and columns.) (c) We can manipulate the above formula to solve for â. i. For the system from (a) verify that ATA is invertible. (Note: AT A is invertible whenever the columns of A are linearly independent.) ii. Use the fact that AT A is invertible to solve the equation AT (b- A) for â. iii. Compute and Aê for the system from (a). Add A to your plot from (aiv). Compare the results to your earlier findings. (d) Regression Example Suppose you want to predict your average HC/LO score across your next day of classes based on whether you got more or less sleep than your usual 8 hours. You decide to make a regression model b = C+Mt, where b is the output, C and M are the coefficients of your model (what you need to find), and t is the number of hours above (or below for negative values) 8 hours of sleep. You feel lazy and only take five measurements: Hours of sleep above/below 8 (t) Mean HC/LO score (b) 1 3 4 3 2 -4 -1 1 3 4 i. Inputting the above into the formula for our linear model gives us a system of five equations and two unknowns - C and M. Write out this system explicitly, then describe it as the matrix equation Ax = b, where x = C ] What are A and 5? ii. Demonstrate that the system is inconsistent and that the columns of A are independent. iii. Use the techniques from above to solve for â.
and columns.) (c) We can manipulate the above formula to solve for â. i. For the system from (a) verify that ATA is invertible. (Note: AT A is invertible whenever the columns of A are linearly independent.) ii. Use the fact that AT A is invertible to solve the equation AT (b- A) for â. iii. Compute and Aê for the system from (a). Add A to your plot from (aiv). Compare the results to your earlier findings. (d) Regression Example Suppose you want to predict your average HC/LO score across your next day of classes based on whether you got more or less sleep than your usual 8 hours. You decide to make a regression model b = C+Mt, where b is the output, C and M are the coefficients of your model (what you need to find), and t is the number of hours above (or below for negative values) 8 hours of sleep. You feel lazy and only take five measurements: Hours of sleep above/below 8 (t) Mean HC/LO score (b) 1 3 4 3 2 -4 -1 1 3 4 i. Inputting the above into the formula for our linear model gives us a system of five equations and two unknowns - C and M. Write out this system explicitly, then describe it as the matrix equation Ax = b, where x = C ] What are A and 5? ii. Demonstrate that the system is inconsistent and that the columns of A are independent. iii. Use the techniques from above to solve for â.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Part C needed
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![(c) We can manipulate the above formula to solve for .
i. For the system from (a) verify that ATA is invertible. (Note: ATA is
invertible whenever the columns of A are linearly independent.)
ii. Use the fact that AT A is invertible to solve the equation AT (b- A) for î.
iii. Compute and A for the system from (a). Add A to your plot from
(aiv). Compare the results to your earlier findings.
(d) Regression Example Suppose you want to predict your average HC/LO score
across your next day of classes based on whether you got more or less sleep than
your usual 8 hours. You decide to make a regression model b = C + Mt, where
b is the output, C and M are the coefficients of your model (what you need to
find), and t is the number of hours above (or below for negative values) 8 hours
of sleep. You feel lazy and only take five measurements:
Hours of sleep above/below 8 (t) | Mean HC/LO score (b)
1
3
4
3
2
-4
-1
1
3
4
i. Inputting the above into the formula for our linear model gives us a system of
five equations and two unknowns - C and M. Write out this system
explicitly, then describe it as the matrix equation Ax = b, where x =
[&]
What are A and b?
ii. Demonstrate that the system is inconsistent and that the columns of A are
independent.
iii. Use the techniques from above to solve for â.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fda8ca31e-ab8e-4c2e-96b3-361b44dfca23%2F9d7693a4-5269-455d-af2d-bff14f026bb8%2Fuw9ndd5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(c) We can manipulate the above formula to solve for .
i. For the system from (a) verify that ATA is invertible. (Note: ATA is
invertible whenever the columns of A are linearly independent.)
ii. Use the fact that AT A is invertible to solve the equation AT (b- A) for î.
iii. Compute and A for the system from (a). Add A to your plot from
(aiv). Compare the results to your earlier findings.
(d) Regression Example Suppose you want to predict your average HC/LO score
across your next day of classes based on whether you got more or less sleep than
your usual 8 hours. You decide to make a regression model b = C + Mt, where
b is the output, C and M are the coefficients of your model (what you need to
find), and t is the number of hours above (or below for negative values) 8 hours
of sleep. You feel lazy and only take five measurements:
Hours of sleep above/below 8 (t) | Mean HC/LO score (b)
1
3
4
3
2
-4
-1
1
3
4
i. Inputting the above into the formula for our linear model gives us a system of
five equations and two unknowns - C and M. Write out this system
explicitly, then describe it as the matrix equation Ax = b, where x =
[&]
What are A and b?
ii. Demonstrate that the system is inconsistent and that the columns of A are
independent.
iii. Use the techniques from above to solve for â.
Transcribed Image Text:(a) Let A =
1 0
01
00
+-·
=
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