You have the following data: Student A took 2 courses in the Fall semester. His previous CGPA was 3.2. He received GPA 3.5 in the Fall semester. Student B took 5 courses in the Fall semester. Her previous CGPA was 3.9. She received GPA 3.6 in the Fall semester. Student C took 4 courses in the Fall semester. His previous CGPA was 3.6. He received GPA 3.4 in the Fall semester. Using this data, we'll try to build a model using Least Square approximation, that can predict the CGPA of a student in the Fall semester given the number of courses s/he took in Fall, and his/her previous CGPA. (In real life, we'd use many more parameters, but for the sake of the quiz, we are keeping things simple.) The model is as follows - wi × (number of courses) + wz × (previouos CGPA) = GPA in Fall Find the values of wi, and w2 using Least Square approximation.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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You have the following data:
Student A took 2 courses in the Fall semester. His previous CGPA was 3.2. He received GPA 3.5 in the Fall semester.
Student B took 5 courses in the Fall semester. Her previous CGPA was 3.9. She received GPA 3.6 in the Fall semester.
Student C took 4 courses in the Fall semester. His previous CGPA was 3.6. He received GPA 3.4 in the Fall semester.
Using this data, we'll try to build a model using Least Square approximation, that can predict the CGPA of a student in the Fall semester given the number
of courses s/he took in Fall, and his/her previous CGPA.
(In real life, we'd use many more parameters, but for the sake of the quiz, we are keeping things simple.)
The model is as follows -
wi × (number of cour ses) + wz × (previouos CGPA) = GPA in Fall
Find the values of w1, and wy using Least Square approximation.
(Round off up to 3 decimal points)
1(a) wl is equal to ?
1(b) w2 is equal to ?
1(c) If a student took 4 courses in Fall, and his previous CGPA was 3.7,
what would be his FALL GPA according to this model?
1(d) What is the value of the Least Squared Error e of this approximation model?
Transcribed Image Text:You have the following data: Student A took 2 courses in the Fall semester. His previous CGPA was 3.2. He received GPA 3.5 in the Fall semester. Student B took 5 courses in the Fall semester. Her previous CGPA was 3.9. She received GPA 3.6 in the Fall semester. Student C took 4 courses in the Fall semester. His previous CGPA was 3.6. He received GPA 3.4 in the Fall semester. Using this data, we'll try to build a model using Least Square approximation, that can predict the CGPA of a student in the Fall semester given the number of courses s/he took in Fall, and his/her previous CGPA. (In real life, we'd use many more parameters, but for the sake of the quiz, we are keeping things simple.) The model is as follows - wi × (number of cour ses) + wz × (previouos CGPA) = GPA in Fall Find the values of w1, and wy using Least Square approximation. (Round off up to 3 decimal points) 1(a) wl is equal to ? 1(b) w2 is equal to ? 1(c) If a student took 4 courses in Fall, and his previous CGPA was 3.7, what would be his FALL GPA according to this model? 1(d) What is the value of the Least Squared Error e of this approximation model?
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