ane the es seterm 45 Aprofessor decides to run an experiment to measure the effect of time pressare on final exam scores. He gives cach of the 400 students in his course the same final exam, but some students have 90 minutes to com- plete the exam, while others have 120 minutes, Each student is randomly assigned one of the examination times, based on the lip of a coin. Let Y, denote the number of points scored on the exam by the student (0 Ys 100), let X, denote the amount of time that the student has to complete the exam (X Y-A+Bx+ u 90 or 120), and consider the regression model a Explain what the term u, represents. Why will different students have different values of u,? b. Explain why E(u] X) G Are the other assumptions in Key Concept 4.3 satisfied? Explain. d. The estimated regression is Y,-49+0.24 X - 0 for this regression model. i. Compute the estimated regression's prediction for the average score of students given 90 minutes to complete the exam. Repeat. for 120 minutes and 150 minutes. ii. Compute the estimated gain in score for a student who is given an additional 10 minutes on the exam.
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
Part A, B, D
![ane the es
seterm
45 Aprofessor decides to run an experiment to measure the effect of time
pressare on final exam scores. He gives cach of the 400 students in his
course the same final exam, but some students have 90 minutes to com-
plete the exam, while others have 120 minutes, Each student is randomly
assigned one of the examination times, based on the lip of a coin. Let
Y, denote the number of points scored on the exam by the student
(0 Ys 100), let X, denote the amount of time that the student has to
complete the exam (X
Y-A+Bx+ u
90 or 120), and consider the regression model
a Explain what the term u, represents. Why will different students have
different values of u,?
b. Explain why E(u] X)
G Are the other assumptions in Key Concept 4.3 satisfied? Explain.
d. The estimated regression is Y,-49+0.24 X
- 0 for this regression model.
i. Compute the estimated regression's prediction for the average
score of students given 90 minutes to complete the exam. Repeat.
for 120 minutes and 150 minutes.
ii. Compute the estimated gain in score for a student who is given an
additional 10 minutes on the exam.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F15075cbb-1585-4001-8b39-493310d05b8a%2F58fae77b-f816-4e07-85ae-b708f4e0077a%2Fablvczp.png&w=3840&q=75)
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