Deck 2: The Simple Regression Model

Question 1

What does the equation denote if the regression equation is y = β₀ + β₁x₁ + u?

A)The explained sum of squares
B)The total sum of squares
C)The sample regression function
D)The population regression function

Answer 1

C

Question 2

Consider the following regression model: y = β₀ + β₁x₁ + u.Which of the following is a property of Ordinary Least Square (OLS)estimates of this model and their associated statistics?

A)The sum,and therefore the sample average of the OLS residuals,is positive.
B)The sum of the OLS residuals is negative.
C)The sample covariance between the regressors and the OLS residuals is positive.
D)The point ( ,
)always lies on the OLS regression line.

Answer 2

D

Question 3

Which of the following is assumed for establishing the unbiasedness of Ordinary Least Square (OLS)estimates?

A)The error term has an expected value of 1 given any value of the explanatory variable.
B)The regression equation is linear in the explained and explanatory variables.
C)The sample outcomes on the explanatory variable are all the same value.
D)The error term has the same variance given any value of the explanatory variable.

Answer 3

D

Question 4

In the equation c = + i + u,c denotes consumption and i denotes income.What is the residual for the 5^th observation if =$500 and =$475?

A)$975
B)$300
C)$25
D)$50

Question 5

is the ratio of the explained variation compared to the total variation.

Question 6

Which of the following is a nonlinear regression model?

A)y = β₀ + β₁x^1/2 + u
B)log y = β₀ + β₁log x +u
C)y = 1 / (β₀ + β₁x)+ u
D)y = β₀ + β₁x + u

Question 7

If a change in variable x causes a change in variable y,variable x is called the _____.

A)dependent variable
B)explained variable
C)explanatory variable
D)response variable

Question 8

The variance of the slope estimator increases as the error variance decreases.

Question 9

In the equation y = + x + u, is the _____.

A)dependent variable
B)independent variable
C)slope parameter
D)intercept parameter

Question 10

What is the estimated value of the slope parameter when the regression equation,y = β₀ + β₁x₁ + u passes through the origin?

A)
B) )
C)
D)

Question 11

The error term in a regression equation is said to exhibit homoskedasticty if _____.

A)it has zero conditional mean
B)it has the same variance for all values of the explanatory variable.
C)it has the same value for all values of the explanatory variable
D)if the error term has a value of one given any value of the explanatory variable.

Question 12

A natural measure of the association between two random variables is the correlation coefficient.

Question 13

In the equation y = + x + u,what is the estimated value of ?

A)
B)
C)
D)

Question 14

In the regression of y on x,the error term exhibits heteroskedasticity if _____.

A)it has a constant variance
B)Var(y|x)is a function of x
C)x is a function of y
D)y is a function of x

Question 15

There are n-1 degrees of freedom in Ordinary Least Square residuals.

Question 16

The sample covariance between the regressors and the Ordinary Least Square (OLS)residuals is always positive.

Question 17

A dependent variable is also known as a(n)_____.

A)explanatory variable
B)control variable
C)predictor variable
D)response variable

Question 18

If the total sum of squares (SST)in a regression equation is 81,and the residual sum of squares (SSR)is 25,what is the explained sum of squares (SSE)?

A)64
B)56
C)32
D)18

Question 19

If the residual sum of squares (SSR)in a regression analysis is 66 and the total sum of squares (SST)is equal to 90,what is the value of the coefficient of determination?

A)0.73
B)0.55
C)0.27
D)1.2

Question 20

The explained sum of squares for the regression function, ,is defined as _____.

A)
B)
C)
D)