Deck 2: The Simple Regression Model

Question 1

In a regression equation, changing the units of measurement of only the independent variable does not affect the _____.

A)​dependent variable
B)​slope
C)​intercept
D)​error term

Answer 1

C

Question 2

Simple regression is an analysis of correlation between two variables.​

Answer 2

True

Question 3

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

Answer 3

C

Question 4

Consider the following regression model: y = ₀ + ₁x₁ + 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.

Question 5

If x_i and y_i are positively correlated in the sample then the estimated slope is _____.​

A)​less than zero
B)​greater than zero
C)​equal to zero
D)​equal to one

Question 6

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 7

In the equation , 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 8

What does the equation denote if the regression equation is ?

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

Question 9

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 10

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

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

Question 11

The sample correlation between xi and yi is denoted by _____.​

A)​
B)​
C)​
D)​

Question 12

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 13

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.

Question 14

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 15

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

Question 16

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

A)
B)
C)
D)

Question 17

In the equation , what is the estimated value of ?

A)
B)
C)
D)

Question 18

What is the estimated value of the slope parameter when the regression equation, y = ₀ + ₁x₁ + u passes through the origin?

A)
B)
C)
D)

Question 19

Which of the following is a nonlinear regression model?

A)y = ₀ + ₁x^1/2 + u
B)log y = ₀ + ₁log x +u
C)y = 1 / ( ₀ + ₁x) + u
D)y = ₀ + ₁x + u

Question 20

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

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

Question 21

R² is the ratio of the explained variation compared to the total variation.

Question 22

In a simple linear regression model, wage = + male + u, where male is a binary variable (1 if a person is male, and 0 otherwise), is the difference in the average wage between males and non-males.

Question 23

In general, the constant that produces the smallest sum of squared deviations is always the sample average.

Question 24

Which of the following is an example of a dummy variable?

A)A person's hourly wage
B)The number of years of education someone has
C)The number of years of work experience someone has
D)Whether or not someone has a college degree

Question 25

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

Question 26

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

Question 27

Consider a simple linear regression model, wage = + male + u, where male is a binary variable (1 if a person is male, and 0 otherwise). Now suppose that we know being a male means there is a lower probability of attaining higher education, another factor that is also expected to affect wage. Which of the key assumptions made to establish unbiasedness of OLS estimates do not hold?

A)Linear in parameters
B)Random sampling
C)Sample variation in the explanatory variable
D)Zero conditional mean

Question 28

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

Question 29

Consider a simple linear regression model, y = β₀+ β₁x + u, . What does the zero conditional mean assumption imply?

A)The expected value of the error term, u , is zero, regardless of what the value of the explanatory variable, x, is.
B)The estimated average value of β₁ is zero.
C)The expected value of the explained variable, y , is zero, regardless of what the value of the explanatory variable, x , is.
D)The estimated average value of β₀ is zero.

Question 30

Which of the following will cause Ordinary Least Square (OLS) estimates of a simple regression model, y = + x + u to be biased?

A)Every individual in the population has the same probability of being observed in the sample.
B)The observed values of span a wide range.
C)The constant, is greater than the coefficient, .
D)The constant, is greater than the coefficient, x .