
166
29.4
The least squares solution is y = -12.1x + 29.4.
A
Rem: Visually:
110f
A 62
"
ATA
84-4
31-75
い
AT
(2x4)
-7
↑ (482)
31-75
い
=
707=-1134
166
21
110
(2x4) -35_
(4x1)
-44
Do it!!
Do it!! ☺
?
m
4
4
-1134
∙12.1
(૪૫(૧)-૯-૫)l)
(84(4)-(-4)(-41) 4 84
40
(ATA)-
166
29.4
↑
b](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e0b636c-084d-4336-93b6-e9af0376f248%2F5a9e2b3d-9c0b-478b-9d9e-3e9e036ae25b%2Fnczmtue_processed.png&w=3840&q=75)
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