1. Let X and Y be two random variables.Then
Var(X+Y)=Var(X)+Var(Y)+2Couv(X,Y).
True False
2. Let c be a constant.Then Var(c)=c^2.
True False
3. Knowing that a university has the following units/campuses: A, B
, the medical school
in another City. You are interested to know on average how many
hours per week the university
students spend doing homework. You go to A campus and randomly
survey students walking
to classes for one day. Then,this is a random sample representing
the entire
university students population.
True False
4. The Law of Large Number(LLN)is related with the concept of
convergence in probability, while The
Central Limit Theorem(CLT)is related with convergence in
distribution.
True False
5.You have a cross-sectional dataset with an independent variable X
and a dependent variable Y.You
find a positive correlation between X and Y.Then you can conclude
that X causes Y.
True False
6. In a cross-sectional dataset the order of the observations is
arbitrary,while in a time series dataset the
order is important because it is likely that we have correlated
observations.
True False
7. Consider the following simple linear regression
model:y=Bo+B1t+u.The essential assumption to
derive the estimators of Bo and B1 through the Method of Moments is
E(u|X)=0.
True False
8. Consider the following simple linear regression model: y=B0+B1x+u. when we derive the estimators for B0 and B1 we get 2 foc
True False
1. The statement is True
2. The statement is False because Variance of a constant is zero.
1. Let X and Y be two random variables.Then Var(X+Y)=Var(X)+Var(Y)+2Couv(X,Y). True False 2. Let c be...
Given are five observations for two variables, x and y. xi 1 2 3 4 5 yi 3 8 5 10 14 (d) Develop the estimated regression equation by computing the values of b0 and b1 using b1 = Σ(xi − x)(yi − y) Σ(xi − x)2 and b0 = y − b1x. ŷ = (e) Use the estimated regression equation to predict the value of y when x = 2.
QUESTION 1 We consider the regression model Y= Bo+B1X u And we found for a sample size of n 974 B1 -0.095 and S 0.02 Does X has a significant effect on Y at the 5 % level? True False
True or False: 1. The fit of the regression equations yˆ = b0 + b1x + b2x2 and yˆ = b0 + b1x + b2x2 + b3x3 can be compared using the coefficient of determination R2. 2. The fit of the models y = β0 + β1x + ε and y = β0 + β1ln(x) + ε can be compared using the coefficient of determination R2. 3. A quadratic regression model is a special type of a polynomial regression model.
True or False: 1. The fit of the regression equations yˆ = b0 + b1x + b2x2 and yˆ = b0 + b1x + b2x2 + b3x3 can be compared using the coefficient of determination R2. 2. The fit of the models y = β0 + β1x + ε and y = β0 + β1ln(x) + ε can be compared using the coefficient of determination R2. 3. A quadratic regression model is a special type of a polynomial regression model.
2. Consider the simple linear regression model: where e1, .. . , es, are i.i.d. N (0, o2), for i= 1,2,... , n. Suppose that we would like to estimate the mean response at x = x*, that is we want to estimate lyx=* = Bo + B1 x*. The least squares estimator for /uyx* is = bo bi x*, where bo, b1 are the least squares estimators for Bo, Bi. ayx= (a) Show that the least squares estimator for...
Enter True or False, depending on whether the corresponding statement is true or false. 1. If the coefficient of correlation r = 0, then there is no linear relationship between the variable y and the variable x. 2. A straight line that slopes upward and exactly fits all data points would produce a correlation coefficient value of one. Consider the linear equation y = Bo + B1x. Enter your answers as a single letter indicating the correct answer, i.e. A...
Given are five observations for two variables, x and y. xi 3 12 6 20 14 yi 50 45 55 15 15 (d) Develop the estimated regression equation by computing the values of b0 and b1 using b1 = Σ(xi − x)(yi − y) Σ(xi − x)2 and b0 = y − b1x. ŷ = (e) Use the estimated regression equation to predict the value of y when x = 9. Observation 1 2 3 4 5 6 7 8...
Problem 2: For logistic regression with 1 predictor variable, the model is specified as E(Y|X=x) 1-E(Y|X=x) Derive the formula to show th 1+e (Bo+B1x)
Question (c) Suppose you have two jointly distributed random variables, X and Y. Suppose you know the following facts. • Var(–7.5 X) = 53.2925 • Var(1.5 x Y) = 1.01765 • Var(2 x X +3 + Y) = 6.26319 i. What is Cov(X,Y)? ii. What is the correlation of X and Y? iii. If you had a random sample of observations of x and y and estimated the regression Y = Bo + BiX +€ What would the
1. Let X and Y b e random variables, with μΧ = E(X), μΥ = E(Y), σ炙= Var(X) and σ Var(Y) (2) Let Ỹ be a linear function of X, ie. Ỹ = +51X where bo and bl are fixed real numbers. We want to minimize the discrepancy of Y from Y, i.e. minimizing the quantity (a) Find the values of bo and bi that minimizes Q (b) Use (a) to show that the minimal value of Q is σ....