A professor decides to run an experiment to measure the effect of time pressure on final exam scores. He gives each of the 400 students in his course the same final exam, but some students have 90 minutes to complete the exam while others have 120 minutes. Each student is randomly assigned one of the examination times based on the flip of a coin. Let Y, denote the number of points scored on the exam by the " student (0 s Y, s100), let X, denote the amount of time that the student has to complete the exam (X, = 90 or 120), and consider the regression model Y; = Bo + B,X; + uj, E (u) =0 Which of the following are true about the unobservable u? (Check all that apply)
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
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A professor decides to run an experiment to measure the effect of time pressure on final exam scores. He gives each of the 400
students in his course the same final exam, but some students have 90 minutes to complete the exam while others have 120
minutes. Each student is randomly assigned one of the examination times based on the flip of a coin. Let Y, denote the number of
points scored on the exam by the " student (0 s Y, s100), let X, denote the amount of time that the student has to complete the
th
exam (X, = 90 or 120), and consider the regression model
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Y; = Bo+B,X; + Uj, E (u) = 0
Which of the following are true about the unobservable u,? (Check all that apply)
A. u represents factors other than time that influence the student's performance on the exam.
B. Different students will have different values of u, because they have unobserved individual specific traits that affect exam
performance.
C. All students will necessarily have the same value of u, because they are part of the same population.
D. u, will be zero for all students because time spent studying is likely the only factor that affects exam performance.
The Least Squares Assumptions
Y, =Po+B,X; + u, i = 1,..., n where
1. The error term u, has conditional mean zero given X E(u|X) = 0,
2. (X,Y), i= 1,., n, are independent and identically distributed (i.i.d.) draws from their joint distribution; and
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of u, because they have unobserved individual specific traits that affect exar
C. All students will necessarily have the same value of u, because they are part of the same population.
D.
will be zero for all students because time spent studying is likely the only factor that affects exam performance.
The Least Squares Assumptions
Y, = Po +B,X; + U,„ i= 1,..., n where
1. The error term u, has conditional mean zero given X; E (uX) = 0;
2. (X,,Y), i= 1,..., n, are independent and identically distributed (i.i.d.) draws from their joint distribution; and
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3. Large outliers are unlikely: X, and Y, have nonzero finite fourth moments.
Assuming this year's class is a typical representation of the same class in other years, are OLS assumption (2) and (3) satisfied?
O A. Only OLS assumption #3 is satisfied.
O B. Neither OLS assumption #2 nor OLS assumption #3 is satisfied.
OC. Both OLS assumption #2 and OLS assumption #3 are satisfied.
O D. Only OLS assumption #2 is satisfied.
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